Bayesian Synthetic Control Method

Bayesian SCM
Bayesian synthetic controls
probabilistic synthetic control
Bayesian SC

2015 (Bayesian formulation); 2003 (original SCM by Abadie & Gardeazabal)

Brodersen, Gallusser, Koehler, Remy & Scott; building on Abadie, Diamond & Hainmueller

The Bayesian Synthetic Control Method estimates the causal effect of an intervention on a single treated unit by constructing a probabilistic counterfactual from a weighted combination of untreated donor units. Unlike the classical SCM, it places a prior distribution over the synthetic weights, yielding full posterior uncertainty intervals for the counterfactual trajectory and the treatment effect at each post-intervention time point.

Bayesian causal inference / synthetic control

Time-series panel data with a single treated unit and multiple donor units

Brodersen, K. H., Gallusser, F., Koehler, J., Remy, N., & Scott, S. L. (2015). Inferring causal impact using Bayesian structural time-series models. Annals of Applied Statistics, 9(1), 247-274.

Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic control methods for comparative case studies: Estimating the effect of California's tobacco control program. Journal of the American Statistical Association, 105(490), 493-505.

synthetic-control-method bayesian-difference-in-differences causal-impact-analysis bayesian-interrupted-time-series difference-in-differences panel-data-synthetic-control-method


Bayesian System Dynamics

Bayesian System Dynamics — Probabilistic parameter estimation and uncertainty propagation in system dynamics models

BSD
Bayesian SD
Bayesian SD modeling
Probabilistic System Dynamics

Rahmandad, H.; Sterman, J. D. and related SD/Bayesian communities

Bayesian System Dynamics (BSD) integrates Bayesian statistical inference with causal stock-and-flow simulation models. Prior knowledge about model parameters is updated using observed time-series data to produce posterior distributions, which are then propagated through the simulation to yield probabilistic forecasts and policy evaluations rather than single deterministic trajectories.

Simulation with probabilistic parameter learning

Time-series, stock-flow numerical data, prior distributions

Rahmandad, H., & Sterman, J. D. (2008). Heterogeneity and network structure in the dynamics of diffusion: Comparing agent-based and differential equation models. Management Science, 54(5), 998–1014.

system-dynamics bayesian-monte-carlo-simulation stochastic-system-dynamics markov-model bayesian-markov-model monte-carlo-simulation


Bayesian System GMM

Bayesian System Generalized Method of Moments

Bayesian Sys-GMM
Bayesian BB estimator
Bayesian Blundell-Bond GMM
B-SGMM

Blundell & Bond (System GMM, 1998); Bayesian integration via Chib and related MCMC literature

Bayesian System GMM combines the Blundell-Bond System Generalized Method of Moments estimator for dynamic panel data with Bayesian prior distributions and posterior inference via MCMC. It handles endogeneity, individual fixed effects, and weak-instrument problems while incorporating prior knowledge and delivering full posterior uncertainty quantification — not just point estimates and asymptotic standard errors.

Panel data with lagged dependent variables (short T, large N)

Blundell, R., & Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics, 87(1), 115–143.

Chib, S., & Ramamurthy, S. (2010). Tailored randomized block MCMC methods with application to DSGE models. Journal of Econometrics, 155(1), 19–38.

arellano-bond-gmm-estimator panel-system-gmm bayesian-arellano-bond-gmm dynamic-panel-data-model panel-dynamic-panel-data-model difference-gmm


Bayesian t-Test

Bayesian t-Test for Two-Group Comparison

bayesian two-sample t-test
bayes factor t-test
Bayesçi t-Testi

The Bayesian t-test, formalised by Rouder and colleagues in 2009, is a two-group comparison method that works within a Bayesian framework. Instead of a p-value, it produces a Bayes Factor (BF₁₀) that quantifies the evidence the data provide for the alternative hypothesis relative to the null, and it reports the full posterior distribution of the standardised effect size δ with a highest-density interval.

Bayes Factor (BF₁₀) / posterior effect-size distribution / 95% HDI

Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D. & Iverson, G. (2009). Bayesian t Tests for Accepting and Rejecting the Null Hypothesis. Psychonomic Bulletin & Review, 16(2), 225–237.

independent-t-test bayesian-regression bayesian-anova mann-whitney-u bayes-factor-test


Bayesian Tabu Search

Bayesian Tabu Search — Probabilistic guidance integrated with memory-based local search

BTS
Bayesian-guided tabu search
probabilistic tabu search
Bayes-TS

1989 (tabu search); hybrid formulations ~2005–2015

Glover, F. (tabu search); Bayesian integration developed by multiple researchers in the 2000s–2010s

Bayesian Tabu Search (BTS) is a hybrid metaheuristic that couples the memory-based forbidden-move mechanism of classic Tabu Search with a Bayesian probabilistic model. The Bayesian component learns from past evaluations to score candidate moves, focusing the search on promising regions while the tabu list prevents cycling. This combination reduces wasted function evaluations in expensive combinatorial and continuous optimization problems.

Hybrid metaheuristic — memory-based local search with Bayesian probabilistic guidance

Combinatorial or continuous optimization problem instances; prior knowledge or historical run data

Glover, F. (1989). Tabu search — Part I. ORSA Journal on Computing, 1(3), 190–206.

Bergstra, J., Bardenet, R., Bengio, Y., Kegl, B. (2011). Algorithms for hyper-parameter optimization. Advances in Neural Information Processing Systems (NIPS), 24, 2546–2554.

tabu-search bayesian-optimization simulated-annealing stochastic-tabu-search bayesian-genetic-algorithm bayesian-simulated-annealing


Bayesian Taguchi method

Bayesian Robust Parameter Design (Taguchi Framework)

Bayesian robust parameter design
Bayesian quality engineering
Bayesian signal-to-noise optimization
Bayes-Taguchi

Synthesized from Genichi Taguchi's robust design and Bayesian statistical methods (Box, Hamada, Wu, and others, 1990s)

The Bayesian Taguchi method integrates Genichi Taguchi's robust parameter design philosophy with Bayesian statistical inference. By encoding prior engineering knowledge as probability distributions and updating these distributions with experimental data, the approach identifies factor settings that simultaneously minimize process variability and keep the mean on target — even when only limited runs are feasible.

Continuous response data from designed experiments (crossed array or combined array); prior distributions on model parameters

Hamada, M., & Wu, C. F. J. (1992). Analysis of designed experiments with complex aliasing. Journal of Quality Technology, 24(3), 130–137.

Box, G. E. P., & Jones, S. (1992). Designing products that are robust to the environment. Total Quality Management, 3(3), 265–282.

taguchi-method robust-taguchi-method bayesian-design-of-experiments response-surface-methodology full-factorial-design design-of-experiments


Bayesian Temporal Network Analysis

Bayesian Inference for Temporal Network Analysis

Bayesian dynamic network analysis
Bayesian time-varying network model
BTNA
Bayesian longitudinal network analysis

Hanneke, S.; Fu, W.; Xing, E. P. (among key contributors)

Bayesian temporal network analysis combines probabilistic Bayesian inference with time-ordered relational data to model how network structures evolve, quantify uncertainty around structural estimates, and make principled predictions about future connectivity patterns. It provides credible intervals on edge probabilities and community assignments rather than bare point estimates.

Longitudinal relational data (edge lists or adjacency matrices across time steps)

Hanneke, S., Fu, W., & Xing, E. P. (2010). Discrete temporal models of social networks. Electronic Journal of Statistics, 4, 585–605.

Peixoto, T. P. (2017). Nonparametric Bayesian inference of the microcanonical stochastic block model. Physical Review E, 95(1), 012317.

temporal-network-analysis bayesian-exponential-random-graph-model bayesian-stochastic-block-model temporal-exponential-random-graph-model dynamic-network-analysis multilayer-temporal-network-analysis


Bayesian TGARCH

Bayesian Threshold Generalized Autoregressive Conditional Heteroscedasticity Model

Threshold GARCH with Bayesian estimation

Zakoian (1994) for TGARCH; Bayesian estimation formalized by Ardia (2008)

Bayesian TGARCH combines the Threshold GARCH volatility model — which captures the asymmetric response of volatility to positive versus negative shocks — with full Bayesian inference via Markov Chain Monte Carlo sampling. The result is a principled, uncertainty-aware framework for modeling leverage effects and fat-tailed financial returns.

Volatility model with asymmetric threshold and Bayesian inference

Financial or macroeconomic time series (returns, log-returns)

Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18(5), 931-955.

Ardia, D. (2008). Financial Risk Management with Bayesian Estimation of GARCH Models: Theory and Applications. Springer.

bayesian-garch-model bayesian-egarch tgarch-model bayesian-arch-model dcc-garch-model egarch-model


Bayesian Tobit Model

Bayesian censored regression
Bayesian Type I Tobit
Bayesian truncated regression
Tobit with priors

1958 (classical); 1992 (Bayesian formulation)

James Tobin (classical Tobit, 1958); Siddhartha Chib (Bayesian Tobit, 1992)

The Bayesian Tobit model extends Tobin's censored regression framework by replacing maximum-likelihood point estimates with a full posterior distribution over regression coefficients and error variance. By embedding Gibbs sampling with data augmentation, it produces credible intervals, handles small censored samples gracefully, and naturally incorporates prior knowledge about effect sizes.

Continuous outcome censored at a threshold (e.g., left-censored at zero)

Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econometrica, 26(1), 24–36.

Chib, S. (1992). Bayes inference in the Tobit censored regression model. Journal of Econometrics, 51(1–2), 79–99.

tobit-model bayesian-probit-model bayesian-multiple-linear-regression zero-inflated-model censored-regression bayesian-generalized-linear-model


Bayesian Toda-Yamamoto Causality

Bayesian Toda-Yamamoto Granger Causality Test

Bayesian TY causality
Bayesian modified Wald causality
Bayesian Granger non-causality in VAR
BTY causality

1995 (base); Bayesian variant developed post-2000

Toda & Yamamoto (1995) for the frequentist base; Bayesian extension by subsequent applied econometricians

The Bayesian Toda-Yamamoto causality procedure combines the Toda-Yamamoto VAR augmentation strategy — which sidesteps the need for pre-testing integration and cointegration — with Bayesian prior-posterior updating. It tests Granger non-causality between time series that may be integrated or cointegrated without requiring differencing or error-correction modeling, while incorporating prior information and producing full posterior distributions over the causal parameters.

Time series, possibly integrated or cointegrated

Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1-2), 225-250.

Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. Wiley.

toda-yamamoto-causality granger-causality bayesian-var vector-autoregression dolado-lutkepohl-test bootstrap-granger-causality


Bayesian Transfer Learning

Bayesian Transfer Learning (Probabilistic Domain Adaptation)

BTL
Bayesian domain adaptation
probabilistic transfer learning
Bayesian knowledge transfer

Raina, R.; Ng, A. Y.; Koller, D. (and subsequent community)

Bayesian Transfer Learning is a probabilistic framework that uses knowledge from a data-rich source domain to construct informative priors for a model trained on a data-scarce target domain. By encoding source-domain knowledge as prior distributions over parameters, the framework lets the model generalize well on the target task even with very limited labeled examples.

Probabilistic transfer / domain adaptation framework

Labeled source domain + limited labeled or unlabeled target domain data

Raina, R., Ng, A. Y., & Koller, D. (2006). Constructing informative priors using transfer learning. In Proceedings of the 23rd International Conference on Machine Learning (ICML), pp. 713–720. ACM.

Pan, S. J., & Yang, Q. (2010). A survey on transfer learning. IEEE Transactions on Knowledge and Data Engineering, 22(10), 1345–1359.

transfer-learning bayesian-gaussian-process semi-supervised-transfer-learning bayesian-neural-network meta-learning few-shot-learning


Bayesian Two-Mode Network Analysis

Bayesian Two-Mode (Bipartite) Network Analysis

Bayesian bipartite network analysis
probabilistic two-mode network analysis
Bayesian affiliation network analysis
Bayesian two-mode SNA

Borgatti & Everett (two-mode SNA); Bayesian extensions by multiple authors

Bayesian two-mode network analysis applies probabilistic Bayesian inference to bipartite (two-mode) networks — graphs linking two distinct sets of nodes such as actors and events, authors and papers, or consumers and products. By placing priors over tie probabilities and structural parameters, analysts obtain uncertainty estimates around centrality, community membership, and projection metrics rather than single-point estimates.

Bipartite (two-mode) adjacency matrices; actor-by-event data

Borgatti, S. P., & Everett, M. G. (1997). Network analysis of 2-mode data. Social Networks, 19(3), 243–269.

Latouche, P., Birmele, E., & Ambroise, C. (2011). Overlapping stochastic block models with application to the French political blogosphere. Annals of Applied Statistics, 5(1), 309–336.

two-mode-network-analysis bayesian-social-network-analysis bayesian-community-detection multilayer-two-mode-network-analysis exponential-random-graph-model weighted-two-mode-network-analysis


Bayesian two-way ANOVA

Bayesian factorial ANOVA
Bayes factor two-way ANOVA
Bayesian 2×k ANOVA
Bayesian two-factor ANOVA

1961 (foundations); 2012 (default Bayes factor formulation)

Harold Jeffreys (foundational); modern default-prior form by Jeffrey N. Rouder et al.

Bayesian two-way ANOVA extends the classical two-way analysis of variance by replacing p-values with Bayes factors and posterior distributions. It quantifies evidence for or against main effects and their interaction using prior-weighted model comparison, yielding conclusions that are directly interpretable in probabilistic terms rather than relying on a fixed significance threshold.

Continuous outcome, two categorical factors

Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56(5), 356–374.

Jeffreys, H. (1961). Theory of Probability (3rd ed.). Oxford University Press.

two-way-anova bayesian-one-way-anova bayesian-t-test three-way-anova mixed-anova bayes-factor


Bayesian Universal Kriging

Bayesian spatial interpolation with covariates

Diggle, Tawn & Moyeed; Kitanidis; Handcock & Stein

Bayesian Universal Kriging (BUK) extends classical universal kriging by placing prior distributions on trend coefficients and spatial covariance parameters, then propagating full posterior uncertainty into predictions. It interpolates spatially referenced continuous data while simultaneously estimating large-scale deterministic trends driven by covariates and small-scale stochastic spatial dependence, yielding prediction intervals that honestly account for both parameter and interpolation uncertainty.

Bayesian geostatistical interpolation with trend

Georeferenced continuous observations with spatially varying covariates

Diggle, P. J., & Ribeiro, P. J. (2007). Model-Based Geostatistics. Springer.

Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data (2nd ed.). CRC Press.

ordinary-kriging universal-kriging bayesian-ordinary-kriging co-kriging spatial-autocorrelation geographically-weighted-regression


Bayesian VAR model

BVAR
Bayesian VAR
Bayesian vector autoregressive model
BVAR model

The Bayesian Vector Autoregression (BVAR) model extends the classical VAR framework by incorporating prior beliefs about the model coefficients. Priors — most commonly the Minnesota prior — shrink VAR coefficients toward economically sensible values, dramatically reducing overfitting and improving out-of-sample forecast accuracy even when the number of variables is large.

Doan, T., Litterman, R., & Sims, C. (1984). Forecasting and conditional projection using realistic prior distributions. Econometric Reviews, 3(1), 1–100.

Koop, G., & Korobilis, D. (2010). Bayesian Multivariate Time Series Methods for Empirical Macroeconomics. Foundations and Trends in Econometrics, 3(4), 267–358.

vector-autoregression structural-var bayesian-vecm bayesian-svar-model panel-var-model bayesian-ardl-bounds-test


Bayesian Variant Calling

Bayesian Statistical Variant Calling from Sequencing Data

Bayesian genotyping
probabilistic variant calling
GATK HaplotypeCaller
Bayesian SNP/indel detection

2010 (GATK framework); Bayesian genotyping principles preceded by Samtools/MAQ ~2008–2009

Mark DePristo, Eric Banks, and the Broad Institute GATK team

Bayesian variant calling is a computational pipeline that uses probabilistic inference to identify single-nucleotide polymorphisms (SNPs), insertions, and deletions in a genome by treating sequencing data as evidence and computing posterior probabilities over candidate genotypes. Unlike deterministic threshold-based callers, Bayesian approaches explicitly model sequencing error, mapping uncertainty, and prior genotype frequencies to produce calibrated genotype likelihoods that can be used for downstream filtering and association testing.

Probabilistic genomic inference pipeline

Aligned short-read or long-read DNA/RNA sequencing data (BAM/CRAM format)

McKenna, A., Hanna, M., Banks, E., Sivachenko, A., Cibulskis, K., Kernytsky, A., ... & DePristo, M. A. (2010). The Genome Analysis Toolkit: A MapReduce framework for analyzing next-generation DNA sequencing data. Genome Research, 20(9), 1297–1303.

Rimmer, A., Phan, H., Mathieson, I., Iqbal, Z., Twigg, S. R., WGS500 Consortium, ... & McVean, G. (2014). Integrating mapping-, assembly- and haplotype-based approaches for calling variants in clinical sequencing applications. Nature Genetics, 46(8), 912–918.

variant-calling sequence-alignment rna-seq-differential-expression bayesian-gwas copy-number-variation-analysis single-cell-variant-calling


Bayesian VECM

Bayesian VECM
B-VECM
Bayesian cointegrated VAR
Bayesian vector error correction

The Bayesian VECM combines the classical Vector Error Correction Model — which captures both short-run dynamics and long-run cointegrating relationships among non-stationary multivariate time series — with Bayesian prior distributions over the cointegrating rank and coefficient matrices. This allows principled uncertainty quantification, incorporation of economic theory as priors, and coherent inference even in small samples.

Multivariate non-stationary time series (cointegrated)

Kleibergen, F., & Paap, R. (2002). Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration. Journal of Econometrics, 111(2), 223–249.

Villani, M. (2005). Bayesian reference analysis of cointegration. Econometric Theory, 21(2), 326–357.

vector-error-correction-model bayesian-var-model johansen-cointegration-test bayesian-arima-model panel-vecm structural-var


Bayesian Wilcoxon signed-rank test

Bayesian nonparametric paired comparison

Benavoli, Corani, Mangili, and colleagues

The Bayesian Wilcoxon signed-rank test is a Bayesian nonparametric method for comparing two paired or related samples. Rather than returning a single p-value, it produces posterior probabilities that one condition is better, practically equivalent, or worse than the other, enabling richer and more interpretable inference for paired continuous or ordinal data without assuming normality.

Paired continuous or ordinal differences

Benavoli, A., Corani, G., & Mangili, F. (2014). Should we really use post-hoc tests based on mean-ranks? Journal of Machine Learning Research, 17(5), 1–10.

Benavoli, A., Corani, G., Demsar, J., & Zaffalon, M. (2017). Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis. Journal of Machine Learning Research, 18(77), 1–36.

wilcoxon-signed-rank-test bayesian-paired-samples-t-test bayesian-mann-whitney-u-test paired-samples-t-test bayesian-friedman-test mann-whitney-u-test


Bayesian WLS

Bayesian weighted regression
BWLS
Bayesian heteroscedastic regression
weighted Bayesian linear regression

Arnold Zellner (Bayesian econometrics framework)

Bayesian Weighted Least Squares combines the classical WLS weighting scheme — which downweights observations with high error variance — with Bayesian prior distributions over the regression coefficients and error variance. The result is a posterior distribution that reflects both the data likelihood and prior beliefs, providing full uncertainty quantification in heteroscedastic settings.

Cross-sectional or panel data with heteroscedastic errors

Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. Wiley, New York.

Koop, G. (2003). Bayesian Econometrics. Wiley, Chichester.

bayesian-ols bayesian-gls panel-wls robust-wls bayesian-fixed-effects-model bayesian-random-effects-model


Bayesian XGBoost

Bayesian-Optimized Extreme Gradient Boosting

Bayesian XGBoost
XGBoost with Bayesian Optimization
BayesOpt-XGBoost
Bayes-tuned XGBoost

Chen, T. & Guestrin, C. (XGBoost); Snoek, J. et al. (Bayesian Optimization)

Bayesian XGBoost combines the predictive power of Extreme Gradient Boosting with Bayesian optimization for hyperparameter tuning. Instead of grid or random search, a probabilistic surrogate model guides the search for optimal learning rate, tree depth, and regularization parameters, achieving near-peak performance with far fewer evaluations than exhaustive search approaches.

Ensemble (gradient boosted trees with Bayesian hyperparameter search)

Tabular (continuous, categorical, binary, ordinal features)

Chen, T. & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794.

Snoek, J., Larochelle, H. & Adams, R. P. (2012). Practical Bayesian Optimization of Machine Learning Algorithms. Advances in Neural Information Processing Systems (NeurIPS), 25, 2951–2959.

xgboost random-forest gradient-boosting lightgbm hyperparameter-tuning gaussian-process-regression


Bayesian Zero-inflated model

Bayesian zero-inflated negative binomial

Lambert (1992) for ZIP; Bayesian extension by Ghosh, Mukhopadhyay & Lu (2006)

The Bayesian zero-inflated model handles count data with excess zeros by combining a binary component — identifying structural zeros — with a count component (Poisson or negative binomial) for the remaining counts. Bayesian inference via MCMC provides full posterior distributions for all parameters, enabling principled uncertainty quantification and regularisation through priors.

Non-negative integer counts with excess zeros

Ghosh, S. K., Mukhopadhyay, P., & Lu, J.-C. (2006). Bayesian analysis of zero-inflated regression models. Journal of Statistical Planning and Inference, 136(4), 1360–1375.

Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34(1), 1–14.

zero-inflated-model bayesian-poisson-regression bayesian-negative-binomial-regression bayesian-generalized-linear-model bayesian-hurdle-model poisson-regression


Bayley Scales of Infant Development

The Bayley Scales of Infant and Toddler Development (BSID), third edition, is a comprehensive standardized assessment tool developed by Nancy Bayley in 2006. It measures cognitive, motor, language, and social-emotional development in children from birth to 42 months. The scale identifies developmental delays and disabilities in infancy and early toddlerhood.

Bayley, N. (2006). Bayley Scales of Infant and Toddler Development (3rd ed.). Pearson Assessment.

Albers, C. A., & Grieve, A. J. (2007). Bayley Scales of Infant and Toddler Development (3rd ed.). Journal of Psychoeducational Assessment, 25(2), 180-190.

ages-stages-questionnaire cbcl-child-behavior achenbach-youth-self-report conners-rating-scales


BCa Bootstrap

Bias-Corrected and Accelerated Bootstrap

BCa Bootstrap (Bias-Corrected Accelerated)

The BCa bootstrap is a resampling method, introduced by Bradley Efron in 1987, that produces more accurate confidence intervals than the plain percentile bootstrap by applying a bias correction and an acceleration adjustment. It is recommended for skewed distributions and small samples.

Bias-corrected, acceleration-adjusted bootstrap percentile

Efron, B. (1987). Better Bootstrap Confidence Intervals. Journal of the American Statistical Association, 82(397), 171-185.

DiCiccio, T. J. & Efron, B. (1996). Bootstrap Confidence Intervals. Statistical Science, 11(3), 189-228.

bootstrap-inference double-bootstrap wild-bootstrap bayesian-bootstrap permutation-test


BCI Motor Imagery

Motor imagery BCI
MI-BCI
EEG motor decoding

Brain-computer interface (BCI) using motor imagery decodes the intent to move from brain activity (typically EEG) recorded while subjects imagine movement without actual muscle contraction. Pioneered by Gert Pfurtscheller and colleagues, motor imagery BCIs enable communication and control for paralyzed patients and enhance motor learning in rehabilitation.

Neural signal processing and decoding pipeline

Pfurtscheller, G., & Neuper, C. (1999). Motor imagery and direct brain-computer communication. Proceedings of the IEEE, 89(7), 1123-1134.

Wolpaw, J. R., Birbaumer, N., McFarland, D. J., Pfurtscheller, G., & Vaughan, T. M. (2002). Brain-computer interfaces for communication and control. Clinical Neurophysiology, 113(6), 767-791.


Beck Depression Inventory-II

Beck Depression Inventory-II: Self-Report Depression Assessment

Beck Depression Inventory Second Edition

The Beck Depression Inventory-II is a 21-item self-report instrument designed to assess the presence and severity of depressive symptoms in adolescents and adults. Originally published by Aaron T. Beck in 1961 and revised significantly in 1996, the BDI-II is one of the most widely used depression assessment tools in clinical psychology and psychiatry. It is copyrighted and distributed by Pearson Assessments, and measures both cognitive and somatic symptoms of depression across a two-week timeframe.

Beck, A. T., Steer, R. A., & Brown, G. K. (1996). Beck Depression Inventory (2nd ed.). San Antonio, TX: The Psychological Corporation.

Steer, R. A., & Clark, D. A. (2001). Psychometric characteristics of the Beck Depression Inventory-II with college students. Assessment, 8(3), 235–242.

Dozois, D. J., Dobson, K. S., & Ahnberg, E. (2003). A psychometric evaluation of the Beck Depression Inventory-II. Psychological Assessment, 10(2), 83–89.

phq-9 hamilton-depression-rating-scale montgomery-asberg-depression patient-global-impression-change


BDT Particle Identification

Boosted Decision Tree Particle Identification

BDT classifier
MVA particle ID
multivariate particle identification

Machine learning / particle physics community

Boosted Decision Trees (BDTs) are powerful multivariate classifiers used in particle physics to distinguish between different particle types based on detector signatures. By combining many weak decision trees through adaptive boosting, BDTs achieve superior discrimination power compared to simple cuts, enabling improved purity and efficiency in particle identification and background rejection.

Breiman, L. (2001). Random Forests. Machine Learning, 45(1), 5–32.

Kieseler, J., et al. (2016). Machine learning for detector trigger optimization at the LHC. Nuclear Instruments and Methods in Physics Research Section A, 824, 29–37.

Aarrestad, T. K., et al. (2021). Machine learning for particle discrimination at the LHC. Journal of Physics: Conference Series, 1525(1), 012034.


Beam Propagation Method

The Beam Propagation Method is a computational technique for simulating the propagation of optical beams through slowly varying, weakly guiding structures. Developed by Feit and Fleck in 1978, BPM exploits the paraxial approximation to reduce the full vector wave equation to a scalar or vector envelope equation, enabling efficient simulation of waveguides, integrated optics, and photonic devices.

Feit, M. D., & Fleck, J. A. (1978). Light propagation in graded-index optical fibers. Applied Optics, 17(24), 3990-3998.

Huang, W. P. (1992). The finite-difference vector beam propagation method: an analysis. Journal of Lightwave Technology, 10(3), 295-305.

Hadley, G. R. (1992). Wide-angle beam propagation using Padé approximant operators. Optics Letters, 17(20), 1426-1428.


Beamforming

Acoustic Beamforming and Directional Microphone Arrays

beamformer
spatial filtering
microphone array
phased array

Beamforming is a spatial signal processing technique that uses microphone arrays to selectively enhance sound from a desired direction while suppressing sounds from other directions. Formalized by Van Veen and Buckley in 1988, beamforming is fundamental to hands-free speech communication, hearing aids, sonar, radar, and spatial audio recording. It enables 'listening' with directional sensitivity despite using omnidirectional microphones, by exploiting time delays and phase differences between array elements.

Van Veen, B. D., & Buckley, K. M. (1988). Beamforming: A versatile approach to spatial filtering. IEEE ASSP Magazine, 5(2), 4–24.

Brandstein, M., & Ward, D. (2001). Microphone Arrays: Signal Processing Techniques and Applications. Springer-Verlag.

Krim, H., & Viberg, M. (1996). Two decades of array signal processing research. IEEE Signal Processing Magazine, 13(4), 67–94.

acoustic-holography speech-intelligibility fxlms-active-noise-control acoustic-ray-tracing psychoacoustic-masking


Beat Tracking

pulse detection
beat detection
metrical analysis

Beat tracking is an algorithm for automatically identifying the temporal positions of musical beats in audio recordings. It has been widely studied since the early 2000s, particularly for rhythm analysis and music synchronization applications. The problem is central to music information retrieval and essential for music-aware systems.

Ellis, D. P. (2007). Beat tracking by dynamic programming. Journal of New Music Research, 36(1), 51-60.

Krebs, F., Böck, S., & Widmer, G. (2015). Rhythmic pattern modeling for beat and downbeat tracking in musical audio. Frontiers in Psychology, 6, 1337.

Rocher, T., Robine, M., & Marsyas-Meuss, J. (2023). Deep learning approaches for beat tracking: State-of-the-art review. IEEE Access, 11, 15824-15842.

music-segmentation tempo-estimation pitch-detection-algorithm music-genre-classification harmonic-analysis-music


Beck Anxiety Inventory

The Beck Anxiety Inventory (BAI) is a 21-item self-report scale designed to measure the severity of somatic and cognitive symptoms of anxiety in adolescents and adults. Developed by Aaron T. Beck and Robert A. Steer in 1993, the BAI is widely used in clinical assessment, treatment monitoring, and research to quantify anxiety symptoms across a broad spectrum of anxiety disorders.

Beck, A. T., & Steer, R. A. (1993). BAI: Beck Anxiety Inventory. San Antonio, TX: The Psychological Corporation.


Beck Depression Inventory

The Beck Depression Inventory (BDI) is a 21-item self-report instrument designed to measure the severity of depressive symptoms in adolescents and adults. Developed by Aaron T. Beck in 1961 and revised as the BDI-II in 1996, it has become one of the most widely used screening and monitoring tools in clinical psychology and psychiatry.

Beck, A. T., Steer, R. A., & Brown, G. K. (1996). Manual for the Beck Depression Inventory-II. Psychological Corporation.

Beck, A. T., Ward, C. H., Mendelson, M., Mock, J., & Erbaugh, J. (1961). An inventory for measuring depression. Archives of General Psychiatry, 4(6), 561–571.


BHS

BHS
Beck Hopelessness Scale
Hopelessness Assessment

Aaron T. Beck, Albert Weissman, David Lester, Lori Trexler

The Beck Hopelessness Scale (BHS) is a 20-item self-report instrument developed by Aaron Beck and colleagues (1974) to measure the degree of hopelessness and pessimism about the future in adolescents and adults. It is grounded in Beck's cognitive theory of depression and suicide and is widely used in clinical, psychiatric, forensic, and research settings to assess suicide risk and identify individuals at elevated risk for self-harm and completed suicide.

Beck, A. T., Weissman, A., Lester, D., & Trexler, L. (1974). The measurement of pessimism: The Hopelessness Scale. Journal of Consulting and Clinical Psychology, 42(6), 861–865.

Beck, A. T., & Steer, R. A. (2000). Beck Hopelessness Scale (BHS). Psychological Assessment Resources, Inc.

novaco-anger-scale hcr-20 suicide-probability-scale psychopathy-checklist-screening


Behaviour Change Wheel

Behaviour Change Wheel (BCW): A Guide for Designing Behavior Change Interventions Using COM-B Model and Intervention Functions

Michie, S., van Stralen, M. M., West, R.

The Behaviour Change Wheel (BCW) is a systematic, evidence-based framework for designing behavior change interventions. Developed by Michie et al. (2011) and built on the COM-B model (Capability, Opportunity, Motivation→Behavior), the BCW guides practitioners through a structured process: diagnose behavior change barriers (using the Theoretical Domains Framework), identify relevant intervention functions (education, persuasion, incentivization, coercion, training, restriction, environmental restructuring, modelling, enablement), and design specific behavior change techniques matched to policy categories. It has become the international standard for systematically designing behavior change interventions in healthcare, public health, and other domains.

Michie, S., van Stralen, M. M., & West, R. (2011). The behaviour change wheel: A new method for characterising and designing behaviour change interventions. Implementation Science, 6, 42.

Michie, S., Atkins, L., & West, R. (2014). The Behaviour Change Wheel: A Guide to Designing Interventions. Silverback Publishing, UK.

Cane, J., O'Connor, D., & Michie, S. (2012). Validation of the theoretical domains framework (TDF) across multiple teams and behavioural problems: A systematic review. Implementation Science, 7, 37.

theoretical-domains-framework cfir-framework implementation-outcome-taxonomy knowledge-translation normalization-process-theory


Paul M. Wilson, Wendy M. Rodgers, and colleagues

The Behavioral Regulation in Exercise Questionnaire—3 (BREQ-3) is a 24-item measure developed by Wilson and colleagues (2012) to assess the type and quality of motivation underlying exercise behavior. Grounded in Self-Determination Theory, the BREQ-3 measures six regulation types positioned on a continuum from amotivation (no intention to exercise) through external regulation (exercising for external rewards or pressure), introjected regulation (exercising due to guilt or internal pressure), identified regulation (exercising because you value the benefits), integrated regulation (exercising because it aligns with your identity and values), and intrinsic motivation (exercising for enjoyment and interest). The BREQ-3 is widely used in exercise science, sports psychology, and health behavior research to understand why people exercise and to predict long-term exercise adherence.

Wilson, P. M., Rodgers, W. M., Loitz, C. C., & Scime, G. (2012). 'It's not about winning. It's about fun': Reconsidering the hedonic and eudaimonic contributions of physical activity across the lifespan. International Journal of Sport and Exercise Psychology, 10(3), 168-185.

Markland, D., & Tobin, V. (2004). A modification of the Behavioral Regulation in Exercise Questionnaire to include an assessment of amotivation. Journal of Sport and Exercise Psychology, 26(2), 191-196.


BEKK-GARCH

BEKK Model
Baba-Engle-Kraft-Kroner GARCH
Multivariate BEKK
BEKK-ÇARCH Modeli

BEKK-GARCH, proposed by Engle and Kroner (1995), is a multivariate GARCH specification that models the time-varying conditional covariance matrix of a system of financial return series. Named after Baba, Engle, Kraft, and Kroner, it is the dominant framework for quantifying volatility spillovers and dynamic correlations across multiple assets or markets simultaneously, widely adopted by financial economists and risk managers since the mid-1990s.

Multivariate conditional volatility model

Engle, R. F., & Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH. Econometric Theory, 11(1), 122–150.


Belief Rule Base

RIMER
Belief Rule-Based System
BRB System
İnanç Kural Tabanlı Çıkarım

Belief Rule Base (BRB), introduced by Yang et al. in 2006 under the RIMER framework, is an expert-system inference methodology that extends classical if-then rules by attaching belief degree distributions to rule consequents. It combines rule-based reasoning with the Evidential Reasoning (ER) approach, enabling the representation and propagation of uncertainty, incompleteness, and vagueness in complex decision problems across engineering, risk assessment, and management domains.

Expert-system inference with belief distributions

Belief degree distribution over consequents

Quantitative or qualitative antecedent attributes with expert-defined rules

Yang, J.-B., Liu, J., Wang, J., Sii, H.-S., & Wang, H.-W. (2006). Belief rule-base inference methodology using the evidential reasoning approach—RIMER. IEEE Transactions on Systems, Man, and Cybernetics—Part A, 36(2), 266–285.


Beliefs about Medicines Questionnaire

Rob Horne, John Weinman, and Michelle Hankins

The Beliefs about Medicines Questionnaire (BMQ) is an 18-item self-report measure developed by Horne, Weinman, and Hankins in 1999 to assess patients' cognitive beliefs about necessity of medications and concerns about potential adverse effects. It is widely used in clinical research to predict medication adherence, particularly in chronic disease management, and has demonstrated strong predictive validity across diverse populations and disease contexts.

Horne, R., Weinman, J., & Hankins, M. (1999). The Beliefs about Medicines Questionnaire: The development and evaluation of a new method for assessing the cognitive representation of medication. Psychology & Health, 14(1), 1-24.


Bellman-Ford Algorithm

Bellman-Ford Algorithm for Shortest Path

The Bellman-Ford Algorithm, developed by Richard Bellman and Lester R. Ford in the 1950s, is a fundamental algorithm for computing shortest paths in weighted graphs that may contain negative edge weights. Unlike Dijkstra's algorithm, it correctly handles negative weights and can detect the presence of negative-weight cycles.

Bellman, R. (1958). On a routing problem. Quarterly of Applied Mathematics, 16(1), 87-90.

Ford, L. R. (1956). Network Flow Theory. RAND Corporation Paper P-923.


Belmont Report

Belmont Principles
Three Ethical Principles

National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research (US DHEW)

The Belmont Report (1979) is the foundational US ethical framework for human subjects research, established by the National Commission following the Tuskegee Syphilis Study scandal. It articulates three core principles—Respect for Persons, Beneficence, and Justice—that form the basis for institutional review and regulatory oversight of human research globally. Every researcher conducting human studies must understand and apply these principles.

National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research. (1979). The Belmont Report: Ethical Principles and Guidelines for the Protection of Human Subjects of Research. Department of Health, Education, and Welfare.

declaration-of-helsinki nuremberg-code informed-consent-research institutional-review-board research-integrity-principles


BEM Acoustics

Boundary Element Method for Acoustic Simulation

BEM
boundary element method
indirect BEM
direct BEM

The Boundary Element Method (BEM) is a numerical technique for solving acoustic wave equations in complex geometries. Unlike finite element methods (FEM) that mesh entire volumes, BEM discretizes only the acoustic boundaries (surfaces), reducing computational cost and memory. First applied to acoustics by Burton and Miller in 1971, BEM is widely used for predicting room acoustics, exterior noise radiation, and acoustic scattering without the need for volumetric meshing.

Burton, A. J., & Miller, G. F. (1971). The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proceedings of the Royal Society A, 323(1553), 201–210.

Ciskowski, R. D., & Brebbia, C. A. (1991). Boundary Element Methods in Acoustics. Computational Mechanics Publications.

Wu, T. W. (2000). Boundary Element Acoustics: Fundamentals and Computer Codes. WIT Press.

acoustic-ray-tracing room-impulse-response acoustic-holography impedance-tube psychoacoustic-masking


BEM Geomechanics

Boundary Element Method for Geomechanical Analysis

Boundary element method
BEM analysis
Indirect methods

The boundary element method (BEM) for geomechanics is a numerical approach that solves problems by discretizing only the boundary of the domain, using analytical solutions for the interior. Introduced by Brebbia in 1978 and refined for geotechnical applications by Crouch and Starfield, BEM is particularly effective for infinite or semi-infinite domains (underground excavations, foundations, rock masses) where finite element methods are impractical.

Mesh-less numerical method for geomechanical problems

Brebbia, C. A. (1978). The Boundary Element Method for Engineers. Pentech Press.

Crouch, S. L., & Starfield, A. M. (1983). Boundary Element Methods in Solid Mechanics. George Allen & Unwin.

Dasgupta, G., & Chopra, A. K. (1988). Dynamic stiffness of foundations on layered soil. Journal of Engineering Mechanics, 114(8), 1264-1286.


Benders Decomposition

cutting plane method
constraint generation

Benders Decomposition, introduced by Jacques F. Benders in 1962, is a powerful algorithmic framework for solving large-scale mixed-integer programming (MIP) problems. It decomposes the problem into a master problem (controlling complicating variables) and subproblems (handling remaining variables), using cutting planes generated from subproblem dual information to iteratively tighten the master problem.

Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252.

Geoffrion, A. M. (1972). Generalized Benders decomposition. Journal of Optimization Theory and Applications, 10(4), 237-260.


Beneish M-Score

Beneish M-Score (Earnings Manipulation Detection)

Beneish Model
M-Score Model
Earnings Manipulation Score
Beneish M-Skoru

The Beneish M-Score is a statistical model developed by Messod Beneish in 1999 to identify whether a company has manipulated its reported earnings. The model combines eight financial-statement ratios into a single composite score using coefficients estimated from a probit regression on a sample of detected earnings manipulators. A score above −2.22 indicates a heightened probability of manipulation, making the M-Score a widely used tool in forensic accounting and investment due-diligence.

Output: Continuous scalar M-Score; threshold at −2.22

Eight financial-statement ratios from two consecutive annual periods

Beneish, M. D. (1999). The detection of earnings manipulation. Financial Analysts Journal, 55(5), 24–36.


Benjamini-Hochberg Procedure

Benjamini-Hochberg False Discovery Rate Procedure

BH procedure
FDR control
false discovery rate procedure
Benjamini-Hochberg düzeltmesi

The Benjamini-Hochberg (BH) procedure, introduced by Yoav Benjamini and Yosef Hochberg in 1995, controls the false discovery rate (FDR) — the expected proportion of false positives among all rejected hypotheses — rather than the probability of any false positive. By tolerating a controlled fraction of false discoveries, it delivers far greater power than family-wise error rate methods such as Bonferroni or Holm, which is why it has become the standard tool for large-scale simultaneous testing in genomics, neuroimaging, and other high-throughput fields.

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57(1), 289–300.

Benjamini, Y., & Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29(4), 1165–1188.

bonferroni-correction holm-correction sidak-correction multiple-linear-regression


Benthic Index of Biotic Integrity

The Benthic Index of Biotic Integrity (B-IBI) is an ecological assessment metric that measures the health and integrity of benthic (seafloor) communities based on the composition, abundance, and diversity of benthic fauna. Developed by James Karr in 1981 for freshwater fish assemblages and later adapted for marine benthic communities, the B-IBI provides a holistic measure of ecosystem condition integrating responses to multiple stressors including pollution, habitat degradation, and resource depletion.

Karr, J. R. (1981). Assessment of biotic integrity using fish communities. Fisheries, 6(6), 21-27.

McLaughlin, R. L., Kahnle, A. W., Danehy, R. J., et al. (2013). Reframing the coastal squeeze: navigating between humans, fish, and rising seas. Fisheries, 38(8), 357-365.


BRI

The Bereavement Risk Index (BRI) is a structured assessment tool designed to identify bereaved individuals at elevated risk for complicated grief, depression, or other adverse bereavement outcomes. By systematically evaluating established risk factors (manner of death, relationship quality, concurrent stressors, prior loss history, social support), the BRI facilitates early identification and risk stratification to guide prevention and targeted intervention.

Structured interview / Risk factor assessment

Arnstein, G. D. (1986). Prediction of complicated grief in recently bereaved individuals. Journal of Mental Health Counseling, 8(4), 266–279.

inventory-complicated-grief prolonged-grief-disorder-scale texas-revised-inventory-grief anticipatory-grief-scale


Berg Balance Scale

The Berg Balance Scale (BBS) is a 14-item performance-based assessment developed by Katherine Berg in 1989 to measure balance ability in older adults and individuals with neurological conditions. It evaluates static and dynamic balance through functional tasks relevant to daily living, providing a reliable and valid tool for fall risk assessment and rehabilitation monitoring.

Berg, K. O., Wood-Dauphinee, S. L., Williams, J. I., & Maki, B. (1992). Measuring balance in the elderly: Validation of an instrument. Canadian Journal of Public Health, 83(Suppl 2), S7-S11.

Berg, K. O., Maki, B. E., Williams, J. I., Holliday, P. J., & Wood-Dauphinee, S. L. (1992). Clinical and laboratory measures of postural balance in an elderly population. Archives of Physical Medicine and Rehabilitation, 73(11), 1073-1080.


Berlin Questionnaire

Berlin Questionnaire for Sleep Apnea Screening

OSA risk stratification; general population screening

Netzer, N. C., Stoohs, R. A., Netzer, C. M., et al.

The Berlin Questionnaire is a 10-item screening instrument designed to identify patients at risk for obstructive sleep apnea in primary care and community settings. Developed by Netzer and colleagues in 1999, it uses a three-category scoring approach (snoring symptoms, daytime somnolence, and hypertension/obesity) to stratify OSA risk. The tool is particularly useful in general population screening and has been extensively validated across international cohorts and clinical populations.

Netzer, N. C., Stoohs, R. A., Netzer, C. M., Clark, K., & Strohl, K. P. (1999). Using the Berlin Questionnaire to identify patients at risk for the sleep apnea syndrome. Annals of Internal Medicine, 131(7), 485-491.


BERT-based Classification

Bidirectional Encoder Representations from Transformers for Text Classification

BERT classifier
BERT fine-tuning for classification
BERT text classification
BERT-CLS

Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (Google AI Language)

BERT-based Classification fine-tunes Google's Bidirectional Encoder Representations from Transformers model on a labelled text dataset, replacing the generic pre-trained head with a task-specific classification layer. It exploits deep bidirectional context from hundreds of millions of pre-trained parameters to deliver state-of-the-art accuracy on short- and medium-length text classification tasks with relatively modest amounts of labelled data.

Pre-trained language model with fine-tuning

Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019). BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. In Proceedings of NAACL-HLT 2019 (pp. 4171–4186). Association for Computational Linguistics.

Sun, C., Qiu, X., Xu, Y., & Huang, X. (2019). How to Fine-Tune BERT for Text Classification? In China National Conference on Chinese Computational Linguistics (CCL 2019), Lecture Notes in Computer Science, vol 11856, pp. 194–206. Springer.

transformer roberta-based-classification sentence-embeddings recurrent-neural-network long-short-term-memory


BERT Embeddings

contextual embeddings
transformer embeddings
BERT Tabanlı Metin Gömülmeleri

Devlin, Chang, Lee & Toutanova (Google AI)

BERT-based text embeddings, introduced by Devlin and colleagues at Google AI in 2019, turn text into context-sensitive dense vectors using a bidirectional Transformer encoder. Because the meaning of a word shifts with its context, BERT produces richer representations than static methods such as Word2Vec or topic models like LDA.

Contextual transformer text-representation method

Output: Context-sensitive dense vectors (embeddings)

Devlin, J., Chang, M.-W., Lee, K. & Toutanova, K. (2019). BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. NAACL-HLT, 4171-4186.

Tenney, I., Das, D. & Pavlick, E. (2019). BERT Rediscovers the Classical NLP Pipeline. Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics (ACL), 4593-4601.


BERT Fine-Tuning

Fine-Tuning of Pre-trained BERT (Bidirectional Encoder Representations from Transformers)

BERT İnce Ayar (Fine-Tuning)
BERT ince ayar
fine-tuning BERT
transfer learning with BERT

BERT fine-tuning, building on the BERT model introduced by Devlin and colleagues in 2019, re-trains a pre-trained BERT model on a small labelled dataset for a target task such as classification, named-entity recognition, or question answering. Through transfer learning it reaches high performance even with relatively little task-specific data.

Transfer learning (fine-tuning a pre-trained transformer)

Text classification, NER, question answering

Devlin, J., Chang, M.-W., Lee, K. & Toutanova, K. (2019). BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. NAACL.

Sun, C., Qiu, X., Xu, Y. & Huang, X. (2019). How to Fine-Tune BERT for Text Classification. CCL.

gpt-finetuning lora-peft vision-transformer random-forest xgboost


BET Surface Area

Brunauer-Emmett-Teller Surface Area Analysis (BET)

BET analysis
nitrogen adsorption
surface area measurement

Brunauer-Emmett-Teller (BET) Surface Area Analysis is a technique for measuring the specific surface area of solids by analyzing their nitrogen adsorption isotherms. Developed by Brunauer, Emmett, and Teller in 1938, BET theory extends monolayer adsorption (Langmuir) to multilayer adsorption, enabling quantification of surface area of porous and powdered materials. It is the industry standard for characterizing catalysts, adsorbents, pharmaceuticals, and porous materials, providing critical data for performance prediction and quality control.

Brunauer, S., Emmett, P. H., & Teller, E. (1938). Adsorption of gases in multimolecular layers. Journal of the American Chemical Society, 60(2), 309-319.

Sing, K. S. W., et al. (1985). Reporting physisorption data for gas/solid systems. Pure and Applied Chemistry, 57(4), 603-619.

Lowell, S., Shields, J. E., Thomas, M. A., & Thommes, M. (2004). Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density. Springer.


Beta Diversity Partitioning

beta diversity
species turnover
nestedness
community dissimilarity

Beta diversity partitioning quantifies how species composition differs among sites, decomposing community dissimilarity into two components: species turnover (replacement of species across sites) and nestedness (loss of species from species-rich sites). Developed by Baselga (2010), this framework reveals whether sites differ because they have different species (turnover) or because some sites are subsets of others (nestedness). This distinction has ecological and conservation implications: turnover suggests environmental heterogeneity or speciation, while nestedness suggests habitat loss or extinction.

Baselga, A. (2010). Partitioning the turnover and nestedness components of beta diversity. Global Ecology and Biogeography, 19(1), 134-143.

Whittaker, R. H. (1972). Evolution and measurement of species diversity. Taxon, 21(2/3), 213-251.

Koleff, P., Gaston, K. J., & Lennon, J. J. (2003). Measuring beta diversity for presence-absence data. Journal of Animal Ecology, 72(3), 367-382.

species-accumulation indicator-value functional-diversity faiths-phylogenetic-diversity


Beta Regression

Beta Regression for Rates and Proportions

beta regression model
proportion regression
Beta Regresyonu

Beta regression is a generalized linear model introduced by Ferrari and Cribari-Neto (2004) for outcomes that are rates or proportions confined to the open interval (0,1). It models the mean of a beta-distributed response through a link function, making it the natural choice for fractions, probability scores, and proportion indices.

Generalized linear model (beta distribution)

Ferrari, S. L. P. & Cribari-Neto, F. (2004). Beta Regression for Modelling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815.

ols-regression logistic-regression gamma-regression fractional-logit-regression quantile-regression


Between Estimator

Between-Groups Estimator
Cross-Sectional Averages Estimator
Panel Between Estimator
Gruplar-Arası Tahmin Edici

The Between Estimator is a panel data regression technique that identifies regression coefficients exclusively from cross-sectional variation across individuals, by collapsing the panel to individual-specific time-averaged observations and applying ordinary least squares to those group means. It is used in economics, sociology, and political science when researchers are interested in long-run or structural differences between units rather than short-run within-unit dynamics.

Balanced or unbalanced panel with T >= 2

Baltagi, B. H. (2008). Econometric Analysis of Panel Data (4th ed.). John Wiley & Sons.


Betweenness Centrality

Betweenness Centrality (Freeman's Geodesic Betweenness)

Freeman betweenness
BC
geodesic betweenness
shortest-path betweenness

Betweenness centrality, formalized by Linton C. Freeman in 1977, measures how often a node lies on the shortest path connecting every other pair of nodes in a network. High-betweenness nodes act as bridges or brokers: removing them fragments the network into disconnected components more severely than removing any other nodes.

Graph / adjacency matrix (weighted or unweighted, directed or undirected)

Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40(1), 35–41.

Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(2), 163–177.

degree-centrality closeness-centrality eigenvector-centrality social-network-analysis modularity-analysis pagerank


Betz Limit

Betz Limit for Wind Turbine Maximum Power

Lanchester-Betz limit
wind turbine efficiency limit

The Betz Limit states that no wind turbine can extract more than 59.3% of the kinetic energy from flowing wind, regardless of design. This fundamental thermodynamic limit arises because extracting energy slows the wind, which then blocks further energy extraction. Albert Betz derived this limit in 1920 from momentum and energy conservation. Modern wind turbines achieve 35-45% efficiency, approaching this theoretical maximum.

Betz, A. (1920). Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren. Zeitschrift für das gesamte Turbinenwesen, 26, 307-320.

Hansen, M. O. L. (2007). Aerodynamics of Wind Turbines (2nd ed.). Earthscan Publishers.


BF-COPRAS

BF-COPRAS (Bipolar extension of COPRAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Zavadskas & Kaklauskas in 1996. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Bipolar outranking/ranking — Bipolar Fuzzy Set (BFS: positive membership μ⁺ ∈ [0,1], negative μ⁻ ∈ [-1,0])

(). UNCONFIRMED — BF-COPRAS specific seminal not confirmed via systematic literature search. PENDING

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


BF-EDAS

BF-EDAS (Bipolar extension of EDAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Jana, C., Pal, M. in 2021. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Jana, C., Pal, M. (2021). Extended bipolar fuzzy EDAS approach for multi-criteria group decision-making process. Computational and Applied Mathematics


BF-MARCOS

BF-MARCOS (Bipolar extension of MARCOS) is a ranking multi-criteria decision-making (MCDM) method introduced by Stević et al. in 2020. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Stević et al. (2020). Bipolar Fuzzy Measurement of Alternatives and Ranking according to Compromise Solution. Computers & Industrial Engineering


BF-TOPSIS

BF-TOPSIS (Bipolar extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Hwang & Yoon in 1981. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Alghamdi, M. A., Alshehri, N. O., Akram, M. (2018). Multi-criteria decision-making methods in bipolar fuzzy environment. International Journal of Fuzzy Systems


BF-VIKOR

BF-VIKOR (Bipolar extension of VIKOR) is a ranking multi-criteria decision-making (MCDM) method introduced by Opricovic in 1998. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.


BF-WASPAS

BF-WASPAS (Bipolar extension of WASPAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Arshad, M. in 2020. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

(). UNCONFIRMED — no peer-reviewed BF-WASPAS-specific paper found via systematic literature search. PENDING


Big Five Inventory

BFI
Big Five Personality Inventory
Five-Factor Model

The Big Five Inventory (BFI) is a 44-item self-report measure operationalizing the Five-Factor Model of personality, capturing Openness, Conscientiousness, Extraversion, Agreeableness, and Neuroticism. Developed by Oliver John and colleagues in 1991, the BFI is a more concise alternative to longer personality instruments while maintaining strong psychometric properties. The measure has become one of the most widely used personality assessments in organizational, clinical, social, and personality psychology research.

John, O. P., Donahue, E. M., & Kentle, R. L. (1991). The Big Five Inventory—versions 4a and 54. Technical Report, Institute of Personality and Social Research, University of California, Berkeley.

John, O. P., Robins, R. W., & Pervin, L. A. (Eds.). (2008). Handbook of personality: Theory and research (3rd ed.). Guilford Press.

Rammstedt, B., & John, O. P. (2007). Measuring personality in one minute or less: A 10-item short version of the Big Five Inventory in English and German. Journal of Research in Personality, 41(1), 203–212.


BGP

exterior gateway protocol
inter-domain routing

BGP is the de facto standard routing protocol for interconnecting autonomous systems (ASs) on the Internet. Since its introduction in 1989, BGP has scaled the Internet to millions of routers and trillions of destinations. BGP is path-vector-based, using a flexible policy system to control route propagation and selection. While BGP convergence can be slow and policies complex, it remains the only viable protocol for Internet-scale inter-domain routing.

Rekhter, Y., Li, T., & Hares, S. (2006). A Border Gateway Protocol 4 (BGP-4). RFC 4271.

Stewart, J. W. (2014). BGP Design and Implementation (2nd ed.). Cisco Press.


Bibliographic Coupling

document coupling
bibliographic similarity

Bibliographic coupling is a method that identifies intellectual relationships between documents by measuring their shared references. Two papers are considered 'coupled' when they cite the same sources, indicating they address related research questions or draw from the same conceptual foundations. Introduced by Kessler in 1963, this approach enables researchers to map knowledge domains and discover thematically similar publications without relying on subject cataloging or keywords.

Kessler, M. M. (1963). Bibliographic coupling between scientific papers. American Documentation, 14(3), 123–131.

Small, H. (1973). Co-citation in the scientific literature: A new measure of the relationship between two documents. Journal of the American Society for Information Science, 24(4), 265–269.

co-citation-analysis bibliographic-coupling keyword-co-occurrence science-mapping journal-co-citation-analysis


Bibliometric Analysis

bibliometrics
bibliometric study
bibliometric mapping
publication analysis

1969 (term coined); practice dates to 1920s–1930s

Alan Pritchard (coined term); earlier quantitative work by Paul Otlet (1934) and S. C. Bradford (1934)

Bibliometric analysis applies statistical and mathematical methods to bibliographic records — publications, citations, authors, journals, and keywords — to measure and map the structure, output, and intellectual evolution of a research field. It is widely used to identify influential works, prolific authors, productive journals, collaboration networks, and emerging research themes across any academic discipline.

Bibliographic records (titles, authors, journals, citations, keywords)

Pritchard, A. (1969). Statistical bibliography or bibliometrics? Journal of Documentation, 25(4), 348–349.

Donthu, N., Kumar, S., Mukherjee, D., Pandey, N., & Lim, W. M. (2021). How to conduct a bibliometric analysis: An overview and guidelines. Journal of Business Research, 133, 285–296.

scientometric-analysis co-citation-analysis bibliographic-coupling co-word-analysis systematic-literature-review science-mapping


Bibliometric Coupling Analysis Conducted with the bibliometrix R Package

bibliometrix bibliographic coupling
R-based bibliographic coupling
coupling analysis via bibliometrix
biblioNetwork coupling

Base method 1963; R-package workflow 2017

Bibliographic coupling: M. M. Kessler (1963); bibliometrix package: Aria & Cuccurullo (2017)

Bibliometrix-assisted bibliographic coupling applies the open-source R package bibliometrix to construct and analyse bibliographic coupling networks, in which two documents are linked by the number of references they share. The workflow automates record import, network construction, community detection, and summary statistics within a single reproducible R environment, making it accessible to researchers without dedicated scientometric software licences.

Quantitative scientometric network analysis

Bibliographic records (Web of Science or Scopus exports) with reference lists

Aria, M., & Cuccurullo, C. (2017). bibliometrix: An R-tool for comprehensive science mapping analysis. Journal of Informetrics, 11(4), 959–975.

Kessler, M. M. (1963). Bibliographic coupling between scientific papers. American Documentation, 14(1), 10–25.


bibliometrix bibliometric analysis
R-based bibliometric analysis
bibliometrix workflow
bibliometrix package analysis

Massimo Aria and Corrado Cuccurullo (bibliometrix R package)

bibliometrix-assisted bibliometric analysis is a structured quantitative approach to mapping a scientific field using the bibliometrix R package. Developed by Aria and Cuccurullo (2017), it provides an integrated environment for importing bibliographic records from Scopus or Web of Science, computing performance indicators, building co-authorship and citation networks, and generating thematic maps — all within a reproducible R or Shiny workflow.

Quantitative review method with software toolkit

Bibliographic records (Web of Science, Scopus exports in BibTeX/CSV format)

bibliometric-analysis scientometric-analysis co-citation-analysis bibliographic-coupling co-word-analysis science-mapping


bibliometrix-assisted citation analysis

bibliometrix citation analysis
R-based citation analysis
bibliometrix CA
citation analysis with bibliometrix

2017 (bibliometrix package); citation analysis since 1955

Massimo Aria & Corrado Cuccurullo (bibliometrix R package); citation analysis concepts from Eugene Garfield (1955)

Bibliometrix-assisted citation analysis uses the bibliometrix R package to systematically retrieve, clean, and analyze citation data exported from major databases such as Web of Science and Scopus. By automating reference parsing, frequency counting, and network construction, it enables researchers to identify the most-cited works, map intellectual influence, and trace the evolution of scholarly fields at a scale that manual analysis cannot match.

Bibliographic records (Web of Science, Scopus, PubMed exports; citation counts, reference lists)

Garfield, E. (1955). Citation indexes for science: A new dimension in documentation through association of ideas. Science, 122(3159), 108–111.

bibliometric-analysis co-citation-analysis bibliographic-coupling scientometric-analysis science-mapping systematic-literature-review


co-citation network analysis with bibliometrix

2017 (bibliometrix implementation); 1973 (co-citation concept)

Co-citation: Henry Small (1973); bibliometrix package: Massimo Aria & Corrado Cuccurullo (2017)

bibliometrix-assisted co-citation analysis combines Henry Small's co-citation measure with the open-source R package bibliometrix to map the intellectual structure of a research field. When two documents are frequently cited together by third papers, they are considered intellectually linked; the bibliometrix package automates construction of the co-citation matrix, similarity normalization, community detection, and network visualization, turning raw bibliographic exports into interpretable science maps.

Bibliographic records (Web of Science, Scopus, PubMed exports; RIS/BibTeX formats)

co-citation-analysis bibliometric-analysis bibliographic-coupling science-mapping vosviewer-assisted-co-citation-analysis network-based-co-citation-analysis


bibliometrix-assisted mapping review

bibliometrix-Assisted Evidence Mapping Review

bibliometrix mapping review
R-bibliometrix evidence map
bibliometric-assisted systematic map
bibliometrix evidence synthesis map

2017 (bibliometrix tool); mapping review approach formalised c. 2010s

Aria & Cuccurullo (bibliometrix, 2017); mapping review methodology developed in evidence synthesis community (~2000s)

A bibliometrix-assisted mapping review combines the structured scope-and-search logic of an evidence mapping review with the analytical power of the bibliometrix R package. Instead of manually categorising studies, the researcher leverages bibliometrix functions — keyword co-occurrence networks, thematic clustering, and yearly trend analysis — to chart the landscape of a research field systematically and at scale, producing an interactive, reproducible evidence map.

Bibliographic records (Web of Science, Scopus, PubMed exports); citation and keyword metadata

Miake-Lye, I. M., Hempel, S., Shanman, R., & Shekelle, P. G. (2016). What is an evidence map? A systematic review of published evidence maps and their definitions, methods, and products. Systematic Reviews, 5(1), 28.


bibliometrix-assisted narrative review

bibliometrix narrative review
R-bibliometrix narrative synthesis
quantitative-assisted narrative review

2017 (bibliometrix package); narrative review methodology is older

Aria & Cuccurullo (bibliometrix R package); narrative review as a traditional form predates this tool

A bibliometrix-assisted narrative review combines the quantitative field-mapping capabilities of the bibliometrix R package with the interpretive flexibility of a traditional narrative review. Bibliometric indicators — publication trends, author and country productivity, co-citation networks, keyword co-occurrence — are computed and visualised first to orient the reviewer, then a discursive, thematic narrative synthesises the intellectual content of key sources. The result is a structured yet flexible overview of a field that is more transparent and reproducible than a purely informal narrative.

Mixed quantitative-qualitative review methodology

Bibliographic records (Web of Science, Scopus exports) and full-text sources

Green, B. N., Johnson, C. D., & Adams, A. (2006). Writing narrative literature reviews for peer-reviewed journals: secrets of the trade. Journal of Chiropractic Medicine, 5(3), 101–117.

narrative-review bibliometric-analysis systematic-literature-review scoping-review co-citation-analysis science-mapping


bibliometrix-Assisted PRISMA-Based Systematic Review

Aria & Cuccurullo (bibliometrix package); Moher et al. / Page et al. (PRISMA statement)

A bibliometrix-assisted PRISMA-based review combines the structured, transparent reporting framework of PRISMA with the quantitative science-mapping capabilities of the bibliometrix R package. The approach embeds bibliometric analyses — such as citation analysis, co-authorship mapping, and keyword co-occurrence — into the evidence-synthesis steps of a PRISMA-guided systematic review, enabling both rigorous literature screening and macro-level visualization of the intellectual landscape.

Software-assisted systematic review workflow

Bibliographic records from databases (Web of Science, Scopus, PubMed); structured citation metadata

Page, M. J., McKenzie, J. E., Bossuyt, P. M., Boutron, I., Hoffmann, T. C., Mulrow, C. D., … Moher, D. (2021). The PRISMA 2020 statement: An updated guideline for reporting systematic reviews. BMJ, 372, n71.


bibliometrix-assisted rapid review

bibliometrix rapid review
R-based rapid review
rapid bibliometric review
tool-assisted rapid synthesis

2017 (bibliometrix); rapid review practice established ~2010s

Aria & Cuccurullo (bibliometrix package); rapid review tradition from Cochrane and evidence synthesis community

A bibliometrix-assisted rapid review combines the speed and pragmatic focus of a rapid review with the computational power of the bibliometrix R package. Researchers use bibliometrix to automate citation import, deduplication, descriptive statistics, and science-mapping tasks, compressing the bibliometric phase of a rapid review from days to hours while maintaining transparent, reproducible workflows within a single open-source environment.

Expedited evidence synthesis with computational bibliometric support

Bibliographic records (titles, abstracts, citations, keywords) exported from databases such as Web of Science or Scopus

Aria, M., & Cuccurullo, C. (2017). bibliometrix: An R-tool for comprehensive science mapping analysis. Journal of Informetrics, 11(4), 959-975.

Garritty, C., Gartlehner, G., Nussbaumer-Streit, B., King, V. J., Hamel, C., Kamel, C., Affengruber, L., & Stevens, A. (2021). Cochrane Rapid Reviews Methods Group offers evidence-informed guidance to conduct rapid reviews. Journal of Clinical Epidemiology, 130, 13-22.

rapid-review bibliometric-analysis scoping-review systematic-literature-review science-mapping vosviewer-assisted-rapid-review


bibliometrix-assisted science mapping

bibliometrix science mapping
R-based science mapping
bibliometrix bibliometric mapping
bibliometrix-driven knowledge mapping

Massimo Aria & Corrado Cuccurullo (bibliometrix R package)

bibliometrix-assisted science mapping is a computational approach that uses the bibliometrix R package to retrieve, clean, and analyze large bibliographic datasets, producing structured visual maps of how knowledge in a field is organized, interconnected, and evolving over time. It combines descriptive bibliometrics with network analysis and strategic clustering techniques to reveal intellectual structure, thematic frontiers, and influential actors in a research domain.

Bibliographic records (Web of Science, Scopus, PubMed exports; metadata: titles, abstracts, citations, keywords)

Cobo, M. J., López-Herrera, A. G., Herrera-Viedma, E., & Herrera, F. (2011). Science mapping software tools: Review, analysis, and cooperative study among tools. Journal of the American Society for Information Science and Technology, 62(7), 1382–1402.

bibliometric-analysis science-mapping co-citation-analysis bibliographic-coupling co-word-analysis vosviewer-assisted-science-mapping


science-of-science analysis with bibliometrix

2017 (bibliometrix package); scientometrics as a field: 1969

Massimo Aria & Corrado Cuccurullo (bibliometrix package); scientometrics founded by Derek J. de Solla Price

bibliometrix-assisted scientometric analysis is a reproducible, R-based workflow that applies the bibliometrix package to analyse the structure and dynamics of scientific fields using publication metadata. It integrates descriptive statistics, citation metrics, and network analysis — co-citation, bibliographic coupling, co-authorship, and co-word — into a single scriptable environment, enabling systematic, transparent mapping of research landscapes at scale.

Quantitative literature analysis workflow

Bibliographic records (Web of Science, Scopus, PubMed exports; CSV/BibTeX)


bibliometrix-Assisted Systematic Literature Review

bibliometrix SLR
R-bibliometrix systematic review
bibliometrix-based literature review
bibliometrix-enhanced SLR

A bibliometrix-assisted systematic literature review integrates the R package bibliometrix — developed by Aria and Cuccurullo (2017) — into the standard systematic review pipeline to automate and visualize bibliometric performance and science-mapping analyses. It combines the transparency and reproducibility of a protocol-driven systematic search with quantitative tools for tracking publication trends, author collaboration networks, keyword co-occurrence, and thematic evolution across a field.

Bibliographic records (Web of Science, Scopus, PubMed exports)

Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & PRISMA Group. (2009). Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement. PLOS Medicine, 6(7), e1000097.


bibliometrix-assisted thematic evolution analysis

Bibliometrix-Assisted Thematic Evolution Analysis

thematic evolution analysis with bibliometrix

2017 (bibliometrix package); thematic evolution approach ~2011

Massimo Aria & Corrado Cuccurullo (bibliometrix package); thematic evolution method from Cobo et al.

Bibliometrix-assisted thematic evolution analysis uses the bibliometrix R package to trace how research themes emerge, mature, decline, or transform across successive time periods within a scientific field. By combining co-word analysis with strategic diagram visualisation, the workflow maps the intellectual structure of a field and reveals longitudinal shifts in topic centrality and development, producing reproducible, publication-ready outputs within a single R environment.

Cobo, M. J., Lopez-Herrera, A. G., Herrera-Viedma, E., & Herrera, F. (2011). An approach for detecting, quantifying, and visualizing the evolution of a research field: A practical application to the Fuzzy Sets Theory field. Journal of Informetrics, 5(1), 146-166.


Bidirectional RNN

Bidirectional Recurrent Neural Network (BiLSTM / BiGRU)

Çift Yönlü RNN / BiLSTM / BiGRU
bidirectional recurrent neural network
BiLSTM
BiGRU
bidirectional LSTM

A Bidirectional RNN, introduced by Schuster and Paliwal in 1997, processes a sequence in both forward and backward directions so that every position has access to its full surrounding context. With LSTM or GRU cells (BiLSTM/BiGRU) it is the standard approach for named-entity recognition, sequence labelling, and speech recognition.

Recurrent neural network (sequence model)

Classification & prediction on sequences

Schuster, M. & Paliwal, K.K. (1997). Bidirectional Recurrent Neural Networks. IEEE Transactions on Signal Processing, 45(11), 2673–2681.

Graves, A. & Schmidhuber, J. (2005). Framewise Phoneme Classification with Bidirectional LSTM Networks. IJCNN, 2047–2052.

seq2seq attention-mechanism self-attention-transformer random-forest xgboost


Bifactor Model

Bifaktör Modeli — Genel ve Spesifik Faktörler

Holzinger & Swineford (1937); modern revival by Reise (2012)

The bifactor measurement model specifies that every indicator loads simultaneously on a single general factor and on one of several specific (group) factors. Formally introduced by Holzinger and Swineford in 1937 and brought into mainstream psychometrics by Reise (2012), it is now the standard tool for evaluating whether a multidimensional scale can legitimately yield a single composite score.

General factor loadings, specific factor loadings, ω and ωh reliability indices

ECV (Explained Common Variance), ωh (omega-hierarchical)

Reise, S. P. (2012). The Rediscovery of Bifactor Measurement Models. Multivariate Behavioral Research, 47(5), 667–696.

Rodriguez, A., Reise, S. P. & Haviland, M. G. (2016). Evaluating Bifactor Models: Calculating and Interpreting Statistical Indices. Psychological Methods, 21(2), 137–150.

confirmatory-factor-analysis exploratory-factor-analysis omega-reliability sem item-response-theory cronbach-alpha


Bilevel Optimization

Stackelberg Optimization
Hierarchical Programming
Nested Optimization
İki Düzeyli Optimizasyon

Bilevel optimization is a class of mathematical programming problems in which one optimization problem is nested inside another. The upper-level (leader) problem optimizes its objective subject to constraints that include the solution of a lower-level (follower) problem. Formalized comprehensively by Jonathan Bard in 1998, the framework models hierarchical decision-making where the leader anticipates and accounts for the rational response of the follower.

Two nested optimization problems (leader and follower)

Bard, J. F. (1998). Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers.

Colson, B., Marcotte, P., & Savard, G. (2007). An overview of bilevel optimization. Annals of Operations Research, 153(1), 235–256.


Binary Decision Diagram

Binary Decision Diagrams (BDDs) are a canonical, memory-efficient representation of Boolean functions developed by Randal Bryant in 1986. A BDD is a directed acyclic graph encoding all variable assignments and results; reduced BDDs are unique for each function and enable efficient manipulation of combinatorial logic in model checking, circuit design, and symbolic computation.

Bryant, R. E. (1986). Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, 35(8), 677–691.

Andersen, H. R. (1997). An introduction to binary decision diagrams. Technical Report, IT University of Copenhagen.

Becker, B., & Drechsler, R. (1998). Binary Decision Diagrams: Theory and Implementation. Kluwer.

boolean-satisfiability model-checking circuit-verification sat-solving


BES

Binge Eating Scale Gormally
BES screening tool

John Gormally, Susan Black, Sarah Daston, Diane Rardin

The BES is a 16-item self-report questionnaire designed specifically to measure the behavioural and emotional features of binge eating in obese and non-obese populations. Developed by Gormally and colleagues in 1982, the BES uses a forced-choice format and focuses on the subjective experience of loss of control, severity of binge episodes, and affective triggers. It is widely used in obesity treatment research and clinical screening for binge eating patterns.

Gormally, J., Black, S., Daston, S., & Rardin, D. (1982). The assessment of binge eating severity among obese persons. Addictive Behaviors, 7(1), 47–55.

Timmerman, G. M. (1990). Binge eating scale: Further assessment of validity and reliability. Journal of Applied Biobehavioral Research, 1(1), 1–12.

Celio, A. A., Wilfley, D. E., Crow, S. J., Mitchell, J., & Walsh, B. T. (2004). A comparison of the binge eating scale, questionnaire for eating and weight patterns-revised, and eating disorder examination-questionnaire with instructions (EDE-QI) in the assessment of binge eating. International Journal of Eating Disorders, 36(4), 434–444.

ede-q scoff-questionnaire three-factor-eating-questionnaire yale-food-addiction-scale


Binomial Option Pricing

Cox-Ross-Rubinstein Binomial Option Pricing Model

binomial tree model
Cox-Ross-Rubinstein model
CRR model
lattice option pricing
binom opsiyon fiyatlama

John Cox, Stephen Ross & Mark Rubinstein

The binomial option pricing model, introduced by John Cox, Stephen Ross, and Mark Rubinstein in 1979, prices options by modelling the underlying as a discrete tree in which the price moves up or down by fixed factors at each step. Working backward from the option's payoff at maturity using risk-neutral probabilities, it produces a no-arbitrage price that converges to Black-Scholes as the number of steps grows — while naturally handling American early exercise, which the closed-form formula cannot.

Discrete-time lattice option-pricing model

American (early-exercise) and European options

Output: No-arbitrage option price via backward induction

Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.

black-scholes-model stochastic-volatility-model interest-rate-models jump-diffusion-model


Binomial Test

exact binomial test
binomial probability test
exact test for a proportion
Tam Binom Testi

Classical exact test; textbook treatment by Siegel & Castellan

The exact binomial test checks whether the observed number of successes in a fixed number of independent trials is consistent with a pre-specified success probability p₀. Because it computes exact binomial tail probabilities rather than relying on a normal approximation, it is the gold standard for testing a proportion in small samples; this two-sided formulation follows Siegel & Castellan's classic treatment (1988).

Exact binomial tail probability (no normal approximation)

Siegel, S. & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences (2nd ed.). McGraw-Hill.

proportion-test chi-square-goodness-of-fit sign-test fisher-exact-test one-sample-z-test


Bioaccumulation Model

Bioaccumulation and Biomagnification Modeling

accumulation model
toxicokinetics
persistent organic pollutants
POPs
heavy metals

Bioaccumulation models predict how chemical contaminants accumulate in organisms from environmental exposure (water, food, sediment). Developed by Gobas and colleagues (2006), these models quantify the kinetics of chemical uptake, metabolism, and clearance. Bioaccumulation factors (BAF) and bioconcentration factors (BCF) measure the ratio of chemical concentration in organisms to concentration in the environment. Understanding bioaccumulation is critical for assessing ecological risk from persistent organic pollutants (POPs), heavy metals, and other contaminants.

Arnot, J. A., & Gobas, F. A. (2006). A review of bioaccumulation factor (BAF) and bioconcentration factor (BCF) assessments for organic chemicals in aquatic organisms. Environmental Reviews, 14(4), 257-297.

Clark, K. E., Gobas, F. A., & Mackay, D. (1990). Model of organic chemical uptake and clearance by fish from food and water. Environmental Science & Technology, 24(7), 1203-1213.

Meador, J. P., Stein, J. E., Hom, T., & Varanasi, U. (2006). Bioaccumulation of polycyclic aromatic hydrocarbons by marine organisms. Reviews of Environmental Contamination and Toxicology, 143, 79-165.

siar-mixing-model food-web-topology metabolic-theory-of-ecology population-viability-analysis


Biodiversity Index in Forests

Forest Biodiversity Assessment and Diversity Quantification

Forest diversity index
Species richness assessment
Shannon index forestry

Ecological diversity assessment and conservation

Forest biodiversity indices quantify species richness, evenness, and overall diversity in forest ecosystems. Rooted in information theory (Shannon) and statistical ecology (Simpson, Magurran), these indices compress complex multispecies data into interpretable metrics. Applied to forest inventory data, biodiversity indices guide conservation planning, assess ecological health, and track responses to management or disturbance.

Shannon, C. E. (1948). A Mathematical Theory of Communication. The Bell System Technical Journal, 27(3), 379–423.

Simpson, E. H. (1949). Measurement of Diversity. Nature, 163, 688.

Magurran, A. E. (2004). Measuring Biological Diversity. Blackwell Publishing.

Hubbell, S. P. (2001). The Unified Neutral Theory of Biodiversity and Biogeography. Princeton University Press.

forest-inventory-sampling canopy-cover-estimation silvicultural-treatment-design forest-fire-risk-assessment


Bioequivalence Analysis

Bioequivalence Analysis (Two One-Sided Tests)

TOST Procedure
Average Bioequivalence
BE Analysis
Biyoeşdeğerlik Analizi

Bioequivalence Analysis is a regulatory-grade statistical framework used to determine whether a test drug formulation (generic or reformulated) delivers the active ingredient to the systemic circulation at a rate and extent comparable to a reference product. Introduced by Donald J. Schuirmann in 1987, the method operationalizes equivalence through the Two One-Sided Tests (TOST) procedure, replacing the ambiguous absence-of-difference paradigm with an explicit equivalence margin evaluated on log-transformed pharmacokinetic endpoints such as AUC and C_max.

Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15(6), 657–680.


Biogas Production Modeling

Anaerobic Digestion and Biogas Yield Prediction

anaerobic digestion
biogas yield
methane production
AD modeling

Biogas production modeling is a quantitative method to predict methane and carbon dioxide generation from anaerobic digestion of organic residues (wastewater sludge, food waste, agricultural manure, slaughterhouse waste). Developed from microbial kinetics and thermodynamics, these models account for substrate composition, microbial consortia (acetogens, methanogens), process conditions (temperature, pH, retention time), and inhibition factors (ammonia, volatile fatty acids). Biogas modeling supports reactor design, energy recovery planning, and operational optimization.

Rittmann, B. E., & McCarty, P. L. (2001). Environmental Biotechnology: Principles and Applications (2nd ed.). McGraw-Hill.

Appels, L., Baeyens, J., Degrève, J., & Dewil, R. (2011). Principles and Potential of the Anaerobic Digestion of Waste-Activated Sludge. Progress in Energy and Combustion Science, 37(2), 183-214.

Stams, A. J. (1994). Metabolic Interactions Between Anaerobic Bacteria in Methanogenic Environments. Antonie van Leeuwenhoek, 66(1–3), 271–294.


Biographical Research

life history research
biographical method
life story research
biographical narrative inquiry

Late 19th–early 20th century (Dilthey ~1883; Thomas & Znaniecki 1918–1920)

Wilhelm Dilthey (hermeneutic foundations); Thomas & Znaniecki (sociological application); Norman Denzin (interpretive biography)

Biographical research is a qualitative method that examines individual lives in depth — through life-history interviews, personal documents, letters, and autobiographical narratives — to understand how personal experience intersects with social, historical, and cultural forces. Rooted in Wilhelm Dilthey's hermeneutics and made prominent in sociology by Thomas and Znaniecki's study of Polish immigrants, it treats the individual life story as a window onto broader social structures and processes. It belongs to the narrative inquiry subfamily alongside oral history and life-story research.

Life-history interviews, personal documents, letters, diaries, autobiographies, oral histories

1–20 participants (often 1–5 for intensive life-history studies)

Denzin, N. K. (1989). Interpretive Biography. Sage Publications.

Roberts, B. (2002). Biographical Research. Open University Press.

narrative-analysis phenomenology ethnography grounded-theory case-study discourse-analysis


Biomass Allometric Equation

Biomass allometric equations are regression models that predict tree or stand aboveground biomass from easily measurable variables such as diameter at breast height (DBH) and height. These equations embody the principle of allometry: the scaling relationship between body parts or organisms. In forestry, allometric equations are essential tools for estimating carbon storage, nutrient cycling, fuel loads, and resource inventory without destructive harvesting. Thousands of species-specific and regional equations have been developed and compiled in public databases.

Chojnacky, D. C., Heath, L. S., & Jenkins, J. C. (2014). Updated generalized biomass equations for North American tree species. Forestry, 87(1), 129–151.

Zianis, D., & Mencuccini, M. (2005). On simplifying allometric analyses of forest biomass. Forest Ecology and Management, 187(2–3), 311–332.


Bipartite Network Analysis

Bipartite Network Analysis (Two-Mode Networks)

İki Modlu Ağ Analizi (Bipartite Networks)

Borgatti & Everett (1997) formalised the two-mode network framework

Bipartite network analysis, formalised by Borgatti and Everett in 1997, is a graph-structural method for studying networks in which nodes are divided into two disjoint sets — actors and events — and edges exist only between sets, never within them. It is the natural framework for author–paper, patient–disease, user–product, and any other affiliation data, and it extends one-mode network analysis by providing metrics and projection techniques tailored to the two-mode structure.

Incidence matrix or edge list with two disjoint node sets

Output: Structural metrics, projected one-mode graphs, centrality rankings

Borgatti, S.P. & Everett, M.G. (1997). Network Analysis of 2-Mode Data. Social Networks, 19(3), 243-269.

Guillaume, J.L. & Latapy, M. (2006). Bipartite Structure of All Complex Networks. Information Processing Letters, 90(5), 215-221.

social-network-analysis community-detection ego-network-analysis network-motif-analysis collaborative-filtering


Biplot

Gabriel biplot
PCA biplot
JK biplot
Çift grafik

A biplot is a low-dimensional graphical representation of a multivariate data matrix that simultaneously displays both the observations (rows) and the variables (columns) as points or vectors in the same plot. Introduced by Ruben Gabriel in 1971, the technique decomposes the data matrix into a rank-2 approximation using singular value decomposition, allowing the approximate value of any data entry to be read as the inner product of the corresponding row and column markers.

Output: Simultaneous row and column markers in low-dimensional space

Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58(3), 453–467.


BIRCH

Balanced Iterative Reducing and Clustering using Hierarchies

BIRCH is a scalable, incremental clustering algorithm introduced by Zhang, Ramakrishnan, and Livny in 1996. It is designed to cluster very large datasets — potentially larger than available memory — in a single pass, by compressing the data into a compact in-memory summary structure called a CF-tree (Clustering Feature tree) before applying any standard clustering procedure.

Incremental hierarchical clustering (CF-tree)

Unsupervised clustering of very large datasets

Zhang, T., Ramakrishnan, R., & Livny, M. (1996). BIRCH: An efficient data clustering method for very large databases. Proceedings of the 1996 ACM SIGMOD International Conference on Management of Data, 25(2), 103–114.

Han, J., Kamber, M., & Pei, J. (2011). Data Mining: Concepts and Techniques (3rd ed., Ch. 10). Morgan Kaufmann.

k-means dbscan agglomerative-clustering mini-batch-k-means gaussian-mixture-model


Childbirth Experience Questionnaire

The Childbirth Experience Questionnaire (CEQ) is a 22-item self-report instrument designed to comprehensively assess women's subjective experiences of childbirth. Developed by Dencker, Tully, and Begley, the CEQ measures four key dimensions of the birth experience: Capacity (feelings of being in control, coping, and managing labor), Perceived Safety (confidence in provider competence and safety), Professional Support (quality of care received), and Participation (involvement in decision-making). It captures women's experiences across diverse birth settings and contexts.

Dencker, A., Tully, G., & Begley, C. (2010). Midwifery continuity of carer in a group practice: a pilot study. British Journal of Midwifery, 18(10), 650-660.

Dencker, A., Tully, G., & Begley, C. (2012). Assessing women's childbirth experience: a review of the literature. Evidence Based Midwifery, 10(2), 45-50.


Bitewing Radiography

bitewing X-ray
bitewings
posterior radiography

Multiple innovators, formalized in 20th century

Bitewing radiography is a standard intraoral radiographic technique that captures the coronal portions of both maxillary and mandibular teeth in a single image, with the patient biting on a film holder or digital sensor. Introduced in the early 20th century and formalized as a diagnostic standard, bitewing radiographs are the primary image type for detecting approximal caries, monitoring alveolar bone level for periodontal disease assessment, and evaluating dental restorations and radiographic density changes. Digital bitewings have reduced radiation exposure and improved image quality and archiving.

Ludlow, J. B., Davies-Ludlow, L. E., Brooks, S. L., & Howerton, W. B. (2006). Dosimetry of 3 intraoral digital imaging systems. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology and Endodontology, 101(2), 226-234.

White, S. C., & Pharoah, M. J. (2014). Oral radiology: Principles and interpretation (7th ed.). Mosby Elsevier.

Pitts, N. B., Ekstrand, K. R., Foundation, I. C. D. A., & Organization, W. H. (2013). International caries detection and assessment system (ICDAS) and its applications. Community Dentistry and Oral Epidemiology, 43(1), 41-49.

dmft-index orthodontic-cephalometry root-canal-length-determination occlusal-analysis


Bivariate Probit

Bivariate Binary Probit
Joint Probit Model
Two-Equation Probit
İki Değişkenli Probit

The Bivariate Probit Model, introduced by Ashford and Sowden (1970), jointly estimates two binary outcome equations whose error terms are allowed to be correlated. By modeling both outcomes simultaneously under a bivariate normal distribution, it corrects for the dependence between decisions that separate probit regressions would ignore, producing consistent and efficient parameter estimates for researchers studying interrelated binary choices.

Two binary dependent variables modeled jointly

Error correlation rho (ρ) between equations

Ashford, J. R., & Sowden, R. R. (1970). Multi-variate probit analysis. Biometrics, 26(3), 535–546.


BK Filter

Baxter-King Filter
Band-Pass Filter (Baxter-King)
BK Band-Pass Filter
Bant Geçiren Süzgeç

The Baxter-King (BK) band-pass filter, introduced by Marianne Baxter and Robert King in 1999, is a linear symmetric moving-average filter designed to isolate cyclical fluctuations in macroeconomic time series that fall within a specified range of periodicities. It removes both very low-frequency trends and very high-frequency noise, retaining only the business-cycle component—typically oscillations with a period of six to thirty-two quarters for quarterly data.

6–32 quarters (business cycle frequencies)

Baxter, M., & King, R. G. (1999). Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics, 81(4), 575–593.


Black-Litterman Model

Black-Litterman Portfolio Allocation Model

Black-Litterman
BL model
Black-Litterman Portföy Modeli

The Black-Litterman model, introduced by Fischer Black and Robert Litterman in 1992, is a Bayesian portfolio allocation framework that blends market-equilibrium returns with an investor's own views to produce more stable, intuitive portfolios. It was designed to cure the extreme concentration and input sensitivity of classical Markowitz mean-variance optimisation.

Bayesian combination of equilibrium prior and investor views

continuous (asset weights / expected returns)

Black, F. & Litterman, R. (1992). Global Portfolio Optimization. Financial Analysts Journal, 48(5), 28-43.

He, G. & Litterman, R. (1999). The Intuition Behind Black-Litterman Model Portfolios. Goldman Sachs Investment Management Division.

risk-parity-model ols-regression har-rv-model tail-risk-measures pairs-trading


Black-Scholes Model

Black-Scholes-Merton Option Pricing Model

Black-Scholes formula
Black-Scholes-Merton model
BSM model
Black-Scholes opsiyon fiyatlama modeli

Fischer Black, Myron Scholes & Robert Merton

The Black-Scholes-Merton model, published by Fischer Black and Myron Scholes in 1973 with the theoretical framework extended by Robert Merton, gives a closed-form no-arbitrage price for European options. By assuming the underlying asset follows geometric Brownian motion with constant volatility, it derives a partial differential equation whose solution expresses the option price in terms of the stock price, strike, time to maturity, risk-free rate, and volatility — transforming option pricing from intuition into a rigorous, tractable formula.

Geometric Brownian motion, constant volatility, no arbitrage

Output: No-arbitrage price of European options

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.

Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4(1), 141–183.

binomial-option-pricing stochastic-volatility-model jump-diffusion-model realized-volatility