HFGPE

HFGPE (Hesitant Fuzzy Generalized Peer-Evaluation (strategy-blended cross-efficiency with BFM, Zhou-Chen-Xu-Meng 2018)) is a dea multi-criteria decision-making (MCDM) method introduced by Zhou, W. Chen, J. Xu, Z. S. Meng, S. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Generalization of HFPE: cross-efficiency E_{el}(d) = d·E^max_{el} + (1-d)·E^min_{el} blends benevolent (d=1) and aggressive (d=0) strategies via parameter d ∈ [0,1]. When d is unknown, the Backward Fitting Method (BFM) estimates the optimal d from historical/preference ranking constraints by solving a quadratic programme. Final ranking by column-mean of the blended cross-efficiency matrix.


HFL-AHP

HFL-AHP (Hesitant Fuzzy Linguistic AHP (HFLTS-envelope family: Yavuz 2015 + Özdağoğlu 2018)) is a weight subjective multi-criteria decision-making (MCDM) method introduced by Yavuz, M., Öztaysi, B., Çevik Onar, S., Kahraman, C. in 2015. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

HFLTS-envelope pairwise comparison — interval/2-tuple aggregation — preference-degree (Yavuz) or defuzz (Özdağoğlu) ranking

Yavuz, M., Öztaysi, B., Çevik Onar, S., Kahraman, C. (2015). Multi-criteria evaluation of alternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model. Expert Systems with Applications

ahpsort aras cobra cocoso codas copras edas gra


HFL-CODAS

HFL-CODAS (Hesitant Fuzzy Linguistic CODAS (HFLTS-envelope, Combinative Distance-based Assessment)) is a ranking multi-criteria decision-making (MCDM) method introduced by Yalçın, N., Pehlivan, N.Y. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy linguistic ranking — HFLTS envelope (linguistic interval / trapezoidal Liu-Rodriguez envelope) + combinative distance-based assessment

Yalçın, N., Pehlivan, N.Y. (2019). Application of the Fuzzy CODAS Method Based on Fuzzy Envelopes for Hesitant Fuzzy Linguistic Term Sets: A Case Study on a Personnel Selection Problem. Symmetry (MDPI)


HFL-MABAC

HFL-MABAC (Hesitant Fuzzy Linguistic Projection-Based MABAC with Bonferroni Mean (Sun et al. 2018)) is a ranking multi-criteria decision-making (MCDM) method introduced by Sun, R., Hu, J., Zhou, J., Chen, X. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy linguistic ranking — HFLTS subscript-symmetric LTS + projection-based signed difference + Bonferroni Mean criterion aggregation

Sun, R., Hu, J., Zhou, J., Chen, X. (2018). A Hesitant Fuzzy Linguistic Projection-Based MABAC Method for Patients' Prioritization. International Journal of Fuzzy Systems


HFL-PROMETHEE

HFL-PROMETHEE (Hesitant Fuzzy Linguistic PROMETHEE (Liang-Wang-Zhang 2018)) is a outranking multi-criteria decision-making (MCDM) method introduced by Liang, R. X. Wang, J. Q. Zhang, H. Y. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Projection-based PROMETHEE outranking for Hesitant Fuzzy Linguistic Term Sets (HFLTS); preference functions computed via hesitant fuzzy linguistic projection scores; net flow Φ for final ranking.

Liang, R. X., Wang, J. Q., Zhang, H. Y. (2018). Projection-based PROMETHEE methods based on hesitant fuzzy linguistic term sets. International Journal of Fuzzy Systems


HFLPR-PRIORITY

HFLPR-PRIORITY (Hesitant Fuzzy Linguistic Preference Relation Priority Programming (Ren-Zhu-Xu 2018)) is a preference relations multi-criteria decision-making (MCDM) method introduced by Ren, P. J. Zhu, B. Xu, Z. S. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Derives priority vectors directly from Hesitant Fuzzy Linguistic Preference Relations (HFLPRs) without a consistency-checking/repair step. Input is one n×n HFLPR per criterion plus one HFLPR for criteria themselves. The hyperplane-consistency programming model (Model 6.1) maximises the minimum decision-maker satisfaction across all pairwise constraints simultaneously. A sensitivity parameter t is calibrated empirically from 10,000 Monte-Carlo MCDM problems.

Ren, P. J., Zhu, B., Xu, Z. S. (2018). Assessment of the impact of hydropower stations on the environment with a hesitant fuzzy linguistic hyperplane-consistency programming method. IEEE Transactions on Fuzzy Systems


HFPE

HFPE (Hesitant Fuzzy Peer-Evaluation (benevolent / aggressive cross-efficiency, Zhou-Chen-Xu-Meng 2018)) is a dea multi-criteria decision-making (MCDM) method introduced by Zhou, W. Chen, J. Xu, Z. S. Meng, S. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Cross-efficiency DEA extended to HFS — each alternative is evaluated by both its own optimal HFEA weights (self-evaluation, score E_{ee}) and by the optimal weights of every other alternative (peer evaluation, cross-efficiency E_{el}). Benevolent strategy maximises peer scores; aggressive strategy minimises them. Final ranking by column-mean of cross-efficiency matrix.

Zhou, W., Chen, J., Xu, Z. S., Meng, S. (2018). Hesitant fuzzy preference envelopment analysis and alternative improvement. Information Sciences


HFPEA

HFPEA (Hesitant Fuzzy Preference Envelopment Analysis (DHFPEA / SHFPEA, Zhou-Chen-Xu-Meng 2018)) is a dea multi-criteria decision-making (MCDM) method introduced by Zhou, W. Chen, J. Xu, Z. S. Meng, S. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

HFEA extension with ordinal attribute preference constraints — same score/deviation LP as HFEA but with additional weight ordering inequalities p_g ≥ p_t ≥ … ≥ p_m encoding the decision maker's stated preference order over criteria; produces preference-consistent efficiency rankings and improvement schedules.


Hi-C Analysis

Hi-C Analysis of 3D Genome Organization and Chromatin Interactions

Chromosome conformation capture
3D genome
Chromatin contact mapping

Hi-C (High-Chromosome Conformation Capture) is a technique and associated computational methods for mapping the 3D architecture of the genome within cells. Developed by Lieberman-Aiden and Dekker in 2009, Hi-C identifies physical interactions between genomic regions that may be distant in linear sequence but spatially proximal in 3D nuclear space. Hi-C analysis has revealed fundamental principles of genome organization, including the existence of topologically associating domains (TADs), and provides insights into how 3D structure regulates gene expression and DNA replication.

Lieberman-Aiden, E., van Berkum, N. L., Williams, L., Imakaev, M., Ragoczy, T., Telling, A., & Dekker, J. (2009). Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science, 326(5950), 289–293.

Dixon, J. R., Selvaraj, S., Yue, F., Kim, A., Li, Y., Shen, Y., & Ren, B. (2012). Topological domains in mammalian genomes identified by analysis of chromatin interactions. Nature, 485(7398), 376–380.

Szabo, Q., Bantignies, F., & Cavalli, G. (2019). 3D chromatin architecture. Nature Reviews Molecular Cell Biology, 20(4), 207–220.


Hick-Hyman Law

The Hick-Hyman Law predicts that human decision time increases logarithmically with the number of equally likely choices. Independently formulated by William Edmund Hick and Ray Hyman in the early 1950s, this law describes how long it takes a person to make a choice among alternatives. In human-computer interaction, the law is widely applied to menu design, navigation hierarchies, and command selection, showing that users take longer to select from larger sets of options, but the relationship is logarithmic, not linear.

Empirical model of choice reaction time as logarithmic function of number of choices

Hick, W. E. (1952). On the rate of gain of information. Quarterly Journal of Experimental Psychology, 4(1), 11–26.

Hyman, R. (1953). Stimulus information as a determinant of reaction time. Journal of Experimental Psychology, 45(3), 188–196.

klm-goms cognitive-walkthrough system-usability-scale think-aloud-protocol


Hiemstra-Jones Causality

Hiemstra-Jones Nonlinear Granger Causality Test

Nonlinear Granger Causality (Hiemstra-Jones)

The Hiemstra-Jones test, introduced in 1994, is a nonparametric procedure for detecting nonlinear causal relationships between two time series after removing their linear interdependencies. Developed in the context of stock price and trading volume dynamics, it extends the standard linear Granger causality framework by using correlation integral statistics to detect predictability arising from nonlinear mechanisms that linear VAR models cannot capture.

Hiemstra, C., & Jones, J. D. (1994). Testing for linear and nonlinear Granger causality in the stock price-volume relation. The Journal of Finance, 49(5), 1639–1664.


Hierarchical Approximate Bayesian Computation

hierarchical ABC
ABC for hierarchical models
multilevel ABC
population ABC

Toni, Welch, Strelkowa, Ipsen & Stumpf (building on Pritchard et al. 1999 and Beaumont et al. 2002)

Hierarchical ABC is a likelihood-free Bayesian inference method designed for multilevel data structures in which individual-level parameters are themselves drawn from a population-level distribution. By combining simulation-based rejection sampling with hierarchical pooling, it recovers both within-group and between-group posterior distributions without requiring a tractable likelihood function.

individual-level and group-level continuous or discrete observations

Toni, T. & Stumpf, M. P. H. (2010). Simulation-based model selection for dynamical systems in systems and population biology. Bioinformatics, 26(1), 104–110.

Wilkinson, R. D. (2013). Approximate Bayesian computation (ABC) gives exact results under the assumption of model error. Statistical Applications in Genetics and Molecular Biology, 12(2), 129–141.


Hierarchical Bayesian Inference

multilevel Bayesian modeling
Bayesian hierarchical model
nested Bayesian model
partial pooling model

1972 (Lindley & Smith); consolidated 1995–2013

Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate.

grouped / nested / clustered observations

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press.

Gelman, A. (2006). Multilevel (hierarchical) modeling: what it can and cannot do. Technometrics, 48(3), 432-435.

bayesian-regression mcmc gibbs-sampling hierarchical-markov-chain-monte-carlo variational-inference mixed-effects-model


Hierarchical Bayesian Model Averaging

Bayesian model averaging in hierarchical models

Extension formalised by Hoeting, Madigan, Raftery, and Volinsky; hierarchical application developed through 1990s–2000s Bayesian literature

Hierarchical Bayesian model averaging (HBMA) combines Bayesian model averaging with hierarchical model structure, averaging posterior quantities over a set of candidate models weighted by each model's posterior probability. Rather than selecting a single best model, HBMA propagates model uncertainty through a hierarchical framework, producing predictions and parameter estimates that honestly reflect uncertainty about which model is correct.

Bayesian model averaging within hierarchical models

continuous, count, binary, clustered / grouped data

Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999). Bayesian model averaging: A tutorial. Statistical Science, 14(4), 382–417.

Fragoso, T. M., Bertoli, W., & Louzada, F. (2018). Bayesian model averaging: A systematic review and conceptual classification. International Statistical Review, 86(1), 1–28.

bayesian-model-averaging hierarchical-bayesian-inference bayesian-regression hierarchical-markov-chain-monte-carlo bayesian-information-criterion model-selection


Hierarchical Bayesian Network

hierarchical probabilistic graphical model

A hierarchical Bayesian network is a probabilistic graphical model that organizes variables across multiple levels of abstraction. Higher-level nodes govern the prior distributions of lower-level nodes through hyperparameters, enabling structured sharing of information across groups, contexts, or data subsets while preserving the directed acyclic graph (DAG) representation of conditional dependencies.

multivariate, structured, hierarchically organized

Koller, D. & Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. MIT Press.

Friedman, N., Getoor, L., Koller, D. & Pfeffer, A. (1999). Learning probabilistic relational models. Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI-99), 1300-1307.


Hierarchical Bootstrap Simulation

cluster bootstrap
multilevel bootstrap
nested bootstrap resampling
hierarchical resampling

Davison & Hinkley; Cameron, Gelbach & Miller

Hierarchical bootstrap simulation is a resampling technique designed for data with nested or clustered structure — students within schools, patients within hospitals, repeated measures within subjects. It preserves the natural grouping of the data by resampling at each level of the hierarchy in sequence, producing a sampling distribution that correctly reflects both between-group and within-group variability.

Davison, A. C. & Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press.

Cameron, A. C., Gelbach, J. B. & Miller, D. L. (2008). Bootstrap-based improvements for inference with clustered errors. Review of Economics and Statistics, 90(3), 414-427.

multilevel-bootstrap-simulation hierarchical-monte-carlo-simulation sequential-monte-carlo hierarchical-bayesian-inference gibbs-sampling kalman-filter


Hierarchical Causal-Comparative Research Design

multilevel causal-comparative design
nested causal-comparative research
HLM causal-comparative study
hierarchical ex post facto comparison

1960s (causal-comparative); 1980s–2002 (hierarchical/multilevel extension)

Kerlinger (causal-comparative logic); Raudenbush & Bryk (hierarchical extension)

Hierarchical causal-comparative research is a non-experimental quantitative design that compares pre-existing groups on an outcome variable while explicitly modeling the nested structure of the data. Participants are clustered within higher-level units — students within classrooms, employees within organizations — and the design uses multilevel analytical techniques to distinguish group differences at each level. The cause-and-effect inference is strengthened by accounting for variance attributable to the hierarchy rather than misattributing it to individual-level group membership.

Non-experimental quantitative research design

Numerical group-membership and outcome data from nested/clustered samples

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage.

Kerlinger, F. N. (1986). Foundations of Behavioral Research (3rd ed.). Holt, Rinehart and Winston.


Hierarchical Clustering

Hiyerarşik Kümeleme
hiyerarşik kümeleme
agglomerative clustering
hierarchical agglomerative clustering
HAC

Hierarchical clustering is an unsupervised method that groups observations into nested clusters and draws the result as a dendrogram, so the number of clusters need not be fixed in advance. Its agglomerative form rests on the objective-function grouping criterion introduced by Joe Ward in 1963.

Ward, J. H. (1963). Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association, 58(301), 236–244.

kmeans-clustering dbscan gaussian-mixture pca factor-analysis


Hierarchical Confirmatory Research

Hierarchical Confirmatory Research Design

Hierarchical confirmatory research is a quantitative design that tests pre-specified hypotheses about relationships or group differences in data that have a natural nested (hierarchical) structure — such as students clustered within classrooms, patients within hospitals, or employees within organizations. By explicitly modeling the hierarchy, it avoids the inflation of Type I error that occurs when nested data are analyzed as though observations were independent.

Quantitative confirmatory research design

Nested/clustered quantitative data (e.g., students within schools, employees within firms)

Hox, J. J. (2010). Multilevel Analysis: Techniques and Applications (2nd ed.). Routledge.

confirmatory-research hierarchical-longitudinal-research multilevel-modeling structural-equation-modeling hierarchical-model-testing-research confirmatory-factor-analysis


Hierarchical Cross-Sectional Research

Hierarchical Cross-Sectional Research Design

multilevel cross-sectional design
nested cross-sectional study
clustered cross-sectional research
HCS design

1980s–1990s (formalized with HLM software and methodology)

Raudenbush & Bryk; Goldstein; Snijders & Bosker (multilevel modeling tradition)

Hierarchical cross-sectional research is a quantitative observational design that collects data from individuals nested within higher-level units — such as students within schools, patients within hospitals, or employees within organizations — at a single point in time. By accounting for the non-independence of clustered observations through multilevel modeling, it enables researchers to simultaneously examine individual-level and group-level predictors of an outcome without violating the independence assumption of ordinary regression.

Cross-sectional survey or administrative data with nested units (individuals within groups)

Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling (2nd ed.). Sage.

multilevel-modeling cross-sectional-survey cluster-sampling hierarchical-linear-modeling stratified-random-sampling nested-anova


Hierarchical Descriptive Research

Hierarchical Descriptive Research Design

multilevel descriptive design
nested descriptive study
hierarchical survey design
stratified descriptive research

1980s–1990s (multilevel descriptive formalization)

Formalized within survey and educational research traditions; associated with Hox, Raudenbush, Bryk, and Creswell

Hierarchical descriptive research is an observational design that documents the current state of a phenomenon across two or more nested levels — for example, students within classrooms within schools, or employees within teams within organizations. Rather than testing hypotheses or explaining causation, it describes distributions, frequencies, and relationships at each level, making explicit the structured, layered nature of the population being studied.

Structured survey data, archival records, observational counts from nested units

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (4th ed.). Sage.

cross-sectional-survey multilevel-modeling stratified-sampling descriptive-survey-design cluster-sampling comparative-descriptive-research


Hierarchical Exploratory Quantitative Research Design

multilevel exploratory quantitative design

Developed from survey research traditions (Kish, 1965; Babbie, 1990s)

Hierarchical exploratory quantitative research is a survey and observational design that structures both sampling and analysis across nested population levels — such as students within classrooms within schools — to explore patterns, distributions, and relationships in numerical data without a pre-specified directional hypothesis. It is oriented toward discovery and description rather than confirmation, making it appropriate early in a research programme when the phenomenon is not yet well-mapped.

Quantitative observational and survey design

Structured questionnaire / survey data collected across hierarchically organized population strata

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (4th ed.). Sage Publications.

Babbie, E. (2016). The Practice of Social Research (14th ed.). Cengage Learning.

stratified-random-sampling hierarchical-linear-modeling cluster-sampling exploratory-factor-analysis cross-sectional-survey descriptive-quantitative-research


Hierarchical Hamiltonian Monte Carlo

Hamiltonian Monte Carlo for Hierarchical Models

Hierarchical HMC
HMC for hierarchical models
HMC with reparameterization
NUTS for hierarchical Bayesian models

Hierarchical Hamiltonian Monte Carlo (Hierarchical HMC) applies Hamiltonian Monte Carlo sampling to Bayesian hierarchical models, addressing the severe geometric challenges those models pose. By combining non-centered parameterizations with HMC's gradient-driven proposals, it achieves efficient posterior exploration of the multi-level funnel-shaped geometries that standard MCMC methods struggle with.

Betancourt, M. & Girolami, M. (2015). Hamiltonian Monte Carlo for hierarchical models. In S. K. Upadhyay, U. Singh, D. K. Dey & A. Loganathan (Eds.), Current Trends in Bayesian Methodology with Applications (pp. 79-101). CRC Press.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press.

hamiltonian-monte-carlo hierarchical-bayesian-inference hierarchical-markov-chain-monte-carlo mcmc bayesian-regression nuts-sampler


Hierarchical Kalman Filter

multi-scale Kalman filter
multilevel Kalman filter
hierarchical state-space filter
HKF

The Hierarchical Kalman Filter (HKF) extends the classic Kalman filter to systems with multiple levels or scales of state representation. It applies Kalman recursions at each level of a hierarchy — from coarse to fine resolution or from global to local subsystems — and passes information across levels via upward and downward sweeps, producing optimal linear state estimates throughout a structured state-space.

multivariate time-series / multi-resolution signal data

Chou, K. C., Willsky, A. S., & Benveniste, A. (1994). Multiscale recursive estimation, data fusion, and regularization. IEEE Transactions on Automatic Control, 39(3), 464–478.

Sarkka, S. (2013). Bayesian Filtering and Smoothing. Cambridge University Press.

kalman-filter hierarchical-bayesian-inference particle-filter sequential-monte-carlo hierarchical-sequential-monte-carlo dynamic-kalman-filter


Hierarchical Linear Model

HLM
multilevel linear model
nested data model
random coefficient model

The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates and correct standard errors that ordinary regression cannot provide for nested data.

Continuous outcome; nested / clustered observations

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications.

Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling (2nd ed.). Sage Publications.

multilevel-modeling mixed-effects-model ols-regression panel-multiple-linear-regression random-effects-model generalized-linear-model


Hierarchical Markov Chain Monte Carlo

Markov Chain Monte Carlo for Hierarchical Bayesian Models

hierarchical MCMC
MCMC for multilevel models
Bayesian hierarchical MCMC
multilevel MCMC sampling

Gelfand & Smith (1990), building on Geman & Geman (1984)

Hierarchical Markov chain Monte Carlo applies MCMC sampling to hierarchical Bayesian models, jointly drawing from the posterior over both observation-level parameters and the hyperparameters that govern them. This allows principled uncertainty propagation across all levels of a multilevel structure, from individuals to groups to population, using algorithms such as Gibbs sampling, Metropolis-Hastings, or Hamiltonian Monte Carlo.

any data amenable to hierarchical Bayesian modelling

Robert, C. P. & Casella, G. (2004). Monte Carlo Statistical Methods (2nd ed.). Springer.

hierarchical-bayesian-inference gibbs-sampling metropolis-hastings-algorithm hamiltonian-monte-carlo bayesian-regression variational-inference


Hierarchical Model Testing Research

multilevel model testing
hierarchical SEM
nested model testing
HLM model testing

1980s–1990s (Raudenbush & Bryk 1986; Muthen 1994)

Stephen Raudenbush and Anthony Bryk (HLM); extended to multilevel SEM by Bengt Muthen

Hierarchical model testing research is a quantitative design that evaluates theoretically derived models using data with a nested or clustered structure — for example, students within classrooms, employees within organisations, or patients within hospitals. It applies hierarchical linear models (HLM) or multilevel structural equation models (ML-SEM) to test whether a proposed set of relationships holds after properly accounting for the non-independence introduced by grouping.

Nested/clustered quantitative data (continuous, ordinal, or count outcomes)

multilevel-modeling structural-equation-modeling confirmatory-research hierarchical-regression longitudinal-model-testing-research model-testing-research


Hierarchical Particle Filter

nested particle filter
multilevel particle filter
hierarchical SMC
HPF

A hierarchical particle filter extends Sequential Monte Carlo to state-space models with multiple levels of latent variables. Particles are propagated at each level of the hierarchy, allowing the method to track both fine-grained state dynamics and slower-varying hyperparameters simultaneously, yielding calibrated posterior distributions across all levels of the model.

Sequential Monte Carlo / hierarchical state-space inference

Sequential / time-series data with hierarchical structure

Briers, M., Doucet, A. & Maskell, S. (2010). Smoothing algorithms for state-space models. Annals of the Institute of Statistical Mathematics, 62(1), 61-89.

Chopin, N., Jacob, P. E. & Papaspiliopoulos, O. (2013). SMC2: an efficient algorithm for sequential analysis of state-space models. Journal of the Royal Statistical Society: Series B, 75(3), 397-426.

particle-filter sequential-monte-carlo hierarchical-bayesian-inference kalman-filter hierarchical-markov-chain-monte-carlo hierarchical-sequential-monte-carlo


Hierarchical Quantitative Content Analysis

hierarchical coding content analysis
nested category content analysis
tree-structured content analysis
HQCA

1980s–1990s (formalized in Krippendorff 1980; elaborated through subsequent editions)

Klaus Krippendorff (hierarchical category systems formalized in content analysis methodology)

Hierarchical quantitative content analysis is a systematic method for coding and counting text or media content using nested, tree-structured category schemes. Rather than a flat list of mutually exclusive codes, categories are organized into parent-child levels — broad themes subdivide into specific sub-themes — enabling researchers to aggregate or disaggregate frequencies at any level of the hierarchy and to produce richly structured numerical summaries of large corpora.

Text, media content, documents (coded into nested category systems)

Krippendorff, K. (2018). Content Analysis: An Introduction to Its Methodology (4th ed.). Sage.

Neuendorf, K. A. (2016). The Content Analysis Guidebook (2nd ed.). Sage.

quantitative-content-analysis hierarchical-cluster-analysis thematic-analysis coding-reliability-analysis text-mining systematic-review


Hierarchical Relational Survey

nested relational survey
multilevel relational survey
HLM-based relational survey
hierarchical correlational survey

1980s–2002 (modern HLM-based survey tradition)

Raudenbush & Bryk (multilevel framework); Hox (multilevel survey analysis)

A hierarchical relational survey combines the correlational goals of relational survey research with a multilevel data structure in which respondents are nested within higher-level units such as classrooms, schools, hospitals, or organizations. The design acknowledges that observations within the same group are not independent, and uses hierarchical linear modeling (HLM) or equivalent multilevel techniques to examine relationships among variables both within and between levels simultaneously.

Quantitative survey design with multilevel relational analysis

Survey questionnaire data with nested/clustered structure (e.g., students within schools, employees within organizations)

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage.

Hox, J. J. (2010). Multilevel Analysis: Techniques and Applications (2nd ed.). Routledge.

hierarchical-linear-modeling multilevel-modeling correlational-research relational-survey longitudinal-survey-research hierarchical-cross-sectional-research


Hierarchical Survey Research

Hierarchical Survey Research (Multilevel Survey Design)

multilevel survey research
nested survey design
multilevel survey design
HLM-based survey research

1986–1992 (formalization of multilevel methods for nested survey data)

Developed through contributions of Aitkin, Longford, Goldstein, Bryk, and Raudenbush in the 1980s–1990s

Hierarchical survey research is a quantitative design that collects survey data from respondents who are naturally nested within higher-level units — such as students within classrooms, employees within organizations, or patients within hospitals — and uses multilevel (hierarchical linear) modeling to analyze variation at each level simultaneously. It is the standard approach whenever survey data have a clustered structure that would violate the independence assumption of ordinary regression.

Quantitative survey design with multilevel analysis

Structured survey questionnaire data from nested/clustered samples

Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling (2nd ed.). Sage.

survey-research multilevel-modeling longitudinal-survey-research cluster-sampling comparative-survey-research panel-research


Hierarchical Variational Inference

HVI
hierarchical variational models
hierarchical VI
hierarchical approximate inference

Hierarchical variational inference (HVI) extends standard variational inference by placing a richer, hierarchical structure on the variational family itself. Instead of using a simple mean-field approximation, HVI introduces auxiliary latent variables that capture dependencies among the main latent variables, yielding tighter evidence lower bounds and more accurate posterior approximations for complex Bayesian models.

Ranganath, R., Altosaar, J., Tran, D. & Blei, D. M. (2016). Hierarchical Variational Models. Proceedings of the 33rd International Conference on Machine Learning (ICML 2016), PMLR 48, 324-333.

Jordan, M. I., Ghahramani, Z., Jaakkola, T. S. & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37(2), 183-233.

variational-inference hierarchical-bayesian-inference hierarchical-markov-chain-monte-carlo bayesian-regression mcmc hierarchical-gibbs-sampling


Market Microstructure Analysis

High-Frequency Data and Market Microstructure Analysis

Yüksek Frekanslı Veri ve Piyasa Mikro Yapısı

Hasbrouck (2007); Aït-Sahalia & Jacod (2014)

Market microstructure analysis studies how prices form from tick-level trade and quote data, examining order-book dynamics, the bid-ask spread, and price discovery. The modern econometric framework was set out by Hasbrouck (2007) and extended for high-frequency data by Aït-Sahalia and Jacod (2014).

Market microstructure / high-frequency econometrics

Realized variance with subsampling; effective-spread decomposition

Tick-level intraday trade and quote data

Hasbrouck, J. (2007). Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading. Oxford University Press.

Aït-Sahalia, Y. & Jacod, J. (2014). High-Frequency Financial Econometrics. Princeton University Press.

liquidity-risk-models jump-diffusion-model har-rv-model backtesting-var interest-rate-models


Highly Accelerated Life Testing

Highly Accelerated Life Testing (HALT) is a methodology for rapidly identifying design weaknesses and determining the margin between normal operating conditions and product failure. By applying extreme but non-destructive stress profiles (thermal, vibration, etc.), HALT accelerates the failure clock to reveal latent defects in weeks rather than years. Developed intensively from the 1980s onward and refined by practitioners in electronics and mechanical systems, HALT has become essential in accelerated product development and reliability validation.

Leis, B. N., & Stephens, D. R. (2011). Reliability methodologies for structural integrity assessment. Journal of Pressure Vessel Technology, 133(5), 051204.

Nelson, W. B. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analyses. Wiley.

Hobbs, G. K. (1997). Physical Modeling of Electronic Products for Reliability and Shelf Life. IEEE Transactions on Components, Packaging, and Manufacturing Technology, 20(2), 82-95.

Alfirevic, D., Callerame, F., & Roberts, G. (2011). A comprehensive overview of HALT and HASS. Proceedings of the EPTC 2011.


Hilbert-Huang Transform

HHT
EMD-Hilbert Spectral Analysis
Hilbert Spektral Analizi
Adaptive Time-Frequency Decomposition

The Hilbert-Huang Transform (HHT) is an adaptive, data-driven method for analyzing non-linear and non-stationary time series, introduced by Norden E. Huang and colleagues in 1998. It combines Empirical Mode Decomposition (EMD), which decomposes a signal into intrinsic mode functions (IMFs), with the Hilbert spectral analysis to produce instantaneous frequency and amplitude representations without assuming signal stationarity or linearity.

Huang, N. E., et al. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A, 454(1971), 903–995.


Hill-Bone Compliance Scale

Marjorie T. Kim, Mozella N. Hill, Lisa R. Bone, and Debra M. Levine

The Hill-Bone Compliance Scale (HBCS) is a brief, disease-specific self-report measure designed to assess medication and lifestyle adherence in hypertension management. Developed by Kim, Hill, Bone, and Levine at Johns Hopkins University in 1999, the HBCS measures three dimensions of hypertension adherence: medication-taking, dietary sodium restriction, and appointment keeping. Unlike generic adherence measures, the HBCS captures the multifaceted nature of hypertension self-management, recognizing that many hypertensive patients struggle equally with medication adherence and behavioral changes (diet, exercise, weight management, stress management). The scale has demonstrated strong reliability and validity in diverse hypertensive populations and remains widely used in hypertension research and clinical management.

Kim, M. T., Hill, M. N., Bone, L. R., & Levine, D. M. (1999). Development and Testing of the Hill-Bone Compliance Scale. Journal of Cardiovascular Nursing, 4(1), 54-59. (Also: Hill, M. N., Bone, L. R., & Kim, M. T. (1996). Perspective on compliance research in hypertension. Journal of Clinical Hypertension, 8(1), 12-17.)


Hip Outcome Score

Phillip M. Philippon, Ryan L. Martin, Bryan T. Kelly

The Hip Outcome Score (HOS) is a 29-item patient self-report instrument designed to measure symptoms, functional limitations, and activity restrictions in individuals with hip disorders. Originally developed and published by Philippon, Kelly, and Martin in 2006 in Arthroscopy, the HOS has become the standard outcome measure in hip arthroscopy, hip preservation surgery, and hip rehabilitation research, providing comprehensive assessment of pain, function in daily activities, and return-to-sport capability in hip-specific populations.

Martin RL, Kelly BT, Philippon MJ. Evidence of validity for the Hip Outcome Score. Arthroscopy. 2006;22(12):1304-1311.

patient-specific-functional-scale lower-extremity-functional-scale faos global-rating-of-change-scale


Histogram Equalization

Histogram Equalization for Image Contrast Enhancement

Histogram stretching
Contrast enhancement

Histogram equalization is an image preprocessing technique that redistributes pixel intensities to improve contrast and visibility of details. By spreading the histogram of pixel values evenly across the available range, histogram equalization enhances images with poor contrast, making features more visually distinct and easier to process algorithmically.

Gonzalez, R. C., & Woods, R. E. (1992). Digital Image Processing. Addison-Wesley, 2nd edition, Chapter 3.

Pizer, S. M., Amburn, E. P., Austin, J. D., et al. (1987). Adaptive histogram equalization and its variations. Computer Vision, Graphics, and Image Processing, 39(3), 355–368.

image-morphology contour-analysis canny-edge-detection blob-detection template-matching


Historical Archival Research

archival research
historical document analysis
archival history
primary source research

Historians and archivists; systematised through the professionalization of historical scholarship in the 19th century

Historical archival research is a systematic method of investigating the past through the critical examination of primary source documents preserved in archives, libraries, and institutional collections. Researchers locate, access, authenticate, and interpret original records — such as government documents, correspondence, diaries, maps, and institutional files — to reconstruct events, trace processes, and build evidence-based historical arguments. It is foundational to historiography and widely applied across humanities and social science disciplines.

Primary documents, manuscripts, government records, correspondence, photographs, maps, institutional files

Hill, M. R. (1993). Archival Strategies and Techniques. Sage Publications.

oral-history-method doctrinal-legal-research textual-criticism hermeneutic-analysis content-analysis case-study


HJM Framework

Forward Rate Model
No-Arbitrage Drift Condition

David Heath, Robert Jarrow, and Andrew Morton

The Heath-Jarrow-Morton (HJM) framework (1992) is a general no-arbitrage approach to modeling the entire term structure of forward rates. Unlike short-rate models, HJM works directly with forward rates f(t,T) and specifies their volatility; the drift is then determined by arbitrage constraints. This flexibility enables multi-factor modeling and accurate calibration to swaption matrices.

Heath, D., Jarrow, R. A., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60(1), 77-105.

Brigo, D., & Mercurio, F. (2006). Interest Rate Models: Theory and Practice (2nd ed.). Springer-Verlag.

hull-white-model libor-market-model risk-neutral-valuation change-of-numeraire


HKA Test

Hudson-Kreitman-Aguade Test for Detecting Selection

Richard Hudson, Martin Kreitman & Montserrat Aguade

The Hudson-Kreitman-Aguade (HKA) test is a statistical method that tests for neutral evolution by comparing levels of within-population polymorphism and between-population divergence at multiple loci. Developed by Hudson, Kreitman, and Aguade in 1987, this test uses the principle that neutral loci should show expected relationships between polymorphism and divergence. Loci deviating from these relationships are candidates for selection. The HKA test is particularly useful for detecting selection in genome-wide surveys because it uses relative comparisons across loci rather than requiring external calibration.

Hudson, R. R., Kreitman, M., & Aguadé, M. (1987). A test of neutral molecular evolution based on nucleotide data. Genetics, 116(1), 153–159.

Wakeley, J., Nielsen, R., Liu-Cordova, S. N., & Ardlie, K. (2012). The discovery of single-nucleotide polymorphisms and inferences about human demographic history. American Journal of Human Genetics, 69(6), 1332–1347.

Biswas, S., & Akey, J. M. (2006). Genome-wide scan for selection on derived alleles. Evolutionary Biology, 36(1), 64–79.

mcdonald-kreitman-test selection-sweep f-statistics coalescent-theory


Hierarchical Linear Modeling

Hierarchical Linear Modeling (HLM / Multilevel Modeling)

Hiyerarşik Doğrusal Modelleme (HLM / MLM)

Raudenbush & Bryk (popularized); Goldstein (parallel development)

Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a parametric statistical method for analyzing nested or clustered data — for example students within classrooms, patients within hospitals, or employees within organizations. Formalized by Raudenbush and Bryk in their 2002 seminal text (building on work from the mid-1980s), HLM simultaneously estimates individual-level and group-level effects while correctly partitioning variance across levels.

Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage.

Hox, J.J. (2010). Multilevel Analysis: Techniques and Applications (2nd ed.). Routledge.

linear-regression mixed-effects-model repeated-measures-anova one-way-anova sem


HMAC

HMAC (Hash-Based Message Authentication Code) is a cryptographic algorithm for authenticating messages using a secret key and a hash function. Standardized in RFC 2104 (1997), HMAC can be combined with any cryptographic hash function (SHA-256, SHA-3, etc.) to create a message authentication code (MAC). HMAC provides both data integrity and authentication, detecting both accidental corruption and deliberate tampering, and is widely used in web security (TLS/SSL), API authentication, and network protocols.

Krawczyk, H., Bellare, M., & Crechanko, R. (1997). HMAC: Keyed-Hashing for Message Authentication. RFC 2104.

Bellare, M., Canetti, R., & Krawczyk, H. (1996). Keying hash functions for message authentication. In Advances in Cryptology - CRYPTO 1996, LNCS 1109, pp. 1-15.


HMMER Profile Search

Hidden Markov Model Profile Search for Sequence Homology

profile-hidden Markov model
HMM profile search
HMMER

HMMER profile search identifies distant protein sequence homologs using probabilistic models of protein families, known as profile Hidden Markov Models (HMMs). Developed by Eddy and colleagues, this method captures sequence variation patterns within protein families and detects homologs with far greater sensitivity than position-weight matrices or pairwise alignment.

Krogh, A., Brown, M., Mian, I. S., Sjölander, K., & Haussler, D. (1994). Hidden Markov models in computational biology: applications to protein modeling. Journal of Molecular Biology, 235(5), 1501-1531.

Eddy, S. R. (1998). Profile hidden Markov models. Bioinformatics, 14(9), 755-763.

Finn, R. D., Clements, J., & Eddy, S. R. (2011). HMMER web server: interactive sequence similarity searching. Nucleic Acids Research, 39(Web Server issue), W29-W37.


Hodgkin-Huxley Model

Hodgkin-Huxley Model of Neuronal Excitability

Hodgkin-Huxley equations
Action potential model
Ionic channel dynamics

The Hodgkin-Huxley model is a mathematical description of how action potentials in neurons are generated by the flow of sodium and potassium ions across the cell membrane. Developed by Alan Hodgkin and Andrew Huxley in 1952, it is a foundational model in neuroscience and earned them the Nobel Prize, establishing quantitative biophysics as a discipline.

Differential equation model of neuronal dynamics

Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500-544.

Koch, C. (2004). Biophysics of Computation: Information Processing in Single Neurons. Oxford University Press.


Hoek-Brown Criterion

Hoek-Brown Failure Criterion for Rock Masses

Generalized Hoek-Brown Criterion
HB Criterion

The Hoek-Brown Criterion, developed by Evert Hoek and E. T. Brown starting in 1980, is an empirical failure criterion that predicts the shear strength of rock masses as a function of confining pressure. It accounts for rock quality (via the Geological Strength Index, GSI) and thus bridges laboratory rock mechanics and field behavior. The criterion is widely used in mining for slope stability, pillar design, and stress analysis.

Empirical criterion for rock mass strength prediction

Hoek, E., & Brown, E. T. (2002). The Hoek-Brown failure criterion and GSI: 2018 update. Journal of Rock Mechanics and Geotechnical Engineering, 10(2), 445-463.

Carter, T. G., Marinos, V., & Marinos, P. (2018). Guidelines for the classification of rock masses in Turkey. Bulletin of Engineering Geology and the Environment, 77(4), 1639-1681.


HGRC

The Hogan Grief Reaction Checklist (HGRC) is a 61-item comprehensive measure developed by Nancy S. Hogan and colleagues in 2001 to assess the full spectrum of grief reactions—encompassing not only grief distress and symptoms but also post-loss growth and resilience. Unique among grief instruments, the HGRC explicitly measures positive outcomes of bereavement (personal growth, meaning, strengthened relationships), reflecting contemporary understanding that grief can coexist with adaptive change.

Hogan, N. S., Greenfield, D. B., & Schmidt, L. A. (2001). Development and validation of the Hogan Grief Reaction Checklist. Death Studies, 25(1), 1–32.

inventory-complicated-grief texas-revised-inventory-grief grief-experience-questionnaire anticipatory-grief-scale


Hohmann Transfer

Hohmann-Vallado transfer
two-impulse maneuver

The Hohmann transfer is a maneuver that transfers a spacecraft between two circular orbits using two impulsive burns (velocity changes). Introduced by German engineer Walter Hohmann in 1925, it is the most fuel-efficient method for coplanar orbital transfers when the transfer time is not severely constrained. The transfer orbit is an ellipse tangent to both the initial and final orbits.

Hohmann, W. (1925). Die Erreichbarkeit der Himmelskörper. R. Oldenbourg.

Curtis, H. D. (2013). Orbital Mechanics for Engineering Students (3rd ed.). Butterworth-Heinemann.

Vallado, D. A., Crawford, P., Hujsak, R., & Kelso, T. S. (2006). Revisiting Spacetrack Report #3: Orbit Determination using Modern Computers. In AIAA/AAS Astrodynamics Specialist Conference.

orbit-determination n-body-simulation gravity-assist light-curve-analysis


Holistic Caring Inventory

Dossey, B. M.; Keegan, L.; Guzetta, C. E.

The Holistic Caring Inventory (HCI) is a clinical assessment tool measuring nurses' and healthcare providers' capacity to deliver holistic, person-centered care that integrates physical, emotional, spiritual, and social dimensions. Developed in the context of Watson's theory of human caring, it operationalizes the philosophical principles of holistic nursing.

Dossey, B. M., Keegan, L., & Guzetta, C. E. (2005). Holistic nursing: A handbook for practice (4th ed.). Jones & Bartlett Publishers.

Watson, J. (1999). Postmodern nursing and beyond. Edinburgh: Churchill Livingstone.

spiritual-care-competence-scale attitudes-cam-scale integrative-medicine-attitudes therapeutic-touch-assessment


Holm Correction

Holm Step-Down Family-Wise Error Rate Correction

Holm-Bonferroni method
Holm step-down procedure
Holm's sequentially rejective procedure
Holm düzeltmesi

The Holm correction, introduced by Sture Holm in 1979, is a step-down multiple-comparison procedure that controls the family-wise error rate (FWER) at level α while rejecting at least as many hypotheses as the classical Bonferroni correction. It orders the observed p-values from smallest to largest and compares each against a threshold that starts strict and relaxes as testing proceeds, making it uniformly more powerful than Bonferroni at the same level of error control.

Family-wise error rate (FWER) correction

Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2), 65–70.

Bonferroni, C. E. (1936). Teoria statistica delle classi e calcolo delle probabilità. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze, 8, 3–62.

bonferroni-correction benjamini-hochberg-procedure sidak-correction tukey-hsd-test one-way-anova


Holt-Winters

Holt-Winters Triple Exponential Smoothing

triple exponential smoothing
Winters' method
Holt-Winters seasonal method
Holt-Winters Üçlü Üstel Düzleştirme

Holt-Winters triple exponential smoothing is a forecasting model that extends Holt's double smoothing by adding a seasonal component, introduced by Peter Winters in 1960 building on Charles Holt's work. It tracks three evolving quantities — level, trend, and season — and combines them to forecast a continuous time series.

Recursive level, trend, and seasonal updating

Winters, P. R. (1960). Forecasting Sales by Exponentially Weighted Moving Averages. Management Science, 6(3), 324-342.

Holt, C. C. (2004). Forecasting Seasonals and Trends by Exponentially Weighted Moving Averages. International Journal of Forecasting, 20(1), 5-10.

simple-exponential-smoothing state-space-model structural-time-series arima seasonal-arima


Holtrop-Mennen Method

Holtrop-Mennen Ship Resistance and Propulsion Method

Holtrop method
Mennen method
ship resistance prediction

The Holtrop-Mennen Method is an empirical regression-based technique for predicting total ship resistance from geometric parameters and operating conditions. Developed by Jelte Holtrop and Gert Mennen in 1982, the method decomposes total resistance into friction, pressure, wave-making, and form drag components, each estimated from ship dimensions, hull shape, and speed. Widely adopted in maritime engineering, the Holtrop-Mennen method remains the industry standard for preliminary ship design and propulsion power estimation.

Holtrop, J., & Mennen, G. G. J. (1984). An approximate power prediction method for fast monohull ships. International Shipbuilding Progress, 29(335), 166–170.

Holtrop, J. (2001). Ship propulsion and trim. Maritime Engineering Proceedings, 153(1), 35–42.

Birk, L. (2019). The influence of nonlinear viscous pressure drag on ship resistance. Ocean Engineering, 171, 62–74.


HFEQ

HFEQ
Home Food Environment
Food Environment Assessment

Boles et al.; Fulkerson et al.; Environmental Research on Child Health

The HFEQ is a parent-report questionnaire measuring the household food environment—the availability of healthy and unhealthy foods, parent feeding practices, and family mealtime characteristics. Developed by Boles, Fulkerson, and colleagues, the HFEQ captures multiple dimensions of the home environment that influence children's dietary intake and weight status. The home food environment is a key modifiable target for childhood obesity prevention interventions.

Parent-report questionnaire; household food availability and feeding practices

Boles, R. E., Scharf, C., Fiese, B. H., et al. (2013). Differences in the home food environment and eating behaviors by child weight status: A qualitative study. Journal of the Academy of Nutrition and Dietetics, 113(7), 926–933.

Fulkerson, J. A., Larson, N., Horowitz, M., & Neumark-Sztainer, D. (2014). A qualitative study of factors affecting family food choices and the home food environment of lower-income families with preschool children. Appetite, 76, 76–85.


Homology Modeling

Homology-based Protein Structure Prediction

comparative modeling
template-based modeling

Homology modeling, also called comparative modeling, predicts the three-dimensional structure of a protein using an experimentally-solved structure of a homologous protein as a template. Introduced by Sali and Blundell in 1993, this method exploits the principle that homologous proteins share similar spatial structures despite differing in amino acid sequence.

Comparative structure prediction pipeline

Sali, A. & Blundell, T. L. (1993). Comparative protein modelling by satisfaction of spatial restraints. Journal of Molecular Biology, 234(3), 779-815.

Arnold, K., Bordoli, L., Kopp, J., & Schwede, T. (2006). The SWISS-MODEL workspace: a web-based environment for protein structure homology modelling. Bioinformatics, 22(2), 195-201.

Fiser, A., Do, R. K., & Sali, A. (2000). ModellerX and SOAP protein structure modelling. Trends in Biochemical Sciences, 25(12), 589-592.

molecular-docking pharmacophore-modeling cryo-em-reconstruction ppi-network-topology


Homomorphic Encryption

FHE
Fully Homomorphic Encryption
Leveled Homomorphic Encryption
Homomorfik Şifreleme

Homomorphic Encryption (HE) is a cryptographic framework that allows arbitrary computations to be performed directly on encrypted data without requiring decryption. First realized as a fully general construction by Craig Gentry in 2009 using ideal lattices, it enables a server to process sensitive data and return an encrypted result that, when decrypted by the data owner, equals the result of performing the same computation on the plaintext. It is foundational to privacy-preserving machine learning, secure cloud computing, and confidential analytics.

Learning With Errors (LWE) / ideal lattices

Addition and multiplication over ciphertexts

Gentry, C. (2009). Fully homomorphic encryption using ideal lattices. ACM Symposium on Theory of Computing (STOC), 169–178.


Honey Badger Algorithm

The Honey Badger Algorithm (HBA) is a nature-inspired metaheuristic optimization algorithm presented by Hashim et al. in 2023, modeled on the hunting behavior and intelligent strategies of honey badgers (Mellivora capensis). Honey badgers are known for their remarkable problem-solving abilities, fearlessness, and persistent pursuit of prey and food sources despite significant obstacles. HBA captures these behavioral traits to create an effective optimization framework.

Hashim, F. A., Hussain, K., & Houssein, E. H. (2023). Honey badger algorithm: A new meta-heuristic optimization algorithm. Neural Computing and Applications, 35(17), 12265-12287.

harris-hawks-optimization slime-mould-algorithm aquila-optimizer grey-wolf-optimizer particle-swarm-optimization


The Hip Disability and Osteoarthritis Outcome Score (HOOS) is a patient-reported outcome measure developed to assess pain, symptoms, function, and quality of life in patients with hip osteoarthritis and hip disability. Developed by Nilsdotter and colleagues in 2003, HOOS parallels the structure of KOOS (Knee Injury and Osteoarthritis Outcome Score) but is specifically tailored for the hip joint, making it the reference standard for hip osteoarthritis outcomes in clinical trials and practice.

Nilsdotter, A. K., Lohmander, L. S., Klassbo, M., & Roos, E. M. (2003). Hip Disability and Osteoarthritis Outcome Score (HOOS): development and validation against generic outcome measures in hip osteoarthritis. Arthritis & Rheumatism, 48(11), 3336–3345.

Nilsdotter, A. K., Ackermann, P. W., & Roos, E. M. (2007). Scoring instructions and guide for the hip disability and osteoarthritis outcome score (HOOS) v2.0 and HOOS junior. Stockholm, Sweden: Karolinska Institute.


Adult Dispositional Hope Scale

Adult Dispositional Hope Scale (Hope Scale)

The Adult Dispositional Hope Scale, developed by C. Rick Snyder in 1991, is a 12-item measure assessing hope as a cognitive motivational system composed of two independent dimensions: Agency (the motivation and determination to pursue goals) and Pathways (the ability to generate routes to achieve those goals). Grounded in hope theory, the scale operationalizes hope not as wishful thinking but as an actionable psychological state combining goal-directed determination with flexible problem-solving.

Snyder, C. R., Harris, C., Anderson, J. R., Holleran, S. A., Irving, L. M., Sigmon, S. T., ... & Harney, P. (1991). The will and the ways: Development and validation of an individual-differences measure of hope. Journal of Personality and Social Psychology, 60(4), 570–585.

flourishing-scale optimism-life-orientation-test meaning-in-life-questionnaire positive-mental-health-scale


Hospital Bed Occupancy Model

Stochastic Hospital Bed Occupancy Forecasting Model

Bed Occupancy Forecasting
Hospital Census Prediction

Hospital bed occupancy models forecast the number of occupied beds at future times by analyzing admission patterns, length of stay distributions, and discharge dynamics. These models support tactical decisions about staffing, supply chain management, and strategic decisions about capacity expansion.

Stochastic simulation and time-series forecasting

Tikk, D., Kóczy, L. T., & Gedeon, T. D. (2003). A survey on fuzzy relational equations and their applications in web intelligence. In W. Pedrycz (Ed.), Handbook of Granular Computing (pp. 521–542). John Wiley & Sons.

McCarthy, M. L., Zeger, S. L., Ding, R., Levin, S. R., Desmond, J. S., Lee, J., & Aronsky, D. (2008). The challenge of predicting demand for emergency department services. Academic Emergency Medicine, 15(4), 337–346.

Helm, J. E., AhmadBeygi, S., & Van Oyen, M. P. (2011). Design and analysis of hospital admission control for optimizing quality of care. Operations Research, 59(5), 1153–1166.

queuing-theory-healthcare patient-flow-simulation hospital-readmission-model staffing-ratio-analysis lean-healthcare


HCAHPS Hospital Consumer Assessment Survey

Centers for Medicare & Medicaid Services (CMS) and Agency for Healthcare Research and Quality (AHRQ)

The Hospital Consumer Assessment of Healthcare Providers and Systems (HCAHPS) is a 27-item, CMS-mandated patient experience survey administered to a random sample of hospital inpatients after discharge. Launched in 2006 by the Centers for Medicare & Medicaid Services and the Agency for Healthcare Research and Quality, HCAHPS measures patient perceptions of hospital care across 10 key composites: communication with nurses, communication with physicians, responsiveness to patient needs, pain management, communication about medications, discharge information, cleanliness and quietness of the hospital environment, and overall rating of the hospital. HCAHPS is publicly reported on the CMS Hospital Compare website, incorporated into hospital payment incentive programs, and is one of the most widely recognized measures of hospital quality from the patient perspective.

Centers for Medicare & Medicaid Services and Agency for Healthcare Research and Quality. (2006). Hospital Consumer Assessment of Healthcare Providers and Systems. U.S. Department of Health and Human Services.

Hargraves, J. L., Hays, R. D., & Cleary, P. D. (2003). Psychometric properties of the Agency for Healthcare Research and Quality's Healthcare Experiences with Care questionnaire. Health Services Research, 38(6), 1457–1479.

Jaipaul, C. K., & Rosenthal, G. E. (2005). Are differences in medical complications, length of stay, and mortality rate useful markers of hospital quality? Journal of Hospital Medicine, 1(2), 107–118.


Hospital Readmission Prediction Model

Predictive Modeling for Hospital Readmission Risk and Prevention

Readmission Risk Prediction
Hospital Readmission Forecasting

Predictive modeling, Patient risk stratification

Healthcare data analytics and outcomes research

Hospital readmission prediction models use statistical and machine learning techniques to identify patients at high risk of returning to the hospital shortly after discharge. These models guide targeted discharge planning and follow-up to improve outcomes and reduce costs.

Logistic regression and machine learning methodology

Jencks, S. F., Williams, M. V., & Coleman, E. A. (2009). Rehospitalizations among patients in the Medicare fee-for-service program. New England Journal of Medicine, 360(14), 1418–1428.

Krumholz, H. M., Normand, S. L. T., & Wang, Y. (2014). Trends in hospitalizations and outcomes for acute myocardial infarction, 2006 to 2011. Circulation, 132(4), 362–366.

Philbin, E. F., & DiSalvo, T. G. (1998). Prediction of hospital readmissions for heart failure: development of a simple risk score based on administrative data. Journal of the American College of Cardiology, 33(6), 1560–1566.

lean-healthcare patient-flow-simulation dea-hospital-efficiency staffing-ratio-analysis hospital-bed-occupancy-model


Agency for Healthcare Research and Quality (AHRQ) in collaboration with researchers at Westat, Inc.

The Hospital Survey on Patient Safety Culture (HSOPS) is a 42-item standardized instrument developed by the Agency for Healthcare Research and Quality (AHRQ) to measure patient safety culture in hospital settings. First released in 2004 and revised in 2018, the HSOPS assesses 12 composite dimensions of safety culture across organizational, unit, and individual levels. It is one of the most frequently used and publicly reported safety culture measures, with data from over 1,000 hospitals contributing to AHRQ's national benchmarking database.

Sorra, J. S., & Dyer, N. (2010). Multilevel analysis of the Agency for Healthcare Research and Quality Hospital Survey on Patient Safety Culture. BMJ Quality & Safety, 19(5), 413–417.

Westat, Inc. (2008). Hospital Survey on Patient Safety Culture 2008: Summary of Results for a Large Convenience Sample. Agency for Healthcare Research and Quality, U.S. Department of Health and Human Services.

Nieva, V. F., & Sorra, J. (2003). Safety culture assessment: a tool for improving patient safety in healthcare organizations. Quality & Safety in Health Care, 12(2), ii17–ii23.

safety-attitudes-questionnaire patient-safety-climate-scale teamstepps-perceptions nurse-work-environment-scale


Hot Spot Analysis

Getis-Ord Gi* statistic
spatial hot spot detection
cluster and outlier analysis
HSA

Hot Spot Analysis uses the Getis-Ord Gi* local spatial statistic to identify geographic locations where high or low attribute values cluster together to a degree that is statistically significant. Each feature is evaluated in relation to its neighbours, producing a z-score that flags genuine spatial hot spots and cold spots against a background of random variation.

Georeferenced point or polygon data with a continuous attribute

Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3), 189-206.

Ord, J. K., & Getis, A. (1995). Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis, 27(4), 286-306.

local-indicators-of-spatial-association spatial-autocorrelation kernel-density-estimation local-morans-i morans-i geographically-weighted-regression


Hotel Service Quality Scale

The Hotel Service Quality Scale (HSQS), including the Lodging Quality Index (LQI) developed by Getty & Getty (2003), measures guest perceptions of hotel service quality across multiple dimensions (room comfort, staff responsiveness, facilities, value). Using expectancy-disconfirmation theory, it captures not only perceived quality but the gap between expectations and reality, enabling precise diagnosis of service strengths and improvement priorities. Essential for hospitality managers seeking competitive positioning through service excellence and for franchisees maintaining brand standards.

Self-report questionnaire / Expectancy-disconfirmation scale

Getty, J. M., & Getty, R. L. (2003). Lodging quality index (LQI): Assessing Expectations and Perceptions of Lodging Quality. Cornell Hotel and Restaurant Administration Quarterly, 44(2), 33-46.

Parasuraman, A., Zeithaml, V. A., & Berry, L. L. (1988). SERVQUAL: A multiple-item scale for measuring consumer perceptions of service quality. Journal of Retailing, 64(1), 12-40.

Rauch, D. A., Collins, M. D., Nale, R. D., & Barr, P. B. (2015). Measuring Service Quality in Mid-Scale Hotels. International Journal of Contemporary Hospitality Management, 27(1), 119-106.

Lockyer, T. (2005). The perceived importance of price as one hotel selection factor. International Journal of Hospitality Management, 24(4), 617-628.

tourist-satisfaction-scale perceived-value-scale-tourism destination-image-scale tourist-loyalty-scale place-attachment-scale


Hotelling's T² Test

Hotelling T² Testi — Çok Değişkenli t-Testi

Hotelling's T² test is a multivariate parametric hypothesis test that simultaneously compares the mean vectors of two independent groups across multiple continuous outcome variables. It was introduced by Harold Hotelling in 1931 as the direct multivariate generalization of Student's t-test, replacing the scalar mean difference with a vector difference scaled by the pooled variance-covariance matrix.

Hotelling, H. (1931). The Generalization of Student's Ratio. Annals of Mathematical Statistics, 2(3), 360–378.

manova independent-t-test welch-t-test multivariate-regression mancova one-way-anova


Hough Transform

Hough Transform for Line and Shape Detection

Hough Line Detection
Generalized Hough Transform

The Hough Transform is a technique for detecting lines, circles, and other geometric shapes in digital images. Originally patented by Paul Hough in 1962 and popularized in computer vision by Duda and Hart in 1972, the Hough Transform converts edge points in image space to curves in a parameter space (accumulator space), where collinear or co-circular points cluster and become easily identifiable.

Feature extraction and pattern recognition

Hough, P. V. C. (1962). Method and means for recognizing complex patterns. U.S. Patent 3,069,654.

Duda, R. O., & Hart, P. E. (1972). Use of the Hough transformation to detect lines and curves in pictures. Communications of the ACM, 15(1), 11–15.

canny-edge-detection contour-analysis template-matching image-morphology harris-corner-detection


HDDS

The HDDS is a simple, 12-item food group checklist that captures the diversity of the household diet in the preceding 24 hours. Developed by the FAO in 2011 as a proxy indicator of dietary quality and nutrient adequacy, the HDDS enables rapid assessment of the nutritional vulnerability of households in resource-limited settings. A household with access to foods from many groups is more likely to consume adequate calories, protein, and micronutrients.

Kennedy, G., Ballard, T., & Dop, M. C. (2011). Guidelines for measuring household and individual dietary diversity. Food and Agriculture Organization of the United Nations.


HFIAS

Coates, Swindale, Bilinsky; FANTA Project

The HFIAS is a 9-item survey designed to measure the frequency and severity of food insecurity at the household level in resource-limited settings. Developed by the FANTA Project in 2007, it assesses four domains of food access: anxiety, dietary diversity, food consumption frequency, and household member deprivation. It is widely used in low- and middle-income countries for program evaluation and surveillance.

Coates, J., Swindale, A., & Bilinsky, P. (2007). Household Food Insecurity Access Scale (HFIAS) for measurement of food access: indicator guide. Food and Nutrition Technical Assistance Project, Academy for Educational Development.


HP Filter

Hodrick-Prescott Filter
HP Decomposition
Trend-Cycle Filter
HP Filtresi

The Hodrick-Prescott (HP) filter is a penalized least-squares technique used in macroeconomics and empirical finance to decompose a time series into a smooth long-run trend component and a short-run cyclical component. Introduced by Hodrick and Prescott (1997) using postwar U.S. business cycle data, it has become one of the most widely applied filters in business cycle analysis, monetary policy research, and applied econometrics.

λ (lambda); conventional values: 100 for annual, 1600 for quarterly, 14400 for monthly data

Hodrick, R. J., & Prescott, E. C. (1997). Postwar U.S. business cycles: An empirical investigation. Journal of Money, Credit and Banking, 29(1), 1–16.


HPLC

HPLC
high-pressure liquid chromatography

High-Performance Liquid Chromatography (HPLC) is an analytical technique that separates, identifies, and quantifies components in a complex food sample by passing the sample through a pressurized column packed with a stationary phase. Developed by Horváth in the early 1970s, HPLC enables rapid, sensitive measurement of nutrients, contaminants, additives, and bioactive compounds in food products with high precision and accuracy.

Snyder, L. R., Kirkland, J. J., & Dolan, J. W. (2010). Introduction to modern liquid chromatography (3rd ed.). Wiley.

Giddings, J. C. (1965). Dynamics of chromatography. Journal of Chromatography A, 3, 520.


HPSG

Head-Driven Phrase Structure Grammar (HPSG) is a constraint-based grammatical framework developed by Carl Pollard and Ivan Sag in 1987. HPSG represents linguistic information (phonological, syntactic, semantic) in typed feature structures and derives well-formed expressions through constraints on these structures. Unlike movement-based theories, HPSG models word order and long-distance dependencies through feature sharing and principles of grammar. It has been extensively applied to modeling diverse language phenomena and remains influential in computational linguistics.

Pollard, C., & Sag, I. A. (1994). Head-Driven Phrase Structure Grammar. Chicago: University of Chicago Press.

Sag, I. A., Wasow, T., & Bender, E. M. (2003). Syntactic Theory: A Formal Introduction (2nd ed.). Stanford, CA: CSLI Publications.

Borsley, R. D. (2011). A Grammar of Welsh. Berlin: De Gruyter.


HRAF Cross-Cultural Analysis

Human Relations Area Files (HRAF) Cross-Cultural Analysis

cross-cultural comparison
comparative ethnography

HRAF (Human Relations Area Files) cross-cultural analysis compares ethnographic data from diverse societies to identify patterns and test hypotheses about human social organization and cultural practices. Developed by George Murdock and colleagues, the method uses a standardized database of ethnographic information coded for comparative analysis. HRAF provides a framework for systematic cross-cultural comparison, helping archaeologists interpret prehistoric patterns through ethnographic analogy.

Murdock, G. P. (1967). Ethnographic Atlas. University of Pittsburgh Press.

Murdock, G. P., & White, D. R. (1980). Standard cross-cultural sample. Ethnology, 9(4), 329-369.


HSQC

HSQC NMR
1H-13C HSQC
heteronuclear correlation

Heteronuclear Single-Quantum Coherence (HSQC) is a 2D NMR technique that correlates proton and carbon-13 (or other heteronuclei) chemical shifts through one-bond coupling constants (1JHX). Developed in the early 1980s, HSQC rapidly became the workhorse of structural chemistry because it directly maps which carbons bear which protons, providing a comprehensive view of carbon skeleton connectivity and substitution patterns.

Bodenhausen, G., & Ruben, D. J. (1981). Natural abundance nitrogen-15 NMR by enhanced heteronuclear spectroscopy. Chemical Physics Letters, 69(2), 185-189.

Patt, S. L., & Shoolery, J. N. (1992). Attached proton test (APT). Journal of Magnetic Resonance, 46(3), 535-539.

Bax, A., Griffey, R. H., & Hawkins, B. L. (1983). Correlation of proton and nitrogen-15 chemical shifts by heteronuclear multiquantum NMR. Journal of the American Chemical Society, 105(24), 7188-7190.

hsqc cosy noesy ft-icr-mass-spectrometry


Huber Regression

Huber M-estimator
Huber loss regression
robust regression
Huber Regresyonu

Huber regression is a robust linear regression method, introduced by Peter J. Huber in 1964, that resists the influence of outliers by treating small and large residuals differently. It applies a squared (OLS-like) loss to small residuals and a milder absolute-value loss to large ones, so extreme observations cannot dominate the fit.

Huber M-estimator (quadratic loss for small residuals, absolute loss for large residuals)

Huber, P. J. (1964). Robust Estimation of a Location Parameter. Annals of Mathematical Statistics, 35(1), 73-101.

Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley.

ols-regression m-estimator mm-estimator least-trimmed-squares quantile-regression


Huff Model

Huff Gravity Model
Probabilistic Retail Gravity Model
Huff Trade Area Model
Huff Çekim Modeli

Proposed by David Huff in 1964, the Huff Model is a probabilistic spatial interaction model that estimates the likelihood that consumers located in a given geographic zone will choose to shop at a particular retail outlet. It extends deterministic gravity models by assigning each consumer zone a probability of patronage across all competing stores, weighting store attractiveness (typically measured by floor area) against the friction of travel time or distance. The model is widely used in retail site selection, trade area delineation, and market share forecasting.

Input: Store size, travel time/distance, population

Output: Probability of patronage per store per zone

Huff, D. L. (1964). Defining and estimating a trading area. Journal of Marketing, 28(3), 34–38.


Hull-White Model

Hull-White One-Factor Interest Rate Model

The Hull-White model (1990) is a one-factor short-rate model with time-dependent mean reversion and volatility, designed to fit the initial yield curve exactly. It generalizes the Vasicek model to allow better calibration to observed bond and derivative prices, and is widely used for pricing interest rate exotics and managing interest rate risk.

Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3(4), 573-592.

Brigo, D., & Mercurio, F. (2006). Interest Rate Models: Theory and Practice (2nd ed.). Springer-Verlag.

sabr-model hjm-framework libor-market-model risk-neutral-valuation


The Human Error Assessment and Reduction Technique (HEART), developed by Jeremy Williams in 1988 for the nuclear industry, is a structured method for assessing the probability of human error in safety-critical tasks and identifying error reduction strategies. Unlike scales that measure subjective experience (workload, situational awareness), HEART is an analytical tool combining expert judgment, task analysis, and empirical error rates to quantify task-specific error probability and guide human factors interventions in high-stakes operations.

Williams, J. C. (1988). A data-based method for assessing and reducing human error to improve operational performance. In IEEE Fourth Conference on Human Factors and Power Plants (pp. 436-450). IEEE.

operator-performance-scale situational-awareness-rating workload-profile nasa-task-load-index


Hunt and Hess Scale

Hunt and Hess Grading Scale for Subarachnoid Hemorrhage

Subarachnoid hemorrhage severity and prognosis

The Hunt and Hess Scale is the most widely used clinical grading system for assessing severity and prognosis in subarachnoid hemorrhage (SAH) caused by ruptured intracranial aneurysm. Developed by neurosurgeons William Hunt and Robert Hess in 1968, the five-point ordinal scale measures level of consciousness and presence of focal neurological deficits. Hunt-Hess grade at admission is the single strongest predictor of 30-day mortality and functional outcome and guides urgency of neurosurgical intervention.

Hunt, W. E., Hess, R. M. (1968). Surgical risk as related to time of intervention in the repair of intracranial aneurysms. Journal of Neurosurgery, 28(1), 14-20.

world-federation-neurosurgeons nihss updrs edss-multiple-sclerosis


HD-QoL

Huntington's Disease Health-Related Quality of Life Scale

The HD-QoL is a disease-specific quality-of-life instrument designed to measure the multidimensional impact of Huntington's disease on patients' physical, emotional, social, and cognitive functioning. Developed by Helder and colleagues in 2001, it uniquely addresses the progressive motor, cognitive, and psychiatric manifestations characteristic of HD. The scale recognizes that HD burden extends beyond neurological deficits to profound impacts on identity, family relationships, and existential well-being.

Helder, D. I., Kaptein, A. A., van Kempen, G. M., Weinman, J., van Houwelingen, H. C., & Roos, R. A. (2001). Living with Huntington's disease: Illness perceptions, coping mechanisms, and patients' well-being. Journal of Psychosomatic Research, 50(1), 1-7.


Hurdle Model

hurdle count model
two-part count model
zero-truncated count model
Engel Modeli (Hurdle Model)

The hurdle model is a two-part count-data model introduced by Mullahy (1986). A first stage models the binary choice of crossing a hurdle (a zero versus a non-zero count), and a second stage models the strictly positive counts with a zero-truncated distribution such as a zero-truncated Poisson or negative binomial.

Maximum likelihood (binary stage + zero-truncated count stage)

Mullahy, J. (1986). Specification and Testing of Some Modified Count Data Models. Journal of Econometrics, 33(3), 341–365.

zero-inflated-poisson negative-binomial-regression poisson-regression logistic-regression ols-regression


Hybrid Box-Behnken Design

Hybrid Box-Behnken Response Surface Design

Hybrid BBD
augmented Box-Behnken design
modified Box-Behnken design
extended BBD

1960 (standard BBD); hybrid variants developed from 1970s onward

Box & Behnken (1960), extended by various authors for hybrid configurations

The Hybrid Box-Behnken Design (Hybrid BBD) is a three-level response surface design that extends the classical Box-Behnken Design by incorporating additional design points — such as axial, face-centered, or space-filling runs — to improve estimation efficiency, handle larger factor sets, or achieve better predictive coverage. It retains BBD's avoidance of extreme corner runs while gaining the flexibility needed for complex engineering optimization problems.

Continuous quantitative factor levels; measured response values

Box, G. E. P., & Behnken, D. W. (1960). Some new three level designs for the study of quantitative variables. Technometrics, 2(4), 455–475.

Ferreira, S. L. C., Bruns, R. E., Ferreira, H. S., Matos, G. D., David, J. M., Brandão, G. C., ... & dos Santos, W. N. L. (2007). Box-Behnken design: An alternative for the optimization of analytical methods. Analytica Chimica Acta, 597(2), 179–186.

box-behnken-design central-composite-design response-surface-methodology d-optimal-design face-centered-central-composite-design factorial-design


Hybrid Central Composite Design

Hybrid Central Composite Design for Response Surface Methodology

Hybrid CCD
HCCD
modified central composite design
hybrid RSM design

Hybrid Central Composite Design (Hybrid CCD) is a class of response surface designs introduced by Roquemore (1976) that combines the structural properties of classical central composite designs with modified or reduced point configurations to achieve rotatability or near-rotatability with fewer experimental runs than a standard CCD, making it especially practical when the number of factors is three to six and experimental resources are limited.

Continuous factor settings with quantitative response measurements

Roquemore, K. G. (1976). Hybrid designs for quadratic response surfaces. Technometrics, 18(4), 419–423.

Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2009). Response Surface Methodology: Process and Product Optimization Using Designed Experiments (3rd ed.). Wiley.

central-composite-design box-behnken-design response-surface-methodology full-factorial-design d-optimal-design face-centered-central-composite-design


Hybrid Control Chart

Hybrid Statistical Process Control Chart

combined control chart
hybrid SPC chart
composite control chart
integrated control chart

1982 (CUSUM-Shewhart hybrid); broader hybrid frameworks 1990s–2000s

Developed incrementally; CUSUM-Shewhart hybrid attributed to Lucas & Crosier (1982) and prior work by Page (1954)

A hybrid control chart integrates two or more classical charting schemes — most commonly a Shewhart chart with a CUSUM or EWMA chart — into a single monitoring procedure. By combining the strengths of each component, hybrid charts can detect both large, sudden shifts and small, sustained drifts in a process more effectively than any single chart alone. They are used in manufacturing quality control, healthcare monitoring, and any continuous process where rapid and sensitive detection of out-of-control conditions is critical.

Statistical process monitoring procedure

Continuous or attribute process measurement data collected over time

Lucas, J. M., & Crosier, R. B. (1982). Fast initial response for CUSUM quality-control schemes: Give your CUSUM a head start. Technometrics, 24(3), 199–205.

control-chart statistical-process-control design-of-experiments failure-mode-and-effects-analysis process-capability-analysis six-sigma-dmaic


Hybrid design of experiments

hybrid DOE
combined experimental design
mixed experimental design
hybrid experimental strategy

Multiple contributors; notably Sacks, Welch, Mitchell & Wynn (computer experiments); broader hybrid concept developed across 1980s–2000s

Hybrid design of experiments (hybrid DOE) combines two or more experimental design strategies within a single study to exploit the complementary strengths of each. Common combinations include factorial or fractional-factorial arrays paired with computer simulation runs, space-filling Latin hypercube designs merged with response surface augmentations, or Taguchi orthogonal arrays integrated with response surface methodology. The approach is widely used when a single design type cannot efficiently cover all phases of an engineering investigation — from screening through to optimization.

Continuous, categorical, and/or simulation-based output data

Santner, T. J., Williams, B. J., & Notz, W. I. (2003). The Design and Analysis of Computer Experiments. Springer.

Loeppky, J. L., Sacks, J., & Welch, W. J. (2009). Choosing the sample size of a computer experiment: A practical guide. Technometrics, 51(4), 366–376.


Hybrid Event Tree Analysis

Hybrid ETA
Integrated Event Tree Analysis
Combined Event Tree Analysis
Fuzzy-Bayesian Event Tree Analysis

1990s–2000s (as extensions to classical ETA developed from the 1960s)

Multiple contributors; hybrid extensions emerged from the reliability and safety engineering community

Hybrid Event Tree Analysis (Hybrid ETA) extends classical Event Tree Analysis by integrating complementary methods — such as Bayesian networks, fuzzy set theory, or Monte Carlo simulation — to overcome ETA's limitations in handling uncertainty, dependency between events, and sparse data. It is applied in safety-critical industries to model accident sequences and quantify outcome probabilities with greater fidelity than standalone ETA.

Probabilistic risk and safety assessment technique

Event probabilities, conditional branch probabilities, expert judgements, simulation outputs

Bedford, T., & Cooke, R. (2001). Probabilistic Risk Analysis: Foundations and Methods. Cambridge University Press.

Khakzad, N., Khan, F., & Amyotte, P. (2011). Safety analysis in process facilities: Comparison of fault tree and Bayesian network approaches. Reliability Engineering and System Safety, 96(8), 925–932.

event-tree-analysis fault-tree-analysis bayesian-event-tree-analysis failure-mode-and-effects-analysis hybrid-fault-tree-analysis reliability-analysis


Hybrid FMEA
Fuzzy FMEA
Integrated FMEA
Enhanced FMEA

Hybrid variants pioneered by J. B. Bowles & C. E. Pelaez (fuzzy FMEA, 1995); subsequent integrations with AHP, TOPSIS, and grey theory by multiple researchers

Hybrid Failure Mode and Effects Analysis (Hybrid FMEA) extends classical FMEA by integrating it with multi-criteria decision methods — such as fuzzy logic, AHP, TOPSIS, or grey theory — to overcome the well-documented limitations of the traditional Risk Priority Number. The hybrid approach enables more nuanced, weighted, and uncertainty-aware prioritization of failure risks in engineering systems, manufacturing processes, and complex sociotechnical environments.

Expert judgments, failure records, linguistic ratings, quantitative probability/severity data

Liu, H.-C., Liu, L., & Liu, N. (2013). Risk evaluation approaches in failure mode and effects analysis: A literature review. Expert Systems with Applications, 40(2), 828–838.

Bowles, J. B., & Pelaez, C. E. (1995). Fuzzy logic prioritization of failures in a system failure mode, effects and criticality analysis. Reliability Engineering & System Safety, 50(2), 203–213.


Hybrid Fault Tree Analysis

Hybrid FTA
Fuzzy-Bayesian FTA
Extended Fault Tree Analysis
Integrated FTA

Tanaka et al. (fuzzy extension, 1983); Bobbio et al. (Bayesian integration, 2001)

Hybrid Fault Tree Analysis (Hybrid FTA) extends classical Fault Tree Analysis by integrating complementary modelling paradigms — most commonly fuzzy set theory, Bayesian networks, or event-tree logic — to overcome the strict data requirements and static assumptions of traditional FTA. The hybrid approach allows analysts to handle uncertainty in failure probability estimates, capture dynamic dependencies between components, and update risk assessments as new evidence becomes available, making it especially valuable in complex engineering systems where complete statistical failure data are rarely available.

Quantitative safety and reliability analysis method

Boolean logic, failure probability data, expert elicitation, fuzzy membership functions

Tanaka, H., Fan, L. T., Lai, F. S., & Toguchi, K. (1983). Fault-tree analysis by fuzzy probability. IEEE Transactions on Reliability, 32(5), 453–457.

Bobbio, A., Portinale, L., Minichino, M., & Ciancamerla, E. (2001). Improving the analysis of dependable systems by mapping fault trees into Bayesian networks. Reliability Engineering & System Safety, 71(3), 249–260.

fault-tree-analysis bayesian-network fuzzy-set-theory event-tree-analysis failure-mode-and-effects-analysis reliability-block-diagram


Hybrid Fractional Factorial Design

HFFD
hybrid FFD
combined fractional factorial design
mixed fractional factorial design

1970s–1990s (formalized as a distinct design class)

Developed across the DOE community; foundational contributions by Box, Hunter & Hunter and Wu & Hamada

A hybrid fractional factorial design (HFFD) merges two or more fractional factorial sub-designs — often involving factors at different numbers of levels or with different aliasing structures — into a single coordinated experiment. The goal is to achieve estimation capabilities (main effects, targeted two-factor interactions) that no single standard fractional design can provide within the same run count, making it especially valuable in engineering development and industrial process optimization.

Continuous or categorical factor settings with quantitative response measurements

Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley.

Wu, C. F. J., & Hamada, M. S. (2000). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley.

fractional-factorial-design full-factorial-design response-surface-methodology taguchi-methods central-composite-design plackett-burman-design


Hybrid Full Factorial Design

Hybrid Full Factorial Experimental Design

hybrid factorial design
mixed full factorial design
combined factorial design
HFFD

1980s–2000s (building on Fisher's 1935 factorial framework)

Derived from classical factorial design theory (Fisher, 1935); hybrid extensions developed across engineering literature from the 1980s onward

Hybrid full factorial design is an experimental strategy that applies a full factorial structure to a selected subset of factors — those believed to have the strongest interactions — while treating remaining factors with a reduced or fractional scheme. This hybrid approach balances the complete interaction information of a full factorial with the run-count efficiency of fractional designs, making it practical for studies with many factors where a pure full factorial would be prohibitively expensive.

Continuous or categorical factor levels; numeric response variables

Antony, J. (2014). Design of Experiments for Engineers and Scientists (2nd ed.). Elsevier.

full-factorial-design fractional-factorial-design response-surface-methodology central-composite-design taguchi-method latin-hypercube-sampling


Hybrid process capability analysis

multi-method process capability assessment

Various; systematised through extensions of Kane (1986) and Pearn, Kotz & Johnson (1992)

Hybrid process capability analysis combines two or more capability assessment techniques — for example, classical indices (Cp, Cpk) with fuzzy logic, bootstrap inference, or Bayesian estimation — to overcome the limitations of any single approach. By integrating complementary methods, it delivers more robust capability statements for non-normal, asymmetric, or short-run processes where standard indices alone would mislead quality decisions.

Continuous measurement data from manufacturing or service processes

Pearn, W. L., Kotz, S., & Johnson, N. L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24(4), 216–231.

Chen, K. S., & Pearn, W. L. (2003). Capability indices for processes with asymmetric tolerances. Journal of the Chinese Institute of Engineers, 26(2), 197–208.


Hybrid Quality Function Deployment

Hybrid QFD
Integrated QFD
QFD hybrid approach
Extended Quality Function Deployment

1966 (QFD foundation); hybrid variants from mid-1990s onward

Yoji Akao (QFD foundation); hybrid extensions by various authors integrating fuzzy sets, AHP, TOPSIS, and optimization

Hybrid Quality Function Deployment (Hybrid QFD) extends the classic House of Quality framework by embedding additional analytical techniques — such as fuzzy set theory, Analytic Hierarchy Process, TOPSIS, or optimization algorithms — directly into the QFD pipeline. This integration addresses known weaknesses of standard QFD, such as imprecision in customer ratings and subjectivity in relationship matrices, while preserving the method's core strength: systematically translating the voice of the customer into actionable engineering specifications.

Integrated engineering design and decision method

Customer requirement ratings, engineering specifications, pairwise comparisons, quantitative performance metrics

Akao, Y. (Ed.). (1990). Quality Function Deployment: Integrating Customer Requirements into Product Design. Productivity Press.

Chan, L.-K., & Wu, M.-L. (2002). Quality function deployment: A literature review. European Journal of Operational Research, 143(3), 463–497.


Hybrid Reliability Analysis

Hybrid Probabilistic and Non-Probabilistic Reliability Analysis

1990s–2000s (consolidated formulation ~2000–2006)

Xiaoping Du, Achintya Haldar, and others; synthesized across structural and mechanical engineering communities

Hybrid Reliability Analysis (HRA) quantifies the probability that an engineering system will perform its intended function when uncertain inputs are of two fundamentally different kinds: aleatory uncertainties (natural randomness, modelled with probability distributions) and epistemic uncertainties (lack of knowledge, modelled with intervals or fuzzy sets). By treating both uncertainty types simultaneously rather than collapsing them into a single probabilistic framework, HRA produces more truthful reliability estimates in design, structural, and systems engineering problems.

Quantitative reliability / uncertainty analysis method

Mixed uncertain inputs: probability distributions (aleatory) and intervals or fuzzy sets (epistemic)

Du, X., Sudjianto, A., & Huang, B. (2006). Reliability-Based Design With the Mixture of Random and Interval Variables. Journal of Mechanical Design, 127(6), 1068–1076.

Moore, R. E. (1966). Interval Analysis. Prentice-Hall.

monte-carlo-simulation first-order-reliability-method second-order-reliability-method fuzzy-set-theory bayesian-reliability-analysis sensitivity-analysis


Hybrid Response Surface Methodology

Hybrid RSM
RSM-hybrid optimization
combined RSM
meta-model hybrid optimization

1990s–2000s (systematic hybrid applications)

Box & Wilson (RSM foundation, 1951); hybrid extensions by various authors from the 1990s onward

Hybrid Response Surface Methodology (Hybrid RSM) couples classical response surface designs — which fit low-order polynomial approximations of a system response — with a secondary optimizer such as a genetic algorithm, particle swarm, or artificial neural network. The combination overcomes RSM's limitation of assuming smooth, near-quadratic response landscapes by letting the surrogate model be explored globally, making it widely used in engineering process optimization, product design, and simulation-based studies.

Numerical experimental data, simulation outputs, physical measurements

Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments (4th ed.). Wiley.

Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms. Wiley.

response-surface-methodology central-composite-design box-behnken-design genetic-algorithm artificial-neural-network design-of-experiments


Hybrid Six Sigma DMAIC

Hybrid Six Sigma Define-Measure-Analyze-Improve-Control

Lean Six Sigma DMAIC
Hybrid DMAIC
Integrated Six Sigma DMAIC
DMAIC Hybrid Framework

1980s (Six Sigma); Hybrid/Lean integration widely adopted ~2000–2002

Hybrid formalized through Lean Six Sigma integration; foundational DMAIC rooted in Motorola's Six Sigma program (Bill Smith, Mikel Harry)

Hybrid Six Sigma DMAIC combines the rigorous five-phase DMAIC cycle (Define, Measure, Analyze, Improve, Control) with complementary methodologies — most commonly Lean principles, Agile practices, or Design Thinking — to address quality defects and process inefficiencies simultaneously. By integrating speed-focused tools from Lean with the statistical discipline of Six Sigma, hybrid approaches close the gap that pure Six Sigma frameworks sometimes leave when waste elimination and cycle-time reduction are equally critical goals.

Process improvement and quality management framework

Process performance data, measurement system data, designed experiments, control charts

George, M. L. (2002). Lean Six Sigma: Combining Six Sigma Quality with Lean Speed. McGraw-Hill.

Antony, J., & Banuelas, R. (2002). Key ingredients for the effective implementation of Six Sigma program. Measuring Business Excellence, 6(4), 20–27.

lean-manufacturing dmadv statistical-process-control design-of-experiments total-quality-management failure-mode-effects-analysis


Hybrid Statistical Process Control

Hybrid SPC
combined SPC
integrated SPC
hybrid process monitoring

Evolved from classical SPC (Shewhart, 1920s); hybrid extensions developed broadly from the 1990s onward by researchers including Montgomery, Woodall, and various neural-network SPC authors

Hybrid Statistical Process Control integrates classical control-chart methods (Shewhart, CUSUM, EWMA) with complementary techniques — such as neural networks, fuzzy logic, economic design, or multivariate statistics — to monitor and control manufacturing or service processes more effectively than any single approach alone. The hybrid architecture addresses known weaknesses of conventional SPC, including slow detection of small shifts, pattern-recognition limitations, and inability to handle non-normal or autocorrelated data.

Process monitoring and control methodology

Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6th ed.). Wiley.

Guh, R.-S., & Hsieh, Y.-C. (2008). A Neural Network-Based Model for Abnormal Pattern Recognition of Control Charts. Computers and Industrial Engineering, 35(1–2), 35–38.

statistical-process-control control-charts ewma-control-chart cusum-chart multivariate-spc fuzzy-control-chart


Hybrid Taguchi Method

Taguchi hybrid optimization
integrated Taguchi method
Taguchi-based hybrid design
combined Taguchi approach

1990s–2000s (building on Taguchi's work of the 1950s–1980s)

Genichi Taguchi (foundational Taguchi method); hybrid extensions developed by various engineering researchers from the 1990s onward

The Hybrid Taguchi Method combines Taguchi's orthogonal array experimental design and signal-to-noise ratio analysis with a secondary optimization or analysis technique — such as grey relational analysis, response surface methodology, artificial neural networks, or fuzzy logic — to handle multiple response variables or complex nonlinear relationships that classical Taguchi alone cannot resolve efficiently. It is widely used in manufacturing, materials engineering, and process optimization.

Quantitative experimental data (continuous process/quality responses)

Taguchi, G. (1987). System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs. UNIPUB/Kraus International Publications.

Lin, C. L. (2004). Use of the Taguchi method and grey relational analysis to optimize turning operations with multiple performance characteristics. Materials and Manufacturing Processes, 19(2), 209–220.

taguchi-method grey-relational-analysis response-surface-methodology design-of-experiments robust-parameter-design signal-to-noise-ratio


Hydrogel Rheology

Viscoelastic analysis
Storage modulus
Gel characterization

Hydrogel rheology characterizes the mechanical viscoelastic properties of hydrogels used in tissue engineering, drug delivery, and biomedical devices. By measuring storage modulus (elastic component), loss modulus (viscous component), and their frequency dependence, practitioners assess gel stiffness, degradation, and suitability for specific applications.

Almquist, B. D., & Lu, T. W. (2002). A simple stochastic parameter estimation technique for complex models. IEEE Transactions on Biomedical Engineering, 49(10), 1188-1193.

Macosko, C. W. (1994). Rheology: Principles, Measurements, and Applications. Wiley-VCH.


Hydrogeological Survey

groundwater assessment
hydrogeologic characterization
aquifer mapping

Hydrogeological survey is the systematic characterization of groundwater systems, including aquifer geometry, water quality, flow paths, and recharge-discharge dynamics. Rooted in Darcy's law (1856) and quantified by Theis (1935), this method is essential for water resource management, contaminant remediation, and hazard assessment. Modern surveys integrate geology, geophysics, geochemistry, and numerical modeling to understand complex subsurface flow systems.

Fetter, C. W. (2018). Applied Hydrogeology (5th ed.). Prentice Hall.

Todd, D. K., & Mays, L. W. (2005). Groundwater Hydrology (3rd ed.). John Wiley & Sons.

U.S. Geological Survey. (1998). Groundwater and Surface Water: A Single Resource. USGS Circular 1139.

well-log-analysis geologic-mapping stratigraphic-correlation geomorphological-analysis geochemical-analysis