Spatial Instrumental Variables

Spatial Instrumental Variables Estimation

Spatial IV
Spatial 2SLS
Spatial Two-Stage Least Squares
S-IV

Kelejian & Prucha (generalized spatial 2SLS); Anselin (spatial econometrics framework)

Spatial Instrumental Variables (Spatial IV) is a causal inference method for settings where units — regions, firms, neighborhoods — are spatially interdependent, creating endogeneity that standard IV approaches ignore. It constructs instruments from the spatially lagged values of exogenous characteristics of neighboring units, then applies two-stage least squares to recover unbiased causal estimates in the presence of both endogenous regressors and spatial autocorrelation.

Quasi-experimental causal inference with spatial dependence

Cross-sectional or panel with geographic/spatial unit identifiers

Kelejian, H. H., & Prucha, I. R. (1998). A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances. Journal of Real Estate Finance and Economics, 17(1), 99-121.

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Dordrecht.

instrumental-variables spatial-regression-discontinuity-design spatial-propensity-score-matching panel-data-instrumental-variables spatial-doubly-robust-estimation spatial-causal-impact-analysis


Spatial Interaction Model

gravity model
spatial interaction model
competing destinations model
mekânsal etkileşim modeli

Spatial interaction models predict the volume of flows — migrants, commuters, shoppers, trade, trips — between origins and destinations as a function of the size of each place and the distance or cost separating them. By analogy to Newton's gravity, interaction rises with the 'mass' of origin and destination and falls with separation, and Wilson's 1971 entropy-maximizing family put these models on a rigorous footing for transport, migration, and retail analysis.

Model of flows between spatial origins and destinations

Wilson, A. G. (1971). A family of spatial interaction models, and associated developments. Environment and Planning A, 3(1), 1–32.

Fotheringham, A. S. (1983). A new set of spatial-interaction models: the theory of competing destinations. Environment and Planning A, 15(1), 15–36.

location-allocation poisson-regression multinomial-logit gis-mcda


Spatial Interrupted Time Series

Spatial Interrupted Time Series Analysis

Spatial ITS
Geospatial ITS
Spatially-adjusted ITS
SITS

Extension of McDowall et al. (1980) ITS framework; spatial adaptations developed in epidemiology and geography through the 1990s–2000s

Spatial Interrupted Time Series (Spatial ITS) extends the classic ITS design to settings where units are geo-referenced and outcomes in one location may spill over into or correlate with outcomes in neighbouring locations. It estimates the causal effect of a discrete intervention on an outcome time series while explicitly modelling geographic autocorrelation, preventing biased standard errors and enabling detection of spatial spillovers.

Quasi-experimental causal inference with spatial adjustment

Geo-referenced time series; panel data with spatial coordinates

McDowall, D., McCleary, R., Meidinger, E. E., & Hay, R. A. (1980). Interrupted Time Series Analysis. Sage Publications.

Lawson, A. B. (2018). Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology (3rd ed.). CRC Press.

interrupted-time-series spatial-difference-in-differences spatial-regression-discontinuity-design spatial-propensity-score-matching panel-data-interrupted-time-series spatial-causal-impact-analysis


Spatial Inverse Probability Weighting

Spatial Inverse Probability Weighting Estimator

Spatial IPW
Geographic IPW
Spatially-weighted IPW
SIPW

Extension of Rosenbaum & Rubin (1983) IPW to spatial settings; formal treatment by Papadogeorgou et al. (2019)

Spatial Inverse Probability Weighting extends the classical IPW estimator to settings where units are geo-referenced and spatial location is a confounding dimension. By incorporating geographic coordinates or spatial proximity into the propensity score model, it reweights the observed sample so that treatment and control groups are balanced not only on measured covariates but also on spatial structure, enabling credible causal inference from spatially indexed observational data.

Geo-referenced / spatially indexed observational data

Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score. Econometrica, 71(4), 1161-1189.

Papadogeorgou, G., Choirat, C., & Zigler, C. M. (2019). Adjusting for unmeasured spatial confounding with distance adjusted propensity score matching. Biostatistics, 20(2), 256-272.

inverse-probability-weighting propensity-score-matching spatial-regression geographically-weighted-regression difference-in-differences doubly-robust-estimation


Spatial Kalman Filter

Spatial Kalman Filter for Spatio-Temporal State-Space Models

spatial state-space filter
spatio-temporal Kalman filter
SKF
spatial dynamic linear model

1960 (base); spatial extensions 1990s–2000s

R. E. Kalman (base filter, 1960); extended to spatial settings by Cressie, Wikle and colleagues

The spatial Kalman filter applies classical Kalman filtering to spatio-temporal state-space models, treating a spatially distributed latent field as the hidden state that evolves over time. At each time step, the filter recursively predicts the spatial field forward and then updates the prediction with new spatial observations, producing optimal linear estimates of the field and its uncertainty across all locations.

spatio-temporal observations (gridded or point-referenced)

Cressie, N. & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Wiley.

Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1), 35-45.

kalman-filter particle-filter spatial-bayesian-inference dynamic-bayesian-inference sequential-monte-carlo spatial-mcmc


Spatial Lag Model

Spatial Autoregressive (SAR) / Spatial Lag Model

Uzamsal Gecikme Modeli (SAR / Spatial Lag)

Anselin (textbook formalisation); LeSage & Pace

The Spatial Lag Model is an autoregressive regression that assumes spatial dependence in the dependent variable itself: the outcome values of neighbouring units enter the model as an explanatory term (ρWy). It was formalised in Anselin's Spatial Econometrics (1988) and developed further by LeSage and Pace (2009), and it decomposes spillover effects into direct, indirect, and total impacts.

cross-sectional with spatial coordinates

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic.

LeSage, J. & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press.

spatial-error-model spatial-durbin-model ols-regression kriging-interpolation panel-fixed-effects


Spatial Marginal Structural Model

Spatial Marginal Structural Model with Inverse Probability Weighting

Spatial MSM
Geospatial MSM
Spatial IPW-MSM
Space-time marginal structural model

Robins, Hernan & Brumback (MSM foundation, 2000); spatial extensions developed in spatial epidemiology literature

The Spatial Marginal Structural Model (Spatial MSM) extends the classical marginal structural model to settings where units are geographically distributed and spatial dependencies — such as neighborhood spillovers, clustering, and spatial confounding — may bias causal estimates. It estimates causal effects of spatially varying exposures by constructing inverse probability weights that account for both individual covariates and spatial location, then fitting a weighted outcome model in the resulting pseudo-population.

Geographically referenced observational data (areal or point-referenced units) with time-varying or spatial treatments

Robins, J. M., Hernan, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5), 550-560.

Schnell, P. M., & Papadogeorgou, G. (2020). Mitigating unobserved spatial confounding when estimating the effect of supermarket access on cardiovascular disease deaths. Annals of Applied Statistics, 14(2), 793-816.

marginal-structural-model inverse-probability-weighting spatial-propensity-score-matching spatial-doubly-robust-estimation spatial-instrumental-variables propensity-score-weighting


Spatial Matching Estimator

Spatial Matching Estimator for Causal Inference

geographic matching estimator
spatial nearest-neighbor matching
location-based matching estimator
spatially-weighted matching

Extension of Abadie & Imbens (2006) matching estimator to spatial settings; geographic applications developed in urban/environmental econometrics literature

The Spatial Matching Estimator estimates causal treatment effects by pairing each treated geographic unit with one or more similar untreated units nearby, exploiting the assumption that units close in space share similar unobserved characteristics. By restricting matches to a geographic neighbourhood or weighting by spatial proximity, the method controls for location-specific confounders that standard matching ignores.

Georeferenced unit-level data with treatment assignment and continuous or binary outcomes

Abadie, A., & Imbens, G. W. (2006). Large Sample Properties of Matching Estimators for Average Treatment Effects. Econometrica, 74(1), 235-267.

matching-estimator propensity-score-matching coarsened-exact-matching spatial-regression-discontinuity-design spatial-difference-in-differences spatial-propensity-score-matching


Spatial MCMC

Markov Chain Monte Carlo for Spatial Models

spatial Markov chain Monte Carlo
MCMC for spatial data
spatial Bayesian MCMC
geostatistical MCMC

Gelfand, Smith, and colleagues (early 1990s MCMC for spatial models)

Spatial MCMC applies Markov chain Monte Carlo sampling to Bayesian models that explicitly account for spatial dependence among observations. It draws posterior samples from models such as conditional autoregressive (CAR), simultaneous autoregressive (SAR), or geostatistical (Gaussian process) models, yielding full uncertainty distributions for spatially structured parameters like random effects, regression coefficients, and spatial range.

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

Rue, H., & Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. CRC Press.

gibbs-sampling hamiltonian-monte-carlo spatial-bayesian-inference hierarchical-bayesian-inference conditional-autoregressive-model gaussian-process-regression


Spatial Monte Carlo Simulation

spatial MC simulation
Monte Carlo spatial analysis
stochastic spatial simulation
spatial stochastic simulation

B. D. Ripley and the spatial statistics tradition

Spatial Monte Carlo simulation applies random sampling methods to spatial problems, generating many stochastic realisations of a spatial process — such as a random field, point pattern, or network — to estimate distributional properties, propagate uncertainty, or test spatial hypotheses. It is a cornerstone technique in geostatistics, spatial epidemiology, ecology, and environmental modelling.

georeferenced / spatial point patterns / gridded data

Ripley, B. D. (1987). Stochastic Simulation. John Wiley & Sons.

Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns (2nd ed.). Arnold.

sequential-monte-carlo spatial-bayesian-inference spatial-particle-filter gibbs-sampling markov-chain-monte-carlo spatial-metropolis-hastings


Spatial Panel Event Study

spatial event study
spatial DiD event study
geo-panel event study
spatial panel ES

Synthesized from spatial econometrics and panel event-study literatures; formalized in applied work in the 2010s–2020s

Spatial panel event study extends the classical panel event-study design to settings where units are geographically located and outcomes may spill over across space. By combining event-time indicators with spatial weights matrices, it estimates dynamic treatment effects while explicitly accounting for spatial autocorrelation, geographic spillovers, and cross-unit contamination that would bias conventional event studies.

Geo-referenced panel data (multiple units, multiple periods, spatial coordinates or adjacency)

Sun, L., & Callaway, B. (2021). Difference-in-differences estimators of intertemporal treatment effects. arXiv:2109.10157.

Gibbons, C. E., Serrato, J. C. S., & Urbancic, M. B. (2019). Broken or Fixed Effects? Journal of Econometric Methods, 8(1), 20170002.

event-study-design panel-event-study difference-in-differences spatial-difference-in-differences spatial-regression-discontinuity-design panel-data-event-study-design


Spatial Panel Model

Spatial Panel Data Model (Fixed and Random Effects)

Uzamsal Panel Modeli (Spatial Panel FE/RE)

The spatial panel model is a family of econometric models that adds spatial dependence to panel data (units observed over time). It combines fixed- or random-effects panel structure with spatial lag, spatial error, or spatial Durbin components, and is developed in the modern spatial-econometrics literature by Elhorst (2014) and Lee & Yu (2010).

Maximum likelihood / bias-corrected LSDV (GMM for dynamic models)

Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer.

Lee, L. F., & Yu, J. (2010). Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects. Journal of Econometrics, 154(2), 165–185.

panel-fixed-effects geographically-weighted-regression mgwr getis-ord-gi ols-regression


Spatial Placebo Test

Spatial Placebo Test for Causal Identification

geographic placebo test
spatial falsification test
spatial robustness check
geographic spillover test

Developed organically in spatial econometrics and geographic RDD literature; prominent use in Dell (2010) and related work

A spatial placebo test is a falsification check used in geographic or spatial causal-inference studies. The analyst applies the same estimation procedure to spatial units, boundaries, or zones where no treatment effect should exist — fake borders, shifted cutoffs, or buffer areas beyond spillover range — and checks whether a spurious effect emerges. A non-significant result in the placebo region supports the credibility of the main causal estimate.

Geo-referenced observational data (point, polygon, or raster)

Buonanno, P., Montolio, D., & Vanin, P. (2009). Does Social Capital Reduce Crime? Journal of Law and Economics, 52(1), 145-170.

Dell, M. (2010). The Persistent Effects of Peru's Mining Mita. Econometrica, 78(6), 1863-1903.

placebo-test spatial-regression-discontinuity-design spatial-difference-in-differences regression-discontinuity-design sensitivity-analysis-for-causality spatial-instrumental-variables


Spatial Propensity Score Matching

Spatial Propensity Score Matching Estimator

Spatially-adjusted propensity score matching

Extension of Rosenbaum & Rubin (1983) PSM to spatial settings; spatial adaptation developed in applied econometrics and epidemiology literature from the 2000s onward

Spatial Propensity Score Matching (Spatial PSM) extends the classic propensity score matching framework to settings where units are embedded in geographic space and treatment assignment or outcomes may be spatially correlated. By incorporating spatial covariates and adjacency structure into the propensity model and matching procedure, it produces causal estimates that account for geographic confounding and spillover effects.

Cross-sectional or panel data with geographic coordinates or spatial identifiers

Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41-55.

Kelejian, H. H., & Prucha, I. R. (2004). Estimation of simultaneous systems of spatially interrelated cross sectional equations. Journal of Econometrics, 118(1-2), 27-50.

propensity-score-matching spatial-instrumental-variables spatial-doubly-robust-estimation spatial-regression-discontinuity-design coarsened-exact-matching spatial-synthetic-control-method


Spatial Propensity Score Weighting

Spatial Propensity Score Weighting for Causal Inference

geographically weighted propensity score weighting

spatially adjusted inverse probability weighting

Extended from Hirano, Imbens & Ridder (2003) IPTW with spatial adaptations by Keele, Titiunik and others in geographically structured causal designs

Spatial propensity score weighting extends inverse probability of treatment weighting (IPTW) to settings where units are geographically located and treatment assignment may depend on spatial factors such as location, neighborhood characteristics, or spatial clustering. By incorporating spatial covariates into the propensity score model and adjusting standard errors for spatial autocorrelation, it produces more credible causal estimates from observational geographic data.

Keele, L., & Titiunik, R. (2015). Geographic Boundaries as Regression Discontinuities. Political Analysis, 23(1), 127-155.

Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score. Econometrica, 71(4), 1161-1189.

propensity-score-weighting spatial-propensity-score-matching inverse-probability-weighting spatial-regression-discontinuity-design geographically-weighted-regression spatial-difference-in-differences


Spatial Regression Discontinuity Design

Spatial RDD
Geographic RDD
Border RD Design
Geographic Discontinuity Design

Popularized by Dell (2010); formalized for geographic boundaries by Keele & Titiunik (2015)

Spatial Regression Discontinuity Design uses a geographic or administrative boundary as the threshold that assigns units to treatment. Observations just inside one side of the boundary are compared with those just outside it, exploiting the near-random variation in treatment status near the cutoff to recover a local causal effect. The approach is widely used in economics, political science, and public health when policies or institutions change sharply at a border.

Geo-coded observational data with units on both sides of a geographic or administrative boundary

regression-discontinuity-design difference-in-differences fuzzy-regression-discontinuity instrumental-variables propensity-score-matching spatial-econometrics


Spatial Regression

Spatial Regression (Spatial Lag and Spatial Error Models)

Uzamsal Regresyon (Spatial Lag / Spatial Error)

Spatial regression is a family of regression models that build geographic neighbourhood relationships directly into the model, introduced by Luc Anselin in his 1988 treatment of spatial econometrics. It splits into a spatial lag model, where spatial dependence sits in the dependent variable, and a spatial error model, where the dependence sits in the error term.

Maximum likelihood (spatial lag and spatial error specifications)

Geographic neighbourhood via spatial weight matrix W

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers.

LeSage, J. & Pace, R. K. (2009). Introduction to Spatial Econometrics. Chapman & Hall/CRC.

ols-regression panel-fixed-effects quantile-regression threshold-regression seemingly-unrelated-regression


Spatial SAC Model

Spatial Autoregressive Combined (SAC) Model

Spatial Autoregressive Model with Autoregressive Disturbances

The Spatial Autoregressive Combined (SAC) model, also known as the SARAR model, simultaneously accounts for spatial dependence in both the dependent variable and the error term. Formalized by LeSage and Pace (2009), the SAC model combines the spatial lag model and the spatial error model into a single framework, estimating two distinct spatial autoregressive parameters — one capturing substantive spatial interaction among outcomes and another capturing residual spatial correlation among disturbances.

Combined spatial dependence regression model

Maximum Likelihood or Generalized Spatial Two-Stage Least Squares

Two spatial autoregressive parameters (rho, lambda)

LeSage, J., & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press.


Spatial Sensitivity Analysis for Causality

Spatial Sensitivity Analysis for Causal Inference

spatial causal sensitivity
spatial robustness checks
SSAC
spatial confounding sensitivity

Anselin (1988) for spatial diagnostics; Reich et al. (2021) for spatial causal frameworks

Spatial sensitivity analysis for causality systematically tests whether a causal estimate derived from georeferenced data holds up as spatial structure, spillovers, and the choice of spatial weights matrix are varied. Because nearby units often share unmeasured confounders — soil quality, local infrastructure, neighbourhood norms — a naive regression may yield biased causal estimates. This method reveals how fragile or robust a claimed causal effect is to alternative spatial specifications.

Georeferenced / areal / point-referenced panel or cross-sectional data

Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Dordrecht.

Reich, B. J., Yang, S., Guan, Y., Giffin, A. B., Miller, M. J., & Rappold, A. G. (2021). A review of spatial causal inference methods for environmental and epidemiological applications. International Statistical Review, 89(3), 605-634.

spatial-lag-model spatial-error-model geographically-weighted-regression instrumental-variables difference-in-differences propensity-score-matching


Spatial Stratified Heterogeneity

Spatial Stratified Heterogeneity (Geodetector)

Spatial Stratified Heterogeneity, commonly known as Geodetector, is a framework introduced by Jinfeng Wang and colleagues in 2010 for measuring and detecting spatial heterogeneity in data and identifying environmental risk factors. It quantifies the degree to which a given factor (variable) explains spatial variation in an outcome and is particularly valuable for environmental epidemiology, ecology, and geographical analysis where spatial non-stationarity is common.

Geographical detection and stratification method

Wang, J. F., Li, X. H., Christakos, G., Liao, Y. L., Zhang, T., & Gu, X. (2010). Geographical detectors–based health risk assessment and its application in the neural tube defects study for the C–H plane. International Journal of Geographical Information Science, 24(1), 107–127.

Wang, J. F., Zhang, T. L., & Fu, B. J. (2016). A measure of spatial stratified heterogeneity. Ecological Indicators, 67, 250–256.

Song, Y., Wu, P., Gilmore, D., Zhang, Q., Feng, Z., Wang, J., & Lou, L. (2020). Spatial autoregressive modelling of functional traits: a study case on gap-phase regeneration in a Chinese subtropical forest. Journal of Spatial Science, 65(2), 209–221.

stratified-sampling spatial-analysis cluster-sampling systematic-sampling


Spatial Synthetic Control Method

Spatial Synthetic Control Method for Causal Inference

spatial SCM
geographic synthetic control
spatial SC
spatial counterfactual control

Abadie & Gardeazabal (2003); extended to spatial settings by subsequent applied econometric work

The Spatial Synthetic Control Method adapts the classic synthetic control framework to settings where treated and donor units are defined by geographic location. By constructing a weighted combination of spatially proximate or comparable control regions, the method estimates what would have happened to a treated area absent the intervention, while explicitly accounting for geographic spillovers, spatial autocorrelation, and contiguity among units.

Geo-referenced panel or time-series cross-sectional data

Abadie, A., & Gardeazabal, J. (2003). The Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review, 93(1), 113-132.

Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program. Journal of the American Statistical Association, 105(490), 493-505.

synthetic-control-method spatial-regression-discontinuity-design spatial-difference-in-differences spatial-interrupted-time-series difference-in-differences propensity-score-matching


Spatial-Temporal GCN

Spatial-Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition

Deep Learning, Graph Neural Networks, Action Recognition

Spatial-Temporal Graph Convolutional Networks (ST-GCN) is an architecture introduced by Yan et al. in 2018 for skeleton-based action recognition. By modeling human skeletons as graphs where joints are nodes and bones are edges, ST-GCN applies graph convolutions across space and time to recognize actions from skeleton sequences.

Yan, S., Xiong, Y., & Lin, D. (2018). Spatial temporal graph convolutional networks for skeleton-based action recognition. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 32).

vision-transformer swin-transformer mamba vision-mamba


Spatial Variational Inference

Spatial Variational Inference for Latent Gaussian Models

approximate Bayesian inference for spatial models

Titsias (2009) for sparse GP; Rue, Martino & Chopin (2009) for latent Gaussian spatial models

Spatial variational inference is a scalable approximate Bayesian method that fits latent Gaussian or Gaussian-process models to georeferenced data by optimising a lower bound on the marginal likelihood. It replaces expensive MCMC sampling with a deterministic optimisation step, making full-posterior uncertainty quantification tractable for large spatial datasets.

Approximate Bayesian inference algorithm

Georeferenced / spatial observations, areal data, point-process data

Titsias, M. K. (2009). Variational learning of inducing variables in sparse Gaussian processes. In Proceedings of the 12th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 5, pp. 567-574.

Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B, 71(2), 319-392.

variational-inference gaussian-process spatial-bayesian-inference bayesian-hierarchical-model spatial-mcmc kriging


Spearman Correlation

Spearman's rho
Spearman rank-order correlation
Spearman Sıra Korelasyonu

The Spearman rank correlation coefficient (ρ) is a nonparametric measure of the monotonic association between two variables. Introduced by Charles Spearman in 1904, it converts raw observations to ranks and measures how consistently one variable increases as the other increases, without assuming a normal distribution or a linear relationship.

Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15, 72–101.

pearson-correlation kendall-tau mann-whitney-u point-biserial-correlation


Species Accumulation

Species Accumulation Curve (Rarefaction)

rarefaction
species accumulation curve
species richness curve

Species accumulation curves describe how the number of observed species increases with cumulative sampling effort. Introduced by Sanders (1968) and developed by Colwell and colleagues, this method enables ecologists to compare biodiversity across sites and estimate total species richness despite incomplete sampling. It addresses a fundamental challenge in ecology: observed species counts are biased by sampling intensity.

biodiversity quantification and comparison

Colwell, R. K. (1994). Estimating terrestrial biodiversity through extrapolation. Philosophical Transactions of the Royal Society B, 345(1311), 101-118.

Gotelli, N. J., & Colwell, R. K. (2001). Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecology Letters, 4(4), 379-391.

Sanders, H. L. (1968). Marine benthic diversity: a comparative study. American Naturalist, 102(925), 243-282.

beta-diversity-partitioning faiths-phylogenetic-diversity indicator-value functional-diversity


Species Distribution Models (MaxEnt)

Species Distribution Models using Maximum Entropy Modelling

Steven Phillips, Robert Anderson, Robert Schapire

Species Distribution Models (SDMs) using Maximum Entropy (MaxEnt) are statistical methods developed by Phillips, Anderson, and Schapire (2004) to predict where species are likely to occur based on known occurrence points and environmental variables. MaxEnt has become one of the most widely used algorithms in conservation biology and biogeography for mapping suitable habitat and assessing climate change impacts.

Phillips, S. J., Anderson, R. P., & Schapire, R. E. (2006). Maximum entropy modelling of species geographic distributions. Ecological Modelling, 190(3-4), 231-259.

Elith, J., Phillips, S. J., Hastie, T., Dudík, M., Chee, Y. E., & Yates, C. J. (2011). A statistical explanation of MaxEnt for ecologists. Diversity and Distributions, 17(1), 43-57.

Merow, C., Smith, M. J., & Silander, J. A. (2013). A practical guide to MaxEnt for modelling species' distributions: What it does, and why inputs and settings matter. Ecography, 36(10), 1058-1069.


Specific Excess Power

Ps
energy maneuverability theory
specific power

Specific excess power (Ps) is a metric that quantifies the rate of change of energy per unit weight, representing how quickly an aircraft can trade speed for altitude (or vice versa) at a given flight condition. Developed by John Boyd in the 1970s as part of energy maneuverability theory, Ps is essential for assessing aircraft performance during combat maneuvering, climb, and acceleration. Specific excess power is widely used in military aircraft design, flight envelope analysis, and tactical air combat assessment.

Boyd, J. R., & Hammond, J. A. (1971). The mechanics of air combat. Fighter Weapons Newsletter, US Air Force Tactical Air Command.

Loh, R. N. (1985). Performance Characteristics and Optimization of Air-Breathing Engines for Flight. AIAA Education Series.

Roskam, J., & Lan, C. T. E. (1989). Airplane Aerodynamics and Performance. Design, Analysis and Research Corporation.


Specific Phobia Questionnaire

Ahmet Osman, Frank X. Barrios, and colleagues

The Specific Phobia Questionnaire (SPQ) is a brief self-report measure assessing fear, avoidance, and distress related to specific phobic objects or situations (e.g., heights, spiders, flying, blood-injection-injury). Developed by Osman and colleagues in the 1990s, the SPQ captures the cognitive, behavioral, and physiological dimensions of specific phobia in a concise format. It is useful in clinical screening, diagnosis, and treatment monitoring for diverse phobias.

Osman, A., Barrios, F. X., Aukes, D., & Markway, K. (1996). The Fear-Avoidance Beliefs Questionnaire: Psychometric properties in a nonclinical population. Journal of Psychopathology and Behavioral Assessment, 18(2), 141–160.


Specificity

Specificity measures the proportion of actual negative cases that were correctly identified as negative by the classifier. It answers the question: 'Of all the cases that were truly negative, how many did we correctly reject?' Specificity is complementary to recall and is essential when false positives are costly.

Fawcett, T. (2006). An introduction to ROC analysis. Pattern Recognition Letters, 27(8), 861-874.

Powers, D. M. (2011). Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness and Correlation. Journal of Machine Learning Technologies, 2(1), 37-63.

recall precision balanced-accuracy f1-score matthews-correlation-coefficient


Spectral Bin Microphysics

Bin microphysics
Spectral microphysics
Explicit microphysics

Spectral bin microphysics is a detailed cloud microphysical modeling approach that explicitly represents the particle size distribution (PSD) by dividing particles into discrete size bins. Rather than assuming a fixed shape for the PSD, bin models track the number and mass of particles in each size category, allowing detailed simulation of cloud and precipitation processes.

Explicit particle size distribution model

Khain, A. P., Ovtchinnikov, M., Pinsky, M., Pokrovsky, A., & Krugliak, H. (2000). Notes on the state-of-the-art numerical modeling of cloud microphysics. Atmospheric Research, 55(3–4), 159-224.

Seifert, A., & Beheng, K. D. (2006). A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Meteorology and Atmospheric Physics, 92(1–2), 45-66.


Spectral Clustering

Spectral Clustering via Graph Laplacian Eigenvectors (Ng–Jordan–Weiss Algorithm)

NJW spectral clustering
graph Laplacian clustering
normalized spectral clustering
spectral graph clustering
SC

Spectral Clustering is a graph-based unsupervised learning algorithm, formalized by Ng, Jordan, and Weiss in 2002, that maps data points into a low-dimensional eigenspace derived from the similarity graph's Laplacian before applying k-means. This spectral embedding makes it possible to recover clusters of arbitrary shape — rings, crescents, interleaved spirals — that Euclidean distance-based methods consistently fail to separate.

Graph-based clustering (spectral method)

O(n^3) for full eigendecomposition; O(n^2 k) for approximate methods

Number of clusters k; similarity kernel bandwidth sigma; Laplacian normalization type

Ng, A. Y., Jordan, M. I., & Weiss, Y. (2002). On Spectral Clustering: Analysis and an Algorithm. Advances in Neural Information Processing Systems, 14, 849–856.

von Luxburg, U. (2007). A Tutorial on Spectral Clustering. Statistics and Computing, 17, 395–416.

Shi, J., & Malik, J. (2000). Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), 888–905.

k-means dbscan gaussian-mixture-model hierarchical-clustering t-sne pca


Spectral Methods

Spectral Methods for Differential Equations

spectral Galerkin
spectral collocation
pseudospectral method

Spectral Methods are high-order numerical techniques for solving differential equations using global polynomial expansions (e.g., Fourier or Legendre series) rather than local piecewise polynomials. Developed by Steven Orszag in the 1960s for turbulence simulation, they offer exponential convergence for smooth problems, making them ideal for scientific computing when solution regularity is high.

Orszag, S. A. (1969). Numerical methods for the simulation of turbulence. Physics of Fluids Supplements, 12(12), 250–257.

Gottlieb, D., & Orzag, S. A. (1977). Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.

Canuto, C., Hussaini, M. Y., Quarteroni, A., & Zang, T. A. (2006). Spectral Methods: Fundamentals in Single Domains. Springer.

galerkin-method finite-element-method finite-difference-method legendre-polynomials


Speculation Detection

Speculation and Uncertainty Detection (Hedging Analysis)

Belirsizlik / Spekülasyon Tespiti (Hedging)

1996 (lexicon approach); 2010 (CoNLL shared task)

Hyland, K. (lexicon-based framing, 1996); Farkas et al. (shared-task benchmark, 2010)

Speculation detection, also known as hedging analysis, is a natural-language-processing task that identifies epistemic uncertainty markers — words and phrases such as 'may', 'possibly', 'it is suggested that' — within scientific, biomedical, and news texts. Formalised by Hyland (1996) for scientific writing and benchmarked by the CoNLL-2010 shared task, the method reveals where authors signal incomplete knowledge, tentativeness, or distance from a claim rather than asserting facts directly.

Plain text (scientific articles, news, biomedical documents)

Hedge cue labels per token/sentence + scope boundaries

Hyland, K. (1996). Writing Without Conviction? Hedging in Science Research Articles. Applied Linguistics, 17(4), 433-454.

Farkas, R. et al. (2010). The CoNLL-2010 Shared Task: Learning to Detect Hedges and their Scope in Natural Language Text. Proceedings of the Fourteenth Conference on Computational Natural Language Learning — Shared Task (CoNLL 2010), 1-12.

sentiment-analysis text-classification named-entity-recognition discourse-analysis argument-mining


Speech Act Theory

Speech Act Theory is a framework in pragmatics developed by J. L. Austin and refined by John Searle, analyzing language as action. The core insight is that utterances are not merely vehicles for propositions but acts with pragmatic effects: 'I pronounce you married' creates a marriage; 'Please close the door' issues a request; 'I promise to help' incurs an obligation. By examining the conditions under which acts succeed and the types of effects they produce, Speech Act Theory illuminates how language functions in social interaction.

Austin, J. L. (1962). How to Do Things with Words. Oxford: Oxford University Press.

Searle, J. R. (1969). Speech Acts: An Essay in the Philosophy of Language. Cambridge: Cambridge University Press.

Levinson, S. C. (1983). Pragmatics. Cambridge: Cambridge University Press.


Speech Intelligibility

Speech Intelligibility Assessment and Prediction

intelligibility metrics
STI
Speech Transmission Index
clarity index

Speech intelligibility is a quantitative measure of how well listeners understand spoken content in acoustic environments. Formalized by Steeneken and Houtgast in 1980 with the Speech Transmission Index (STI), intelligibility metrics combine room acoustic parameters (RT60, noise, clarity) to predict listener comprehension. Understanding speech intelligibility is essential for designing classrooms, offices, hearing aids, and public address systems where clear communication is critical.

Steeneken, H. J., & Houtgast, T. (1980). A physical method for measuring speech-transmission quality. Journal of the Acoustical Society of America, 67(1), 318–326.

Houtgast, T., & Steeneken, H. J. (1985). A review of the MTF concept in room acoustics and its use for estimating speech intelligibility in auditoria. Journal of the Acoustical Society of America, 77(3), 1069–1077.

ASTM E2638-19 (2019). Standard Guide for Workplace Acoustics and Noise Reduction. American Society for Testing and Materials.

rt60-reverberation-time psychoacoustic-masking beamforming fxlms-active-noise-control room-impulse-response


Spelling and Grammar Check

spell checking
grammar checking
text proofing
Yazım ve Dilbilgisi Denetimi

Daniel Naber (rule-based checker); Peter Norvig (statistical spelling correction)

Spelling and grammar checking is a text-mining task that detects spelling mistakes and grammatical errors in text and proposes corrections. Building on Naber's rule-based style and grammar checker (2003) and Norvig's statistical spelling corrector (2009), it is used for data-quality assessment and text normalisation before further analysis.

Text-mining preprocessing / quality-assessment task

Dictionary-based / rule-based / language-model-based

Output: Detected errors with correction suggestions

Naber, D. (2003). A Rule-Based Style and Grammar Checker. Diploma Thesis.

Norvig, P. (2009). How to Write a Spelling Corrector.

ngram-language-model paraphrase-detection text-normalization sentiment-analysis


Spike Sorting

unit isolation
single-unit recording
electrophysiology clustering

Spike sorting is an electrophysiological technique for identifying and isolating action potentials of individual neurons from extracellular electrical recordings. Central to single-unit neurophysiology, spike sorting assigns spikes recorded on electrode arrays to their neuron of origin, enabling study of individual neuron firing patterns, timing, and network interactions with single-cell resolution.

Neuronal activity classification pipeline

Harris, K. D., Csicsvari, J., Hirase, H., et al. (2016). Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular recordings. Journal of Neurophysiology, 84(1), 401–414.

Yger, P., Spampinato, G. L., Esposito, E., et al. (2018). A spike sorting toolbox for up to thousands of electrodes validated with ground truth recordings in vitro and in vivo. eLife, 7, e34518.


Social Phobia Inventory

Kathryn M. Connor, Jonathan R. T. Davidson, and colleagues

The Social Phobia Inventory (SPIN) is a 17-item self-report measure of social anxiety disorder symptoms. Developed by Connor, Davidson, and colleagues in 2000, the SPIN assesses fear, avoidance, and physiological symptoms related to social anxiety. It is widely used for screening and monitoring social anxiety disorder in clinical and research settings.

Connor, K. M., Davidson, J. R., Churchill, L. E., Sherwood, A., Foa, E., & Weisler, R. H. (2000). Psychometric properties of the Social Phobia Inventory (SPIN): A new self-rating scale. British Journal of Psychiatry, 176, 379-386.

Antony, M. M., Coons, M. J., McCabe, R. E., Ashbaugh, A. R., & Swinson, R. P. (2006). Psychometric properties of the Social Phobia Inventory: Further evaluation in two community samples. Journal of Anxiety Disorders, 20(8), 1039-1055.


Spiritual Care Competence Scale

The SCCS is a clinical competency assessment tool measuring healthcare professionals' knowledge, attitudes, and skills in providing spiritual care to patients. Developed by Ronaldson and colleagues, it operationalizes spiritual care as an evidence-based competency, reflecting recognition that spirituality significantly impacts patient well-being, coping, and healing outcomes.

Self-report and supervisor-rated competency scale

Ronaldson, S., Dyson, S. J., & Dyson, E. (2012). Spiritual care competency: The views of nurse educators and nurse managers. Journal of Clinical Nursing, 21(19–20), 2826–2836.

McSherry, W., Ross, L., & McSherry, R. (2006). The meaning and significance of spirituality in nursing: A European perspective. In L. Ross (Ed.), Spiritual care in nursing practice (pp. 163–180). London: Quay Books.

holistic-caring-inventory attitudes-cam-scale integrative-medicine-attitudes therapeutic-touch-assessment


Spiritual Well-Being Scale

Raymond F. Paloutzian and Craig W. Ellison

The Spiritual Well-Being Scale (SWBS) is a 20-item self-report measure of spiritual well-being encompassing both religious faith and existential meaning—two dimensions critical to quality of life at end-of-life. Developed by Paloutzian and Ellison in 1982, the SWBS has become a cornerstone assessment tool in palliative care, chaplaincy, and oncology to identify unmet spiritual needs, guide supportive interventions, and evaluate the impact of spiritual care programs on patient outcomes.

Paloutzian, R. F., & Ellison, C. W. (1982). Loneliness, spiritual well-being, and the quality of life. In L. A. Peplau & D. Perlman (Eds.), Loneliness: A sourcebook of current theory, research and therapy (pp. 224–237). Wiley.

Ellison, C. W. (2006). Spiritual well-being: Conceptualization and measurement. Journal of Psychology and Theology, 11(4), 330–340.

patient-dignity-inventory mcgill-quality-of-life facit-palliative good-death-inventory palliative-performance-scale


Split-Plot Design

split-plot ANOVA
whole-plot sub-plot design
Bölünmüş Parsel Deseni (Split-Plot)

The split-plot design is a parametric experimental design that applies one factor to large whole plots and a second factor to subdivisions (sub-plots) within each whole plot. It was introduced by Frank Yates in 1935 to handle agricultural experiments where one factor — such as irrigation or tillage method — is difficult or impractical to change frequently, while a second factor can be varied more easily within the same plot.

Yates, F. (1935). Complex Experiments. Supplement to the Journal of the Royal Statistical Society, 2(2), 181–247.

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

completely-randomized-design randomized-complete-block two-way-anova repeated-measures-anova hlm one-way-anova


Sport Anxiety Scale

Ronald Smith, Frank Smoll, Robert Schutz

The SAS is a 15–21 item questionnaire measuring trait (dispositional) sport-specific anxiety—the tendency to experience worry and physiological arousal in sport-competitive contexts. Developed by Smith, Smoll, and Schutz in 1990, the SAS is the primary instrument for assessing individual differences in sport anxiety proneness and for predicting anxiety management needs across diverse athletic populations.

Self-report sport-specific trait anxiety questionnaire

Smith, R. E., Smoll, F. L., & Schutz, R. W. (1990). Measurement and correlates of sport-specific cognitive and somatic trait anxiety: The Sport Anxiety Scale. Anxiety Research, 2(4), 263–280.

Smith, R. E., Cumming, S. P., & Smoll, F. L. (2006). Measurement of multidimensional sport performance anxiety in children and adults: The Sport Anxiety Scale-2. Journal of Sport & Exercise Psychology, 28(4), 479–501.

competitive-state-anxiety-inventory profile-of-mood-states sport-confidence-inventory mental-toughness-questionnaire


Sport Confidence Inventory

The SCI is a 13-item questionnaire measuring general, trait-level confidence in sport ability—the athlete's habitual belief in their capability to execute skills and perform well in their sport. Developed by Vealey in 1986, the SCI is one of the most widely used instruments for assessing athlete self-confidence and predicting competitive success and psychological wellbeing.

Self-report sport-specific confidence trait questionnaire

Vealey, R. S. (1986). Conceptualization of sport-confidence and competitive orientation: Preliminary investigation and instrument development. Journal of Sport Psychology, 8(3), 221–246.

Vealey, R. S. (1988). Sport-confidence and competitive orientation. In D. Hackfort & C. D. Spielberger (Eds.), Anxiety in Sports: An International Perspective (pp. 117–128). Washington, DC: Hemisphere.

competitive-state-anxiety-inventory mental-toughness-questionnaire task-ego-orientation-sport profile-of-mood-states


Sport Motivation Scale

Luc Pelletier, Marc Fortier, Robert Vallerand

The SMS is a 24–28 item questionnaire measuring the motivational reasons athletes engage in sport, organized along the continuum of Self-Determination Theory: from intrinsic motivation (inherent enjoyment, mastery, excitement) through extrinsic forms (identified goals, introjected norms, external rewards) to amotivation (lack of intent). Developed by Pelletier and colleagues in 1995, the SMS has become the leading instrument for assessing sport motivation quality and predicting athlete engagement, retention, and psychological wellbeing.

Self-report sport motivation questionnaire

Pelletier, L. G., Fortier, M. S., Vallerand, R. J., Tuson, K. M., Brière, N. M., & Blais, M. R. (1995). Toward a new measure of intrinsic motivation, extrinsic motivation, and amotivation in sports: The Sport Motivation Scale (SMS). Journal of Sport & Exercise Psychology, 17(1), 35–53.

Mallett, C. J., & Hanrahan, S. J. (2004). Elite athletes: Why does the 'fire' go out? Conceptualizing athlete burnout through selected organizational theories. Journal of Sport Sciences, 22(5), 389–397.


SPOTIS

SPOTIS (Stable Preference Ordering Towards Ideal Solution) is a ranking multi-criteria decision-making (MCDM) method introduced by Dezert, J., Tchamova, A., Han, D., Tacnet, J. M. in 2020. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Normalised distance to ideal (rank-reversal free)

Dezert, J., Tchamova, A., Han, D., Tacnet, J. M. (2020). The SPOTIS rank reversal free method for multi-criteria decision-making support. 2020 IEEE 23rd International Conference on Information Fusion (FUSION)

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


SPROBID

SPROBID (Simplified PROBID using Top/Bottom Quartile Ideal Sets) is a ranking multi-criteria decision-making (MCDM) method introduced by Wang, Z., Rangaiah, G. P., Wang, X. in 2021. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Multi-ideal distance ranking with quartile-based ideal selection

Wang, Z., Rangaiah, G. P., Wang, X. (2021). Preference ranking on the basis of ideal-average distance method for multi-criteria decision-making. Industrial & Engineering Chemistry Research


SGRQ

The SGRQ is a 76-item disease-specific quality-of-life instrument designed to measure health status in patients with chronic respiratory disease, particularly chronic obstructive pulmonary disease (COPD). Developed by Jones and colleagues at King's College London in 1991, it has become the gold standard for assessing functional impact and symptom burden in respiratory populations. The SGRQ is widely used in clinical trials, epidemiological studies, and routine respiratory care to track changes in patient-reported outcomes.

Jones, P. W., Quirk, F. H., & Baveystock, C. M. (1991). The St George's Respiratory Questionnaire. Respiratory Medicine, 85(Suppl B), 25-31.

Jones, P. W., Quirk, F. H., Baveystock, C. M., & Littlejohns, P. (1992). A self-complete measure of health status for chronic airflow limitation: The St. George's Respiratory Questionnaire. American Review of Respiratory Disease, 145(6), 1321-1327.


Stable Population Theory

Lotka-Coale Stable Population Model
Stable Age Distribution Theory
Stationary Population Theory
Kararlı Nüfus Teorisi

Stable Population Theory is a mathematical framework in demography that describes the age structure and growth dynamics of a closed population subject to constant age-specific fertility and mortality schedules over a long period. Foundational work by Alfred J. Lotka established the core integral equation in the early twentieth century, and Ansley Coale's 1972 mathematical synthesis became the definitive theoretical reference, showing that any population exposed to invariant vital rates will converge to a unique stable age distribution growing at a fixed intrinsic rate of natural increase.

Age-specific fertility and mortality rates

Output: Intrinsic rate of natural increase; stable age distribution

Coale, A. J. (1972). The Growth and Structure of Human Populations: A Mathematical Investigation. Princeton University Press.


Stacked Generalization

Stacked generalization, or stacking, is a two-level ensemble method where base-level classifiers are trained on the original data, and a meta-learner is trained on the predictions of the base classifiers. The meta-learner learns how to best combine base predictions rather than using fixed aggregation rules. Introduced by David Wolpert in 1992, stacking achieves state-of-the-art performance by automatically learning the optimal weighting and interaction patterns among base models.

Wolpert, D. H. (1992). Stacked generalization. Neural Networks, 5(2), 241-259.

Breiman, L. (1996). Stacked regressions. Machine Learning, 24(1), 49-64.

bagging-ensemble boosting-ensemble majority-voting blending super-learner


Stackelberg Competition

Stackelberg Oligopoly Model with Leader-Follower Dynamics

Quantity Leadership
Sequential Oligopoly
Stackelberg Equilibrium

Stackelberg Competition models sequential oligopolistic markets where one firm (the leader) commits to a quantity first, and other firms (followers) observe this choice and respond. Introduced by Heinrich von Stackelberg in 1934, the model captures first-mover advantage in quantity-setting competition. The resulting Stackelberg Equilibrium, found by backward induction, yields the leader higher profit than simultaneous (Cournot) competition.

von Stackelberg, H. (1934). Marktform und Gleichgewicht. Julius Springer.

Tirole, J. (1988). The Theory of Industrial Organization. MIT Press.

cournot-competition subgame-perfect-equilibrium nash-equilibrium bayesian-nash-equilibrium


Stacking

Stacked Generalization (Stacking Ensemble with a Meta-Learner)

Stacking (Yığınlama — Meta-Öğrenme)
stacked generalization
meta-learning ensemble
super learner
yığınlama

Stacking, or stacked generalization, is an ensemble method introduced by David Wolpert in 1992 that combines the outputs of several different base models (Level-0) through a separate meta-model (Level-1). Unlike bagging and boosting, it deliberately uses heterogeneous model types, and it is the standard final-stage strategy in Kaggle competitions.

Wolpert, D.H. (1992). Stacked Generalization. Neural Networks, 5(2), 241–259.

van der Laan, M.J., Polley, E.C. & Hubbard, A.E. (2007). Super Learner. Statistical Applications in Genetics and Molecular Biology, 6(1), Article 25.

random-forest xgboost logistic-regression decision-tree svm-classification


Staffing Ratio Analysis

Workforce Staffing Ratio Analysis for Healthcare Resource Optimization

Healthcare operations and nursing research

Staffing Ratio Analysis is a systematic method for determining appropriate healthcare worker levels (nurses, physicians, technicians) based on patient volume, acuity, and task requirements. Research shows that staffing levels directly impact patient safety, quality, and staff burnout; systematic analysis supports evidence-based workforce planning.

Quantitative workforce planning methodology

Aiken, L. H., Clarke, S. P., Sloane, D. M., Sochalski, J., & Silber, J. H. (2002). Hospital nurse staffing and patient mortality, nurse burnout, and job dissatisfaction. JAMA, 288(16), 1987–1993.

Griffiths, P., Ball, J., Drennan, V., Dall'Ora, C., Jones, J., Maruotti, A., & Saucedo, A. R. (2016). Nurse staffing levels and patient outcomes: Systematic review of longitudinal studies. International Journal of Nursing Studies, 61, 195–213.

U.S. Bureau of Labor Statistics. (2023). Occupational Employment Statistics. Healthcare Support Occupations.

queuing-theory-healthcare hospital-bed-occupancy-model lean-healthcare patient-flow-simulation dea-hospital-efficiency


SoC

SoC
Stages of Concern
SoC Questionnaire
CBAM-SoC

Gene E. Hall, PhD; Susan F. Loucks, PhD (CBAM model); George et al. (SoC measurement)

The Stages of Concern Questionnaire (SoC) is a 35-item self-report instrument that measures the types and intensity of concerns individuals experience when adopting new practices, technologies, or innovations. Developed by Hall and colleagues in the 1970s as part of the Concerns-Based Adoption Model (CBAM), the SoC measures seven stages of concern: Awareness (low concern about the innovation), Informational (interest in learning more), Personal (worry about one's competence and impact on one's role), Management (concern about logistics, time, and workflow integration), Consequence (focus on innovation's impact on students or clients), Collaboration (concern about coordinating with colleagues), and Refocusing (desire to modify or improve the innovation). The SoC has been widely used in education and increasingly in healthcare settings to understand implementation barriers from an individual change perspective and to tailor support strategies to address specific concerns.

George, A. A., Hall, G. E., & Stiegelbauer, S. M. (2006). Measuring implementation in schools: the stages of concern about the innovation. Journal of Educational and Psychological Consultation, 16(3), 189–211.

Hall, G. E., George, A. A., & Rutherford, W. L. (1977). Measuring Stages of Concern about the Innovation: A manual for use of the Stages of Concern Questionnaire. Austin, TX: Southwest Educational Development Laboratory.

evidence-based-practice-attitude implementation-leadership-scale knowledge-to-action-scale normalisation-measure-development innovation-adoption-scale


Stance Detection

Stance Detection (Stance Classification toward a Target)

stance classification
stance identification
Tutum Tespiti (Stance Detection)

Stance detection is a natural-language-processing task that decides the position a text takes toward a specific claim, event, or topic — labelling it as favor, against, or neutral. Formalised by Mohammad et al. in the SemEval-2016 Task 6 shared task, it differs from plain sentiment analysis because the label is always relative to a defined target rather than the overall emotional tone of the text.

NLP text-classification task toward a target

Favor / against / neutral toward a defined claim or topic

Supervised classifier on labelled data / zero-shot transformer model

Mohammad, S. et al. (2016). SemEval-2016 Task 6: Detecting Stance in Tweets. Proceedings of SemEval-2016, 31-41.

Küçük, D. & Can, F. (2020). Stance Detection: A Survey. ACM Computing Surveys, 53(1), 1-37.

sentiment-analysis text-classification fake-news-detection bert-embeddings


Stand Basal Area Measurement

Forest Stand Basal Area Assessment and Density Estimation

Basal area inventory
Tree density measurement
Stand stocking assessment

Classical forestry practice; formalized by Husch and colleagues

Stand basal area is a fundamental forest mensuration metric representing the total cross-sectional area of tree stems per unit land area, typically expressed in square meters per hectare. Formalized across twentieth-century forestry literature (notably by Husch, Beers, and Kershaw), basal area serves as a key indicator of forest density, biomass accumulation, and competitive pressure, essential for yield prediction and stand management planning.

Husch, B., Beers, T. W., & Kershaw, J. A. (2003). Forest Mensuration (4th ed.). John Wiley & Sons.

West, P. W. (1981). Use of Diameter Increment and Basal Area Increment in Tree Growth Studies. Canadian Journal of Forest Research, 11(1), 122–137.

Kershaw, J. A., Ducey, M. J., Beers, T. W., & Husch, B. (2016). Forest Mensuration. John Wiley & Sons.

Crown, P. H. (2000). Effects of Logging on Tree Diversity and Basal Area in Montane Forests of Cameroon. Forest Ecology and Management, 134(1-3), 251–264.

forest-inventory-sampling tree-height-measurement allometric-biomass-equation silvicultural-treatment-design


Stand Density Index

The Stand Density Index (SDI), introduced by Reineke in 1933, is a dimensionless measure of forest density that accounts for both tree number and size. It expresses the number of trees per hectare in a stand, adjusted to a reference quadratic mean diameter (QMD) of 25 cm, providing a standardized metric for comparing tree density across different forest types and sizes. SDI is widely used in forest management to assess stocking levels and to guide thinning decisions.

Reineke, L. H. (1933). Perfecting a stand-density index for even-aged forests. Journal of Agricultural Research, 46(7), 627–638.

Long, J. N. (1985). A practical approach to density management. The Forestry Chronicle, 61(1), 23–27.


Standard Addition Method

spiking method
known-addition method
matrix matching

The standard addition method is a quantitative analytical technique that determines the concentration of an unknown analyte by measuring the response before and after adding a known quantity of the analyte (a standard) to the sample itself. This approach compensates for matrix effects and interference from other sample components, making it invaluable when analyzing complex matrices (biological fluids, environmental samples, geological materials) where the sample composition profoundly affects the measured signal. The standard addition method is widely recognized in analytical chemistry as a primary quantification strategy when external calibration is compromised by matrix variability.

Harris, D. C. (2010). Quantitative Chemical Analysis (8th ed.). Freeman.

Ellison, S. L. R., & Barwick, V. J. (2000). Estimating measurement uncertainty: reconciliation using a phylogenetic approach. Accreditation and Quality Assurance, 5(4), 205–213.

Kochmann, S., Lobera, M. P., Carrera, C., Muller, N., & Guilland, J. C. (2012). Determination of selenium in serum and whole blood by inductively coupled plasma mass spectrometry. Clinical Chemistry and Laboratory Medicine, 50(8), 1371–1377.

potentiometric-titration ion-chromatography uv-vis-spectrophotometry atomic-absorption-spectroscopy inductively-coupled-plasma


Vicente-Serrano, Beguería, and López-Moreno

The Standardized Precipitation Evapotranspiration Index (SPEI) is a climate index that combines precipitation and temperature (via reference evapotranspiration) to characterize water deficits and droughts. Developed by Vicente-Serrano and colleagues in 2010, SPEI extends the SPI framework to account for the combined effect of precipitation deficiency and increased evaporative demand from warming, providing a more physically-based drought metric than precipitation-only indices.

Probability-based water deficit indicator

Vicente-Serrano, S. M., Beguería, S., & López-Moreno, J. I. (2010). A multiscalar drought index sensitive to global warming: the Standardized Precipitation Evapotranspiration Index. Journal of Climate, 23(7), 1696-1718.


Standardized Precipitation Index

Thomas McKee, Neil Doesken, and John Kleist

The Standardized Precipitation Index (SPI) is a climate index that quantifies precipitation anomalies relative to historical norms, standardized to account for differences in precipitation climatology across regions. Introduced by McKee, Doesken, and Kleist in 1993, SPI has become a primary tool for drought detection and characterization, adopted by meteorological agencies worldwide for operational drought monitoring and early warning systems.

McKee, T. B., Doesken, N. J., & Kleist, J. (1993). The relationship of drought frequency and duration to time scales. Proceedings of the Eighth Conference on Applied Climatology, 179-184.

Lloyd-Hughes, B., & Saunders, M. A. (2002). A drought climatology for Europe. International Journal of Climatology, 22(13), 1571-1592.


STAR Model

Yumuşak Geçişli Otoregresif Model (STAR / LSTAR / ESTAR)

Teräsvirta (1994); van Dijk, Teräsvirta & Franses (2002)

The Smooth Transition Autoregressive (STAR) model is a nonlinear time-series model, developed in Teräsvirta's 1994 framework, that lets the dynamics move smoothly rather than abruptly between two regimes. The logistic variant (LSTAR) captures asymmetric business cycles and the exponential variant (ESTAR) captures purchasing-power-parity deviations.

Nonlinear time-series regime-switching model

Nonlinear least squares (with grid search for starting values)

Teräsvirta, T. (1994). Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models. Journal of the American Statistical Association, 89(425), 208–218.

van Dijk, D., Teräsvirta, T. & Franses, P.H. (2002). Smooth Transition Autoregressive Models — A Survey of Recent Developments. Econometric Reviews, 21(1), 1–47.

arfima-model panel-var ols-regression quantile-regression


State of Charge

State of Charge Estimation for Energy Storage Systems

State of Charge (SOC) is the amount of energy available in a battery or energy storage system, expressed as a percentage of its maximum capacity. Accurate SOC estimation is critical for safe operation: underestimating SOC can cause unsafe discharges, overestimating can cause overcharging. SOC estimation combines current integration (coulomb counting), voltage-based methods, and Kalman filtering to achieve accuracy despite measurement noise and model uncertainties.

Plett, G. L. (2004). Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs. Journal of Power Sources, 134(2), 252-261.

He, H., Xiong, R., & Fan, J. (2011). Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an extended Kalman filter. Journal of Power Sources, 196(6), 3365-3373.


State of Health

State of Health Assessment for Battery Aging

State of Health (SOH) quantifies battery degradation by measuring how much capacity and power capability have been lost due to aging. SOH is expressed as a percentage (100% = new, 80% = end of life for many applications). Tracking SOH enables predictive maintenance, end-of-life detection, and accurate range/power predictions in aging systems. SOH reflects cumulative effects of cycling, calendar aging, and operating conditions.

Birkl, C. R., Roberts, M. R., McTurk, E., Bruce, P. G., & Howey, D. A. (2017). Degradation diagnostics for lithium ion cells. Journal of Power Sources, 341, 373-386.

Xiong, R., Sun, F., He, H., & Gong, X. (2018). Online estimation of widespread existence of unmodeled dynamics in lithium-ion battery for electric vehicles. Energies, 11(8), 1943.


State Space Model

Durum Uzayı Modeli (State Space / Kalman Filter)

Harvey; Durbin & Koopman (state space treatment); Kalman filter

A state space model is a general time series framework that describes a series through unobserved (latent) state variables linked by a measurement equation and a transition equation, with the states estimated in real time by the Kalman filter. Developed in the state space tradition of Harvey (1990) and Durbin & Koopman (2012), it nests ARIMA and exponential smoothing as special cases.

Maximum likelihood via the Kalman filter (prediction error decomposition)

Harvey, A. C. (1990). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.

Durbin, J. & Koopman, S. J. (2012). Time Series Analysis by State Space Methods (2nd ed.). Oxford University Press.

structural-time-series arima exponential-smoothing markov-switching bvar


State-Trait Anxiety Inventory

Charles D. Spielberger, Richard L. Gorsuch, Robert E. Lushene

The State-Trait Anxiety Inventory (STAI) is a 40-item self-report questionnaire designed to measure two distinct dimensions of anxiety: state anxiety (temporary anxiety in response to a specific situation) and trait anxiety (stable tendency to experience anxiety across situations). Developed by Charles D. Spielberger and colleagues in 1970, the STAI has become one of the most widely used research instruments for differentiating situational from dispositional anxiety in clinical and non-clinical populations.

Spielberger, C. D., Gorsuch, R. L., & Lushene, R. E. (1970). Manual for the State-Trait Anxiety Inventory. Palo Alto, CA: Consulting Psychologists Press.

Spielberger, C. D. (1983). State-Trait Anxiety Inventory for Adults: Manual, Instrument and Scoring Guide. Redwood City, CA: Mind Garden, Inc.


Static-99 Revised Sex Offender Risk Scale

R. Karl Hanson, David Thornton, Lea Helmus

The Static-99R is an actuarial risk assessment instrument designed to estimate the likelihood of sexual recidivism among adult male sex offenders. Originally developed as the Static-99 by Hanson and Thornton (2000) and revised in 2009 as the Static-99R by Hanson, Helmus, and Thornton, it remains one of the most widely used sexual offender risk assessment tools in correctional, forensic psychiatric, and civil commitment settings across North America, Europe, and Australasia.

Hanson, R. K., Helmus, L., & Thornton, D. (2010). Predicting recidivism among sexual offenders: A multi-site study. Sexual Abuse, 22(1), 133–153.

Phenix, A., Helmus, L., & Hanson, R. K. (2016). Static-99R evaluation guide. Public Safety Canada.

hcr-20 violence-risk-appraisal-guide level-of-service-inventory saprof


Static Application Security Testing

SAST
white-box testing
source code analysis

Static Application Security Testing (SAST) is a security analysis technique that examines source code or compiled binaries without executing the program to identify vulnerabilities, code quality issues, and security flaws. Developed in the 2000s, SAST analyzes code structure, data flow, and control flow to detect potential bugs such as SQL injection, buffer overflows, and insecure cryptographic usage. SAST is widely integrated into development workflows as a shift-left security practice, enabling early detection of vulnerabilities before code reaches production.

Chess, B., & West, J. (2007). Secure Programming with Static Analysis. Addison-Wesley Professional.

Walz, C., Seifert, H. P., & Fischer, A. (2010). Static source code analysis tools. In Secure Software Development (SANS Institute), pp. 1-20.


Static Code Analysis

Static Code Analysis and Automated Inspection

static analysis
code inspection
automated review

Static code analysis automatically examines source code without execution, detecting potential bugs, security vulnerabilities, code smells, and style violations. Pioneered by Engler and Pugh (2001), automated analysis tools scan codebases at scale, identifying defect patterns faster than manual review. Organizations integrate static analysis into continuous integration pipelines to prevent defects early.

Engler, D., Chen, D. Y., Hallem, S., Chou, A., & Chelf, B. (2001). Bugs as deviant behavior: A general approach to inferring errors in systems code. In Proceedings of the 18th ACM Symposium on Operating Systems Principles (pp. 57–72).

Hovemeyer, D., & Pugh, W. (2004). Finding bugs is easy. ACM SIGSOFT Software Engineering Notes, 29(6), 1–8.

software-complexity-metrics code-coverage-analysis defect-prediction-model software-testing-equivalence


Static Timing Analysis

Static Timing Analysis for Digital Circuit Verification

STA
Timing verification
Path-based timing

Static Timing Analysis (STA) is a non-simulation method for verifying that digital circuits meet timing constraints (clock frequencies, setup/hold times, propagation delays). Introduced systematically by Bhatnagar et al. in the 1990s, STA computes worst-case and best-case path delays by analyzing logic paths without simulating vectors. STA is essential for modern VLSI design, enabling fast timing closure before silicon and identifying critical paths for optimization.

Non-simulation timing verification for digital circuits

Bhatnagar, H., & Bhatnagar, R. (1995). Static timing analysis: A primer. In VLSI Handbook (pp. 1-25). CRC Press.

Shen, A., Ghosh, A., Madden, S. H., & Sorkin, F. (2003). Fast algorithms for static timing analysis. In Proc. ICCAD (pp. 126-131). IEEE.

Berkelaar, M., Duffack, M., Flach, G., & Hartoog, R. (2007). OpenTimer: An open-source static timing analyzer. Proc. International Symposium on Circuits and Systems.


Statistical Power and Sample Size

Statistical Power Analysis and Sample Size Determination for Research Studies

power analysis
sample size calculation
1 minus beta
sensitivity

Statistical power is the probability of detecting a true effect if it exists (1 − β). Power analysis determines the sample size required to detect a hypothesized effect size with specified Type I error (α) and Type II error (β) rates. Introduced by Jacob Cohen (1988), power analysis is foundational to research design: underpowered studies produce inflated effect size estimates and are unlikely to replicate. The standard benchmark is 80% power (β = 0.20), though critical studies may require 90% power.

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.

Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A Flexible Statistical Power Analysis Program for the Social, Behavioral, and Biomedical Sciences. Behavior Research Methods, 39(2), 175–191.

Button, K. S., Ioannidis, J. P. A., Mokrysz, C., Nosek, B. A., Flint, J., Robinson, E. S. J., & Munafò, M. R. (2013). Power failure: why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience, 14(5), 365–376.

effect-size type-i-type-ii-error p-value-significance null-hypothesis


Statistical Process Control

SPC
statistical quality control
process control charting
Shewhart control

Statistical Process Control (SPC) is a data-driven quality method that uses statistical techniques — primarily control charts — to monitor a manufacturing or service process over time. By distinguishing natural process variation (common cause) from unusual, actionable variation (special cause), SPC enables practitioners to maintain processes in a stable, predictable state and to detect problems early, before defective output reaches customers.

Process monitoring and quality control method

Continuous or attribute measurement data collected sequentially over time

Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. Van Nostrand.

Montgomery, D. C. (2020). Introduction to Statistical Quality Control (8th ed.). Wiley.

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


Statistical Reporting Standards

Guidelines for Reporting Statistical Analyses and Results

reporting statistics
statistical transparency
effect size reporting

Statistical and methodological literature; emphasized by Cumming (2013), ICMJE, and replication crisis discussions

Transparent reporting of statistical results—including effect sizes, confidence intervals, p-values, and assumptions—is essential for scientific integrity and reproducibility. Many published studies report p-values in isolation without effect sizes or confidence intervals, making it impossible for readers to assess the magnitude of findings. Statistical reporting standards, emphasized by Cumming (2013), the American Statistical Association, and the ICMJE, require effect sizes, confidence intervals, and discussion of uncertainty. This enables readers to judge whether findings are practically significant (not just statistically significant) and to compare effect sizes across studies in meta-analyses. Poor statistical reporting wastes research and prevents proper synthesis of evidence.

Cumming, G. (2013). The new statistics: Why and how. Psychological Science, 25(1), 7–29.

Fidler, F., Thomason, N., Cumming, G., Finch, S., & Leeman, J. (2005). Editors can lead researchers to confidence intervals, but can't make them think: Statistical reform lessons from medicine. Psychological Science, 15(2), 119–126.

International Committee of Medical Journal Editors (2023). Recommendations for the Conduct, Reporting, Editing, and Publication of Scholarly Work in Medical Journals.

imrad-structure figure-table-reporting scientific-writing-clarity equator-network


Stefan-Maxwell Diffusion

Stefan-Maxwell Diffusion for Multicomponent Gas Mixtures

Stefan-Maxwell equation
multicomponent diffusion

The Stefan-Maxwell diffusion equation describes how multiple chemical species diffuse through each other in a mixture, accounting for interactions between all species pairs. Unlike Fick's law, which assumes species diffuse independently, Stefan-Maxwell theory captures the coupling that occurs when species with different diffusivities move at different rates. This is essential for analyzing gas separation, combustion, catalytic processes, and reactive distillation.

Reid, R. C., Prausnitz, J. M., & Poling, B. E. (1987). The Properties of Gases and Liquids (4th ed.). McGraw-Hill.

Taylor, R., & Krishna, R. (1993). Multicomponent mass transfer. John Wiley & Sons.


Stellar Population Synthesis

Stellar Population Synthesis Models for Galaxy Evolution

SPS Models
Population Synthesis
Integrated Light Modeling

Stellar population synthesis is a technique for modeling the integrated light from a galaxy by summing the contributions of all individual stars formed at different times and with different masses and metallicities. Developed systematically by Bruzual and Charlot (2003), this approach enables estimation of fundamental galaxy properties from observations without detailed knowledge of individual stars.

Bruzual, G., & Charlot, S. (2003). Stellar population synthesis at arbitrary metallicity with the Bruzual & Charlot models. Monthly Notices of the Royal Astronomical Society, 344(3), 1000-1028.

Charlot, S., & Fall, S. M. (1995). Dust-free star formation histories of galaxies: consequences for age dating and extinction measurements. Astrophysical Journal, 539(2), 718-730.

Conroy, C., Gunn, J. E., & White, M. (2013). The propagation of uncertainties in stellar population synthesis modeling. Astrophysical Journal, 414(2), 184-207.


Stepped Wedge Cluster Randomized Trial

Stepped Wedge Cluster Randomized Trial Design

A stepped wedge cluster randomized trial is an experimental design where clusters (e.g., schools, hospitals, communities) are randomized to receive an intervention in a phased, staggered manner over time. First formally described by Hussey and Hughes in 2007, this design combines the benefits of cluster randomization with a time-stepped implementation strategy. It is particularly useful for evaluating the effectiveness of interventions in real-world healthcare and public health settings.

Hemming, K., Haines, T. P., Chilton, P. J., Girling, A. J., & Lilford, R. J. (2015). The stepped wedge cluster randomised trial: rationale, design, analysis, and reporting. British Medical Journal, 350, h391.

Hussey, M. A., & Hughes, J. P. (2007). Design and analysis of stepped wedge cluster randomized trials. Contemporary Clinical Trials, 28(2), 182-191.

Baio, G., Copas, A., Ambler, G., Hargreaves, J., Beard, E., & Omar, R. Z. (2015). Sample size calculation for a stepped wedge trial. Trials, 16(1), 354.


Stepwise Regression

Stepwise Variable Selection in Multiple Regression

stepwise selection
forward stepwise regression
backward stepwise regression
forward-backward selection
stepwise multiple regression

Stepwise regression is an automated variable selection procedure for multiple linear regression that adds or removes predictor variables one at a time according to a statistical criterion, typically the F-statistic or a p-value threshold. The forward-selection algorithm was formally described by Efroymson (1960) and the bidirectional variant was popularised by Draper and Smith in their landmark 1966 text Applied Regression Analysis. Despite widespread historical use, the method is now widely critiqued, making its documentation essential in any canonical methods library.

F-to-enter, F-to-remove, AIC, BIC, p-value

forward selection, backward elimination, bidirectional (stepwise)

Efroymson, M. A. (1960). Multiple regression analysis. In A. Ralston & H. S. Wilf (Eds.), Mathematical Methods for Digital Computers (pp. 191–203). Wiley.

Draper, N. R., & Smith, H. (1966). Applied Regression Analysis (1st ed.). Wiley.

Draper, N. R., & Smith, H. (1998). Applied Regression Analysis (3rd ed.). Wiley.

multiple-linear-regression lasso-regression ridge-regression best-subset-selection principal-component-regression elastic-net partial-least-squares


Stereo Matching

Stereo correspondence
Disparity estimation

Stereo matching is a computer vision technique for recovering depth information by finding corresponding points between a pair of stereo images (taken from slightly different viewpoints). By locating the same scene feature in both images and measuring the disparity (horizontal shift), stereo matching reconstructs 3D structure using the principles of triangulation.

Scharstein, D., & Szeliski, R. (2002). A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal of Computer Vision, 47(1), 7–42.

Kanade, T., Okutomi, M., Nakano, T., et al. (1996). A stereo matching algorithm with an adaptive window. Image and Vision Computing, 12(10), 605–618.

template-matching harris-corner-detection optical-flow-lucas-kanade blob-detection histogram-equalization


Stereochemistry Analysis

Stereochemistry Analysis and Configuration Determination

stereochemical analysis
configuration assignment
chirality analysis

Stereochemistry analysis is the systematic study of three-dimensional molecular structures, with emphasis on determining the spatial arrangement of atoms around chiral centers and assigning unambiguous names to stereoisomers. Formalized by Cahn, Ingold, and Prelog in 1966, the CIP (Cahn-Ingold-Prelog) rules provide an objective method for assigning R/S (or E/Z) nomenclature, enabling unambiguous communication of molecular structure.

Cahn, R. S., Ingold, C., & Prelog, V. (1966). Specification of molecular chirality. Angewandte Chemie International Edition, 5(4), 385–415.

Clayden, J., Greeves, N., Warren, S., & Wothers, P. (2012). Organic Chemistry (2nd ed.). Oxford University Press.


Stereographic Slope Analysis

Stereographic Projection for Slope Stability Analysis

Stereonet Analysis
Stereographic Projection
Pole Plot Analysis

Structural Geology and Rock Mechanics Practice

Stereographic projection is a graphical method for analyzing slope stability by representing the three-dimensional orientation of discontinuities (joints, bedding, faults) and the pit slope on a two-dimensional stereographic net (stereonet). The method enables rapid visual identification of potentially unstable slope geometries where discontinuities daylight out of the slope at steeper angles than the slope face.

Graphical method for analyzing slope stability with respect to jointing

Priest, S. D. (1985). Hemispherical projection methods in rock mechanics. In Society for Mining, Metallurgy & Exploration, Technical Library.

Hoek, E., & Bray, J. W. (2007). Rock slope engineering (3rd ed.). Spon Press.


STL Decomposition

STL: Seasonal-Trend Decomposition using Loess

Cleveland, Cleveland, McRae & Terpenning

STL Decomposition, introduced by Cleveland, Cleveland, McRae, and Terpenning (1990), is a nonparametric procedure that separates a time series into three additive components — trend, seasonal, and remainder — using iterative locally weighted regression (loess). Widely used in economics, meteorology, and data science, it handles time series of any periodicity and is robust to the presence of outliers, making it a highly flexible alternative to classical decomposition methods.

robust to outliers via iterative weights

Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1), 3–73.


Stochastic Block Model

SBM
degree-corrected SBM
DCSBM
Stokastik Blok Modeli (SBM)

The Stochastic Block Model (SBM), introduced by Holland, Laskey and Leinhardt (1983), is a probabilistic generative model for graphs that assigns nodes to latent blocks and parametrically estimates the connection probabilities between blocks. It is the foundational approach for community detection, core-periphery identification, and hierarchical structure discovery in network analysis.

Community detection, core-periphery, hierarchical structure discovery

Holland, P.W., Laskey, K.B. & Leinhardt, S. (1983). Stochastic Blockmodels: First Steps. Social Networks, 5(2), 109-137.

Lee, C. & Wilkinson, D.J. (2019). A Review of Stochastic Block Models and Extensions for Graph Clustering. Applied Network Science, 4(1), 122.

gnn graph-attention-network text-network-analysis k-means-clustering hierarchical-clustering dbscan pca


Stochastic Cellular Automata

Stochastic Cellular Automata — Probabilistic Grid-Based Simulation of Complex Spatial Systems

SCA
Probabilistic Cellular Automata
PCA
Stochastic CA

von Neumann, J. / Ulam, S. (deterministic CA); probabilistic extension formalized by various authors including Wolfram, S. and Chopard, B.

Stochastic Cellular Automata (SCA) extend classical cellular automata by replacing deterministic transition rules with probabilistic ones, allowing each cell on a grid to change state according to a probability distribution conditioned on its neighborhood. This makes SCA a powerful tool for simulating real-world spatial processes where randomness, noise, and uncertainty govern local interactions — from epidemic spread and forest fires to traffic flow and material diffusion.

Spatial grid states, probabilistic transition rules, discrete time steps

Wolfram, S. (2002). A New Kind of Science. Wolfram Media, Champaign, IL.

Chopard, B., Droz, M. (1998). Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge.

cellular-automata agent-based-modeling stochastic-agent-based-modeling discrete-event-simulation markov-model monte-carlo-simulation


Stochastic Differential Equations

Stochastic Differential Equations (SDEs)

SDE
Itô equations
Stokastik Diferansiyel Denklemler (SDE)

1944 (theory); 1992 (numerical framework)

Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)

Stochastic differential equations (SDEs) are differential equation models that combine a deterministic drift term — governing the average tendency of a system — with a stochastic diffusion term driven by a Wiener process (Brownian motion). Pioneered through Itô calculus by Kiyosi Itô in 1944 and given a comprehensive numerical treatment by Kloeden and Platen in 1992, SDEs are the standard modelling language for continuous-time systems subject to random noise, including financial asset prices, population dynamics, and physical processes.

Continuous-time stochastic process model

Deterministic drift term + stochastic diffusion term (Wiener process)

Euler-Maruyama (strong order 0.5); Milstein (strong order 1.0)

Itô or Stratonovich — choice affects model interpretation

Strong (pathwise) and weak (distributional) convergence assessed separately

Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer.

Kloeden, P.E. & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer.

monte-carlo-simulation agent-based-modeling time-series-analysis bayesian-inference markov-chain-monte-carlo


Stochastic Discrete-Event Simulation

Stochastic DES
SDES
Probabilistic DES
Monte Carlo DES

Banks, Carson, Nelson, Nicol; Law, A. M.

Stochastic Discrete-Event Simulation (Stochastic DES) models complex systems by advancing simulated time from one discrete event to the next, drawing event durations and inter-arrival times from fitted probability distributions. It is the standard technique for analyzing queues, manufacturing lines, healthcare pathways, and logistics networks under uncertainty, producing output statistics with confidence intervals.

Event-driven time series, probability distributions

Banks, J., Carson, J. S., Nelson, B. L., & Nicol, D. M. (2010). Discrete-Event System Simulation (5th ed.). Prentice Hall.

Law, A. M. (2015). Simulation Modeling and Analysis (5th ed.). McGraw-Hill Education.

monte-carlo-simulation discrete-event-simulation stochastic-system-dynamics queueing-simulation markov-model agent-based-modeling


Stochastic Dynamic Programming

Stochastic Dynamic Programming (SDP) — Sequential decision-making under uncertainty via Markov decision processes

SDP
Markov Decision Process
MDP
Stochastic DP

Bellman, R.; formalized for stochastic settings by Puterman, M. L.

Stochastic Dynamic Programming (SDP) is a mathematical optimization framework for sequential decision problems where outcomes are partly random. It extends Bellman's principle of optimality to stochastic environments, representing problems as Markov Decision Processes (MDPs) and computing optimal policies by solving recursive value equations over states and time periods.

Sequential optimization under uncertainty

Discrete or continuous state/action spaces with probabilistic transition kernels

Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ.

Puterman, M. L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, New York.

dynamic-programming markov-model stochastic-mixed-integer-programming stochastic-multi-objective-optimization monte-carlo-simulation stochastic-linear-programming


Stochastic Frontier Analysis

Stochastic Frontier Production Function Analysis

SFA
stochastic frontier model
stochastic production frontier
Stokastik Sınır Analizi (SFA)

Aigner, Lovell & Schmidt (1977); Battese & Coelli (1995) for panels

Stochastic Frontier Analysis is a frontier regression model, introduced by Aigner, Lovell and Schmidt in 1977, that estimates a production, cost, or profit function while separating each unit's technical inefficiency from ordinary statistical noise. It splits the error term into a symmetric random component and a one-sided inefficiency component, producing firm- or country-level efficiency scores.

Maximum likelihood with a composed error

Composed: symmetric noise (v) plus one-sided inefficiency (u)

Aigner, D., Lovell, C.A.K. & Schmidt, P. (1977). Formulation and Estimation of Stochastic Frontier Production Function Models. Journal of Econometrics, 6(1), 21–37.

Battese, G.E. & Coelli, T.J. (1995). A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data. Empirical Economics, 20(2), 325–332.

ols-regression panel-fixed-effects quantile-regression tobit-regression data-envelopment-analysis


Stochastic Genetic Algorithm

Stochastic Genetic Algorithm — Randomized evolutionary search for combinatorial and continuous optimization

SGA
Canonical Genetic Algorithm
Simple Genetic Algorithm
Evolutionary Algorithm

The Stochastic Genetic Algorithm (SGA) is a population-based metaheuristic that mimics biological evolution — selection, crossover, and mutation — to search for near-optimal solutions in complex, nonlinear, or combinatorial spaces. Its randomized operators make it robust to local optima and broadly applicable across engineering, scheduling, machine learning, and operations research.

Continuous, integer, or combinatorial decision variables; fitness function evaluations

Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.

Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA.

genetic-algorithm stochastic-multi-objective-optimization nsga-ii simulated-annealing particle-swarm-optimization stochastic-particle-swarm-optimization


Stochastic Goal Programming

SGP
Stochastic GP
Chance-Constrained Goal Programming
Probabilistic Goal Programming

Contini, B. (building on Charnes & Cooper's chance-constrained programming)

Stochastic Goal Programming (SGP) extends classical goal programming to handle uncertainty in goal targets, constraint coefficients, or right-hand-side parameters. By incorporating probabilistic constraints and stochastic objective components, it finds solutions that satisfy multiple goals at acceptable probability levels, making it suitable for decision problems where data are inherently uncertain or variable.

Numerical goals/targets with probabilistic parameters or random RHS

Contini, B. (1968). A stochastic approach to goal programming. Operations Research, 16(3), 576–586.

Charnes, A., Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6(1), 73–79.

goal-programming stochastic-linear-programming stochastic-multi-objective-optimization stochastic-integer-programming multi-objective-goal-programming robust-goal-programming


SGD with Momentum / Adam Optimizer

Stochastic Gradient Descent with Momentum and Adaptive Moment Estimation (Adam)

Adam
Adam optimizer
SGD with momentum
momentum SGD
adaptive gradient optimizer
first-order stochastic optimizer

Rumelhart, Hinton & Williams (momentum SGD, 1986); Kingma & Ba (Adam, 2015)

Stochastic Gradient Descent (SGD) with momentum and its adaptive descendant Adam are the foundational parameter-update algorithms used to train virtually every modern deep learning model. Momentum SGD was formalised by Polyak (1964) and brought into neural network training by Rumelhart, Hinton, and Williams (1986). Adam, introduced by Kingma and Ba at ICLR 2015, extended the momentum idea by also maintaining a running average of squared gradients, producing per-parameter adaptive learning rates that make it the default optimizer in contemporary deep learning practice.

First-order adaptive stochastic optimizer

Training neural networks and differentiable models via iterative gradient-based parameter updates

Kingma, D. P., & Ba, J. (2015). Adam: A method for stochastic optimization. International Conference on Learning Representations (ICLR 2015). arXiv:1412.6980.

Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323, 533–536.

Polyak, B. T. (1964). Some methods of speeding up the convergence of iteration methods. USSR Computational Mathematics and Mathematical Physics, 4(5), 1–17.

Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning (Ch. 8: Optimization for Training Deep Models). MIT Press.

rmsprop adagrad adamw sgd-nesterov gradient-descent backpropagation neural-network batch-normalization


Stochastic Gradient Descent

Stochastic Gradient Descent (SGD) Optimization Algorithm

stochastic approximation gradient method

Stochastic Gradient Descent (SGD) is a first-order iterative optimization algorithm, rooted in the stochastic approximation framework introduced by Robbins and Monro in 1951, that minimizes an objective function by updating model parameters using the gradient computed on a single randomly selected training example (or a small mini-batch) at each step. It is the core optimization engine behind modern machine learning and deep learning, enabling the training of models on datasets too large to fit in memory.

First-order iterative optimization algorithm

Parameter estimation / loss minimization

Robbins, H. & Monro, S. (1951). A Stochastic Approximation Method. The Annals of Mathematical Statistics, 22(3), 400–407.

Goodfellow, I., Bengio, Y. & Courville, A. (2016). Deep Learning (Ch. 8). MIT Press.

logistic-regression linear-regression adam-optimizer neural-network random-forest xgboost support-vector-machine


Stochastic Integer Programming

SIP
Stochastic IP
Integer Stochastic Programming
Mixed-Integer Stochastic Programming

Stochastic Integer Programming (SIP) is an optimization framework that combines integer (discrete) decision variables with explicit probabilistic modeling of uncertainty. It seeks the best here-and-now decision that minimizes expected cost (or maximizes expected benefit) across a distribution of future scenarios, accounting for the fact that some decisions must be made before uncertainty is resolved.

Optimization under uncertainty with discrete decisions

Numerical parameters with probability distributions; discrete/binary decision variables

Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer, New York.

Kleywegt, A. J., Shapiro, A., & Homem-de-Mello, T. (2002). The sample average approximation method for stochastic discrete optimization. SIAM Journal on Optimization, 12(2), 479-502.

stochastic-linear-programming stochastic-dynamic-programming mixed-integer-programming stochastic-multi-objective-optimization robust-integer-programming stochastic-mixed-integer-programming


Stochastic Linear Programming

Stochastic Linear Programming — Optimization under uncertainty with random parameters

SLP
Stochastic LP
Linear Programming under Uncertainty
Two-Stage SLP

Stochastic Linear Programming (SLP) extends classical linear programming to settings where some model parameters — costs, demands, resource availability — are uncertain and modeled as random variables. By optimizing expected costs over a probability distribution of scenarios, SLP produces decisions that remain feasible and near-optimal across a range of possible futures rather than for a single assumed state of the world.

Numerical data with probabilistic parameters (random variables, scenario sets)

Dantzig, G. B., & Madansky, A. (1961). On the solution of two-stage linear programs under uncertainty. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 165–176.

stochastic-dynamic-programming stochastic-mixed-integer-programming stochastic-goal-programming monte-carlo-simulation scenario-analysis robust-linear-programming


Stochastic Markov Model

Stochastic Markov Model — Probabilistic State-Transition Simulation with Uncertainty Propagation

Probabilistic Markov Model
Stochastic Markov Chain
SMM
Monte Carlo Markov Model

Markov, A. A. (probabilistic extension developed by Sonnenberg & Beck and others)

A Stochastic Markov Model is a simulation technique that represents a system as a set of mutually exclusive health or decision states, moves a cohort (or individual agents) through those states using probabilistically sampled transition parameters, and aggregates outcomes across thousands of Monte Carlo iterations to produce full probability distributions over costs, outcomes, or rankings rather than single point estimates.

Probabilistic state-transition model with Monte Carlo uncertainty propagation

Transition probabilities, costs/outcomes per state, time horizon, cohort or individual-level data

Sonnenberg, F. A., & Beck, J. R. (1993). Markov models in medical decision making: A practical guide. Medical Decision Making, 13(4), 322–338.

Briggs, A., Sculpher, M., & Claxton, K. (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

markov-model monte-carlo-simulation discrete-event-simulation stochastic-dynamic-programming microsimulation sensitivity-analysis


Stochastic Microsimulation

Probabilistic Microsimulation
Monte Carlo Microsimulation
Stochastic Micro-simulation
SMSM

Stochastic Microsimulation tracks a large population of individual units — people, households, or firms — through time by applying random draws from empirically estimated probability distributions at each transition event. Unlike deterministic counterparts, every state change is decided by chance, preserving realistic heterogeneity and allowing rigorous uncertainty quantification across multiple simulation runs.

Microdata (individual, household, or firm records); probability distributions for state transitions

Orcutt, G. H. (1957). A new type of socio-economic system. The Review of Economics and Statistics, 39(2), 116–123.

Harding, A. (Ed.) (1996). Microsimulation and Public Policy. North-Holland, Amsterdam.

microsimulation monte-carlo-simulation stochastic-discrete-event-simulation stochastic-markov-model agent-based-microsimulation stochastic-system-dynamics


Stochastic Mixed-Integer Programming

SMIP
Stochastic MIP
Mixed-Integer Stochastic Programming
SMILP

Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints.

Uncertain parameters as probability distributions; integer and continuous decision variables

Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer.

Sen, S., & Higle, J. L. (2005). The C3 theorem and a D2 algorithm for large scale stochastic mixed-integer programming: Set convexification. Mathematical Programming, 104(1), 1–20.

mixed-integer-programming stochastic-linear-programming stochastic-dynamic-programming stochastic-multi-objective-optimization scenario-analysis monte-carlo-simulation