Slice Sampling

slice sampler
Neal slice sampler
uniform slice sampling
auxiliary variable slice sampler

Slice sampling is a Markov chain Monte Carlo (MCMC) algorithm introduced by Radford M. Neal in his 2003 Annals of Statistics paper. It generates samples from a target distribution by drawing uniformly from the region under the density curve — called the 'slice' — without requiring the user to specify a step-size or proposal distribution, making it self-tuning and broadly applicable for Bayesian posterior inference.

exact (in distribution), auxiliary-variable

minimal — no step-size parameter required

Neal, R. M. (2003). Slice sampling (with discussion). Annals of Statistics, 31(3), 705–767.

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

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

metropolis-hastings gibbs-sampling hamiltonian-monte-carlo nuts-sampler bayesian-regression mcmc


Sliding Mode Control

SMC
Variable Structure Control
Robust Control with Discontinuities

Sliding Mode Control (SMC) is a robust nonlinear control technique that forces a system to follow a predetermined surface (the sliding surface) in state space by using discontinuous (bang-bang or high-frequency switching) control inputs. Developed by Utkin and further advanced by Slotine, SMC is remarkably insensitive to parameter variations and disturbances—once the system reaches the sliding surface, its behavior is determined solely by the surface geometry, not by uncertainty. This makes SMC powerful for nonlinear systems, manipulators, and uncertain systems where robustness is paramount.

Utkin, V. I. (1977). Variable structure systems with sliding modes. IEEE Transactions on Automatic Control, 22(2), 212-222.

Slotine, J. J. E. (1984). Sliding controller design for non-linear systems. International Journal of Control, 40(2), 421-434.

Utkin, V. I. (2009). Variable structure systems with sliding modes: A survey. IEEE Transactions on Automatic Control, 22(2), 212-222.

feedback-linearization backstepping-control adaptive-control h-infinity-control


Slime Mould Algorithm

The Slime Mould Algorithm (SMA) is a nature-inspired metaheuristic optimization technique introduced by Li et al. in 2020. It mimics the behavior of slime moulds, which spread and contract to find optimal food sources. SMA addresses complex optimization problems by simulating the adaptive foraging and spatial distribution patterns of these organisms.

Li, S., Chen, H., Wang, M., Heidari, A. A., & Chakraborty, S. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems, 111, 300-323.

harris-hawks-optimization aquila-optimizer arithmetic-optimization-algorithm particle-swarm-optimization genetic-algorithm


Slope Stability (Bishop-Janbu)

Slope Stability Analysis Using Bishop and Janbu Methods

Circular slip surface
Limit equilibrium
Factor of safety

The Bishop and Janbu methods are limit equilibrium approaches for analyzing slope stability, computing the factor of safety against shear failure along a potential slip surface. Developed by Bishop (1955) and Janbu (1954), these methods remain the most widely used tools in geotechnical engineering for evaluating cut slopes, embankments, and natural hillsides.

Limit equilibrium method for slope failure analysis

Bishop, A. W. (1955). The use of the slip circle in the stability analysis of slopes. Geotechnique, 5(1), 7-17.

Janbu, N. (1954). Application of composite slip surfaces for stability analysis. Proceedings of the European Conference on Stability of Earth Slopes, Stockholm.

Fellenius, W. (1927). Erdstatische Berechnungen mit Reibung und Kohaesion. Wilhelm Ernst & Sohn.


Slot Filling

slot doldurma
Slot Doldurma (Slot Filling / NER-NLU)
information slot extraction
dialogue slot filling

2018 (joint slot-gate model); BIO tagging foundations earlier

Established via NER/IOB tagging literature; popularised for dialogue by Goo et al. (2018) and Chen et al. (2019)

Slot filling is a natural-language-understanding task that extracts predefined template fields — such as date, location, or product name — from a user utterance. It emerged as a core component of dialogue systems and form-based information extraction, and became widely studied after Goo et al. (2018) introduced the Slot-Gated Model for joint slot filling and intent prediction, followed by Chen et al. (2019) who extended the paradigm with BERT-based joint modelling.

NLP token-classification / information-extraction task

Goo, C.W., Gao, G., Hsu, Y.K., Huo, C.L., Chen, T.C., Hsu, S.C., & Chen, Y.N. (2018). Slot-Gated Modeling for Joint Slot Filling and Intent Prediction. Proceedings of NAACL-HLT 2018.

Chen, Q., Zhuo, Z., & Wang, W. (2019). BERT for Joint Intent Classification and Slot Filling. arXiv preprint arXiv:1902.10909.

named-entity-recognition intent-detection entity-linking text-classification information-extraction


Slotted ALOHA

Slotted ALOHA is a fundamental random access protocol enabling multiple devices to share a wireless channel without centralized coordination. Introduced by Abramson (1970) and refined by Roberts (1975), it divides time into fixed slots and allows devices to transmit at the beginning of a slot with a fixed probability. While simple and elegant, Slotted ALOHA achieves only 37% channel utilization under saturation (optimal traffic load), a fundamental limit discovered by Abramson. Despite this limitation, Slotted ALOHA remains a teaching tool and appears in modern systems like satellite and IoT networks.

Roberts, L. G. (1975). ALOHA packet system with and without slots and capture. ACM SIGCOMM Computer Communication Review, 5(2), 28-42.

Abramson, N. (1970). The ALOHA system—another alternative for computer communications. In Proceedings of the Fall Joint Computer Conference, 281-285.


Slutsky Equation

Slutsky Decomposition
Income and Substitution Effects

The Slutsky equation, derived by Russian economist Eugen Slutsky in 1915, is a fundamental identity in microeconomics that decomposes the total change in demand for a good into two effects: the substitution effect and the income effect. Formalizing John Hicks' later interpretation, it provides the mathematical foundation for understanding consumer response to price changes and for distinguishing welfare-relevant demand responses.

Slutsky, E. E. (1915). On the Theory of the Budget of the Consumer. In G. J. Stigler & K. E. Boulding (Eds.), Readings in Price Theory, 27–56.

Hicks, J. R. (1939). Value and Capital: An Inquiry into Some Fundamental Principles of Economic Theory. Oxford University Press.

Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic Theory. Oxford University Press.


SMAA

SMAA (Stochastic Multiobjective Acceptability Analysis) is a ranking multi-criteria decision-making (MCDM) method introduced by Lahdelma, R., Hokkanen, J., Salminen, P. in 1998. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Stochastic outranking/ranking — Stochastic element (distribution or scenario probabilities)

Lahdelma, R., Hokkanen, J., Salminen, P. (1998). SMAA — Stochastic multiobjective acceptability analysis. European Journal of Operational Research


SMAA2 (SMAA-2 — Stochastic extension of SMAA2) is a ranking multi-criteria decision-making (MCDM) method introduced by Lahdelma, R. & Salminen, P. in 2001. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Lahdelma & Salminen (2001). Stochastic Multicriteria Acceptability Analysis 2. Operations Research


Small Area Estimation

Small Area Estimation (Fay-Herriot Model)

SAE
Model-Based Small Area Estimation
Area-Level Model
Küçük Alan Tahmini

Small Area Estimation (SAE) refers to statistical techniques that produce reliable estimates for subpopulations — geographical regions, demographic groups, or administrative units — where direct survey samples are too sparse to yield acceptable precision. The Fay-Herriot model, introduced by Robert Fay and Roger Herriot in 1979, is the canonical area-level SAE model. It supplements weak direct survey estimates with auxiliary covariate information through an empirical Bayes or BLUP framework, substantially reducing mean squared error for small domains.

Fay, R. E., & Herriot, R. A. (1979). Estimates of income for small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association, 74(366), 269–277.


Small-World and Scale-Free Network Analysis (Watts-Strogatz & Barabási-Albert)

Küçük Dünya ve Ölçek-Bağımsız Ağ Analizi

Small-world and scale-free network analysis tests whether a real-world network exhibits two landmark topological signatures identified in 1998-1999: the Watts-Strogatz small-world property (high local clustering combined with short average path lengths) and the Barabási-Albert scale-free property (a degree distribution that follows a power law, meaning a small number of hubs connect to a disproportionately large share of other nodes). Together these frameworks transformed network science by showing that many social, biological, and technological networks share a common structural grammar.

Duncan J. Watts & Steven H. Strogatz (small-world, 1998); Albert-László Barabási & Réka Albert (scale-free, 1999)

Descriptive / exploratory network analysis

Clustering coefficient, average shortest path length, degree distribution

Power law: P(k) ~ k^{-α}, with α typically 2–3

Watts, D.J. & Strogatz, S.H. (1998). Collective Dynamics of 'Small-World' Networks. Nature, 393(6684), 440-442.

Barabási, A.L. & Albert, R. (1999). Emergence of Scaling in Random Networks. Science, 286(5439), 509-512.

community-detection centrality-analysis network-diffusion network-resilience link-prediction network-embedding exponential-random-graph temporal-network-analysis stochastic-block-model


Smart Grid State Estimation

Power System State Estimation and Smart Grid Monitoring

state estimation
network state estimation
grid state assessment

Real-time power system monitoring and operations

Power system state estimation infers the real-time voltage and phase angle at every bus in a power network from redundant measurements of power flows and voltages. It is the foundation of modern grid operations, enabling real-time monitoring, contingency analysis, and optimal control. Advanced state estimation with synchronized phasor measurements (synchrophasors) enables faster control and detection of instabilities.

Abur, A., & Exposito, A. G. (2004). Power System State Estimation: Theory and Implementation. Marcel Dekker.

Phadke, A. G., & Thorp, J. S. (2002). Synchronized phasor measurements and their applications. IEEE Communications Magazine, 33(4), 56-67.

IEC 61850-7-420:2015: Communication networks and systems in substations—Part 7-420: Basic communication structure—Logical nodes for power quality.

power-flow-analysis load-forecasting protection-relay-coordination harmonic-distortion-analysis


SMART-WEIGHT

SMART-WEIGHT (SMART Weighting — Direct importance rating normalisation (Edwards SMART weight step)) is a weight subjective multi-criteria decision-making (MCDM) method introduced by Edwards, W., Barron, F. H. in 1994. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Subjective weighting — direct rating normalisation

Edwards, W., Barron, F. H. (1994). SMARTS and SMARTER: Improved simple methods for multiattribute utility measurement. Organizational Behavior and Human Decision Processes

ahpsort aploco aras aroman artasi cobra cocoso codas


SMART

SMART (Simple Multi-Attribute Rating Technique) is a ranking multi-criteria decision-making (MCDM) method introduced by Edwards, W. in 1986. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Edwards, W. (1986). How to use multi-attribute utility measurement for social decision making. Organizational Behavior and Human Performance

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


Smartphone Addiction Scale Short Version

Min Kwon, Dai-Jin Kim, Hyun Cho, and Sang Yang

The Smartphone Addiction Scale-Short Version (SAS-SV) is a 10-item self-report instrument that rapidly assesses smartphone dependency and addiction-like behaviors in adolescents and adults. Developed by Kwon and colleagues in 2013 as an abbreviated version of the original 33-item SAS, it measures core dimensions of addiction: daily-life disturbance, withdrawal, virtual-life orientation, and tolerance.

Kwon, M., Kim, D.-J., Cho, H., & Yang, S. (2013). The Smartphone Addiction Scale: Development and validation of a short version for adolescents. PLoS ONE, 8(12), e83558.

social-media-disorder-scale fear-of-missing-out-scale technoference-scale passive-social-media-use-scale


SMED

Single Minute Exchange of Die (SMED) is a systematic approach developed by Shigeo Shingo in the 1980s to drastically reduce the time required to changeover equipment from producing one product to another. The methodology, part of the Toyota Production System, aims to reduce setup time to a single-digit minute range (ideally under nine minutes), enabling smaller batch sizes, faster response to customer demand, and improved flexibility in manufacturing. SMED is a cornerstone of lean manufacturing and just-in-time production.

Shingo, S. (1985). A revolution in manufacturing: The SMED system. Cambridge, MA: Productivity Press.

McIntosh, R. I., Culley, S. J., Mileham, A. T., & Owen, G. W. (2008). Changeover improvement: a structured methodology with supporting tools. International Journal of Production Research, 45(24), 5635-5656.

kanban aggregate-planning assembly-line-balancing job-shop-scheduling total-productive-maintenance


QOD

Thomas Hummel and colleagues; adapted by Benninger et al.

The Questionnaire of Olfactory Disorders (QOD) is a self-report instrument assessing the subjective impact of olfactory dysfunction on quality of life and daily functioning. Derived from olfactory research standardized testing (Sniffin' Sticks) and adapted for clinical use, the QOD measures perceived smell loss, changes in taste (retronasal olfaction), and emotional consequences of anosmia or hyposmia. It is increasingly used in otolaryngology, post-viral olfactory loss assessment, and chronic rhinosinusitis programs to quantify disease burden and monitor treatment response.

Hummel, T., Sekinger, B., Wolf, S. R., Pauli, E., & Kobal, G. (1997). 'Sniffin' Sticks': Olfactory performance assessed by the combined testing of odor identification, odor discrimination and olfactory threshold. Chemical Senses, 22(1), 39-52.

Benigner, C., Rudolph, C., Paolucci, V., Lopinto, A., & Simbruner, R. (2015). Questionnaire of Olfactory Disorders (QOD): Validation and applicability in post-infectious olfactory loss and chronic rhinosinusitis. Rhinology, 53(3), 235-241.


Smith Chart

Smith Chart for Transmission Line Visualization

Impedance chart
Reflection coefficient chart

The Smith Chart is a graphical tool for visualizing and manipulating complex impedances and reflection coefficients on transmission lines. Introduced by Phillip Smith in 1939, the chart maps the complex reflection coefficient plane to a circular chart, enabling intuitive graphical analysis of transmission line problems, impedance matching, and resonance conditions. Despite the advent of computers, the Smith Chart remains invaluable for understanding transmission line physics and designing RF circuits.

Graphical tool for transmission line and impedance analysis

Smith, P. H. (1939). Transmission line calculator. Electronics, 12(1), 29-31.

Pozar, D. M. (2011). Microwave Engineering (4th ed.). Wiley.

Gonzalez, G. (1997). Microwave Transistor Amplifiers: Analysis and Design (2nd ed.). Prentice Hall.


Smoke Dispersion

Smoke Dispersion Modeling and Assessment

air quality
smoke transport
visibility impacts

Smoke dispersion modeling predicts how smoke from wildfires and prescribed burns travels and disperses through the atmosphere, affecting air quality and visibility. Models use fire characteristics (size, intensity, fuel type), atmospheric conditions (wind, stability, mixing height), and topography to forecast smoke plumes and estimate particulate matter (PM2.5) concentrations downwind. Used for air quality forecasting, prescribed burn planning, and public health protection.

Larson, T., Gould, T., Simpson, C., & Liu, L. J. S. (2004). Source apportionment of indoor, outdoor, and personal PM2.5 in Seattle, Washington using positive matrix factorization. Journal of the Air & Waste Management Association, 54(9), 1175–1187.

Reid, C. E., Brauer, M., Johnston, F. H., Jerrett, M., Balmes, J. R., & Elliott, C. T. (2016). Critical review of health impacts of wildfire smoke exposure. Environmental Health Perspectives, 124(9), 1334–1343.


Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics (SPH) is a meshfree particle method for simulating fluid dynamics, developed independently by Lucy in 1977 and Gingold and Monaghan in 1977. Rather than discretizing on a fixed grid, SPH represents fluids as collections of particles that carry mass, momentum, and energy. Each particle interacts with neighbors within a kernel support radius, enabling natural handling of free surfaces, large deformations, and multiphase flows without remeshing. SPH has become indispensable for simulations involving violent flows, impacts, and complex interfaces.

Lucy, L. B. (1977). A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 82(12), 1013-1024.

Gingold, R. A., & Monaghan, J. J. (1977). Smoothed particle hydrodynamics: theory and applications to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181(3), 375-389.

Monaghan, J. J. (2005). Smoothed particle hydrodynamics. Reports on Progress in Physics, 68(8), 1703-1759.

lattice-boltzmann-method direct-numerical-simulation volume-of-fluid level-set-method reynolds-averaged-navier-stokes


Sn and Qn Scale Estimators

Sn estimator
Qn estimator
Rousseeuw-Croux scale estimators
robust scale estimation
Sn ve Qn Ölçek Tahmincileri

Sn and Qn are robust estimators of scale (spread) proposed by Rousseeuw and Croux (1993) as alternatives to the median absolute deviation (MAD). Both attain a 50% breakdown point while delivering higher statistical efficiency than MAD, so they measure dispersion accurately even when the data contain outliers.

Rousseeuw, P. J., & Croux, C. (1993). Alternatives to the Median Absolute Deviation. Journal of the American Statistical Association, 88(424), 1273-1283.

mad-estimation breakdown-point-analysis robust-mixed-model permutation-test quantile-regression


SNHF-TOPSIS

SNHF-TOPSIS (TOPSIS with Maximizing Deviation in Simplified Neutrosophic Hesitant Fuzzy Environment) is a ranking multi-criteria decision-making (MCDM) method introduced by Akram, M. Naz, S. Smarandache, F. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Simplified Neutrosophic Hesitant Fuzzy TOPSIS — decision matrix entries are SVNHFEs (each of T, I, F is a finite set of values in [0,1]); weights derived internally via Maximizing Deviation Method

Akram, M., Naz, S., Smarandache, F. (2019). Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment. Symmetry


Snowball Sampling

Snowball Sampling (Chain-Referral Sampling)

chain-referral sampling
network sampling
respondent-driven sampling
referral sampling

Snowball sampling is a non-probability recruitment technique in which initial participants (seeds) refer the researcher to others who meet the study criteria, and those referrals in turn refer further participants. The sample grows incrementally — like a rolling snowball — until the required size or theoretical saturation is reached. It is the method of choice when a target population has no accessible sampling frame, such as undocumented migrants, illicit drug users, survivors of stigmatised experiences, or members of closed professional networks.

Qualitative or quantitative data collected from hard-to-reach or hidden populations

Goodman, L. A. (1961). Snowball sampling. Annals of Mathematical Statistics, 32(1), 148–170.

Biernacki, P., & Waldorf, D. (1981). Snowball sampling: Problems and techniques of chain referral sampling. Sociological Methods and Research, 10(2), 141–163.

purposive-sampling theoretical-sampling convenience-sampling maximum-variation-sampling respondent-driven-sampling network-analysis


Social Capital Index

Comprehensive Social Capital Assessment Index

Pierre Bourdieu, Robert Putnam, Michael Woolcock

The Social Capital Index measures the stock of social connections, networks, and civic participation within an individual's or community's social ecosystem. Rooted in the theoretical work of Pierre Bourdieu and popularized by Robert Putnam, social capital encompasses bonding capital (ties within homogeneous groups), bridging capital (ties across different groups), and linking capital (connections to institutions and power). Comprehensive indices assess networks, trust, organizational membership, volunteering, and informal mutual aid.

Self-report questionnaire / Behavioral frequency

Putnam, R. D. (2000). Bowling alone: The collapse and revival of American community. Simon & Schuster.

Bourdieu, P. (1986). The forms of capital. In J. Richardson (Ed.), Handbook of theory and research for the sociology of education (pp. 241-258). Greenwood Press.

Woolcock, M., & Narayan, D. (2000). Social capital: Implications for development theory, research, and policy. World Bank Economic Review, 15(2), 225-249.

civic-engagement-scale social-cohesion-scale generalized-trust-scale community-belonging-scale institutional-trust-scale


Social Capital Scale

Robert D. Putnam, Jill Onyx, and Paul Bullen

The Social Capital Scale is a self-report measure designed to assess the presence and extent of social capital in individuals and communities. Building on Robert D. Putnam's influential work on social capital as shared norms, networks, and reciprocity, the scale measures dimensions of social connection, participation in community life, and access to social resources. Multiple versions exist, including the scale developed by Onyx and Bullen (2000) with community-level validation.

Onyx, J., & Bullen, P. (2000). Measuring social capital in five communities. Journal of Applied Behavioral Science, 36(1), 23–42.

interpersonal-reactivity-index collectivism-individualism-scale cultural-values-scale modern-racism-scale


Social Cohesion Scale

Robert Sampson, Ray Forrest, Akhtar Kearns

The Social Cohesion Scale measures the degree to which members of a community feel integrated, connected, and unified by shared values and mutual support. Developed across multiple traditions—notably by Robert Sampson and colleagues in criminology and urban sociology, and by Forrest & Kearns in housing research—it assesses both the structural glue (institutions, networks) and affective bonds (belonging, solidarity) that hold communities together.

Sampson, R. J., Raudenbush, S. W., & Earls, F. (1997). Neighborhoods and violent crime: A multilevel study of collective efficacy. Science, 277(5328), 918-924.

Forrest, R., & Kearns, A. (2001). Social cohesion, social capital and the neighbourhood. Urban studies, 38(12), 2125-2143.

Chan, J., To, H. P., & Chan, E. (2006). Reconsidering social cohesion: Developing a definition and analytical framework for empirical research. Social Indicators Research, 75(2), 273-302.

community-belonging-scale generalized-trust-scale intergroup-contact-scale civic-engagement-scale institutional-trust-scale


Social Communication Questionnaire

Michael Rutter, Ann Bailey, Catherine Lord

The Social Communication Questionnaire (SCQ) is a 40-item parent-report measure of autism-spectrum symptoms in children ages 4–15 years. Developed by Michael Rutter, Ann Bailey, and Catherine Lord in 2003, it serves as a brief screening tool for autism spectrum disorder. The SCQ asks parents to recall or report current child behaviors in three domains: reciprocal social interaction, communication, and restricted/repetitive behaviors/interests. It is frequently used in primary care, developmental pediatrics, and research settings to identify children warranting comprehensive autism evaluation.

Rutter, M., Bailey, A., & Lord, C. (2003). The Social Communication Questionnaire: Manual. Western Psychological Services.

Berument, S. K., Rutter, M., Lord, C., Pickles, A., & Bailey, A. (1999). Autism screening questionnaire: Diagnostic validity. British Journal of Psychiatry, 175(5), 444–451.


Social Comparison Scale (Online Contexts)

Upward Social Comparison Scale for Social Media

USCS
Social Comparison Orientation Online

Various researchers (Vogel, Wang, Suls & Wheeler)

The Social Comparison Scale for online contexts measures the frequency and intensity with which individuals compare themselves to peers on social media platforms, with emphasis on upward comparison (to those perceived as superior in attractiveness, success, wealth). Developed and refined by researchers including Vogel and Wang in the 2010s, this scale specifically captures social media-driven comparison processes distinct from general social comparison orientation.

Wang, J. L., Wang, H. Z., Gaskin, J., & Wang, S. (2015). The role of stress and motivation in social networking sites adoption: From a perspective of uses and gratifications theory. Computers in Human Behavior, 48, 24–32.

online-social-comparison-scale fear-of-missing-out-scale passive-social-media-use-scale social-media-disorder-scale


Social Distance Scale

The Social Distance Scale (SDS), also known as the Bogardus Scale, is a classic sociological instrument designed to measure the degree of social acceptance, prejudice, or social distance that individuals feel toward members of different ethnic, racial, or social groups. Originally developed by Emory Bogardus in 1933 and updated by researchers including Parrillo and Donoghue, the SDS assesses willingness for increasing levels of contact and intimacy with outgroup members, from casual acquaintance to family relationships. The scale is widely used in sociology, psychology, and health research to evaluate attitudes toward diversity and to track changes in intergroup relations.

Bogardus, E. S. (1933). A social distance scale. Sociology and Social Research, 17(3), 265–271.

Parrillo, V. N., & Donoghue, C. (2005). Updating the Bogardus social distance studies: A new national survey. The Social Science Journal, 42(2), 257–271.

ethnic-identity-scale racism-and-life-experiences-scale cultural-competence-assessment acculturative-stress-scale


Social Dominance Orientation Scale

Felicia Pratto, Jim Sidanius, Lisa Stallworth, and Bertram Malle

The Social Dominance Orientation Scale (SDO) is a self-report measure developed by Pratto, Sidanius, Stallworth, and Malle in 1994 to assess individual differences in preference for group-based hierarchy and inequality. The scale measures the extent to which individuals support dominance of some groups over others, reject egalitarianism, and accept hierarchical social organization. It has become central to social dominance theory and is widely used in political psychology and intergroup relations research.

Pratto, F., Sidanius, J., Stallworth, L. M., & Malle, B. F. (1994). Social Dominance Orientation: A personality variable predicting social and political attitudes. Journal of Personality and Social Psychology, 67(4), 741–763.

right-wing-authoritarianism-scale modern-racism-scale ambivalent-sexism-inventory cultural-values-scale


SES

The Social Engagement Scale (SES) is a brief self-report measure assessing the frequency and quality of social contact and participation in social activities in older adults. While multiple versions exist (developed by various researchers in gerontology), the core concept measures social connection—the degree to which individuals maintain relationships with family and friends, participate in community activities, and feel engaged with others. The SES is used in research, clinical gerontology, and public health to evaluate social isolation risk, predict mortality and health outcomes, and measure outcomes of social intervention programs.

Paulson, D., & Willig, C. (2008). Older adults' engagement with online information about health: web site accessibility, usefulness, and trust. Gerontology, 54(5), 523-533.

Beck, F., Voelker, M., & Baumeister, R. F. (2016). Social connection and health: a meta-analytic review. J Psychol Health, 31(5), 584-604.

Holt-Lunstad, J., Smith, T. B., & Layton, J. B. (2010). Social relationships and mortality risk: a meta-analytic review. PLoS Med, 7(7), e1000316.

life-space-assessment geriatric-anxiety-inventory cognitive-telephone-screening activities-balance-confidence edmonton-frail-scale


Social Inclusion Scale

Oades, L. G., Deane, F. P., Crowe, T. P., et al.

The Social Inclusion Scale (SIS) is a brief measure assessing the degree to which individuals with serious mental illness perceive themselves as included, valued members of their community. Developed by Oades, Deane, and colleagues in 2005, the SIS captures subjective experiences of social participation, acceptance, and integration. The scale is used in recovery-oriented mental health services and research to evaluate community integration outcomes and inform interventions promoting social inclusion.

Oades, L. G., Deane, F. P., Crowe, T. P., Gordon, L. M., Relieur, D. H., & Kavanagh, D. J. (2005). Collaborative recovery: An integrative model for working with individuals who experience chronic and recurring mental illness. Australasian Psychiatry, 13(3), 279-284.

recovery-assessment-scale mental-health-recovery-measure empowerment-scale-rogers recovery-oriented-practices-index


Social Interaction Anxiety Scale

The Social Interaction Anxiety Scale (SIAS) is a 20-item self-report questionnaire designed to measure anxiety and distress experienced during social interactions and conversations with others. Developed by Mattick and Clarke in 1998, the SIAS is a brief, user-friendly instrument for assessing social interaction anxiety in clinical, research, and community settings, particularly valued for its focus on direct interpersonal contact rather than public speaking or performance situations.

Mattick, R. P., & Clarke, J. C. (1998). Development and validation of measures of social phobia scrutiny fear and social interaction anxiety. Behaviour Research and Therapy, 36(4), 455-470.


Social Media Anxiety Scale

SMAS
Social Media Anxiety
Fear of Missing Out Anxiety

The Social Media Anxiety Scale measures the extent to which individuals experience anxiety, apprehension, and psychological distress related to social media use. Developed by Przybylski and colleagues (2013) and expanded by Elhai and colleagues, the scale captures the 'Fear of Missing Out' (FOMO) construct—anxiety about missing important social events or information if not actively monitoring social media—alongside broader concerns about social comparison, peer judgment, and online relationships.

Elhai, J. D., Yang, H., & Montag, C. (2015). Whilst FOMO is related to negative mental health consequences, phubbing may be more emotionally disruptive. Computers in Human Behavior, 113, 106480.

Przybylski, A. K., Murayama, K., DeHaan, C. R., & Gladwell, V. (2013). Motivational, emotional, and behavioral correlates of fear of missing out. Computers in Human Behavior, 29(4), 1841–1848.


Social Media Disorder Scale

Roos J. J. M. van den Eijnden, Jeroen S. Lemmens, and Patti M. Valkenburg

The Social Media Disorder Scale (SMD Scale) is a 9-item self-report measure developed by van den Eijnden and colleagues in 2016 to assess problematic social media use characterized by loss of control, withdrawal, tolerance, and conflict—mirroring criteria from behavioral addiction frameworks. It identifies individuals whose engagement with social media platforms has reached clinically concerning levels that interfere with daily functioning.

van den Eijnden, R. J. J. M., Lemmens, J. S., & Valkenburg, P. M. (2016). The social media disorder scale. Computers in Human Behavior, 61, 481–490.

smartphone-addiction-scale-short fear-of-missing-out-scale passive-social-media-use-scale technoference-scale


Social Media Engagement Scale

The Social Media Engagement Scale measures the intensity and quality of user participation and interaction with social media platforms and content. Developed by researchers including Hollebeek (2011) and informed by work on consumer engagement (Zhang & Zhu, 2012), the scale captures cognitive, emotional, and behavioral dimensions of how users interact with social platforms, brands, and online communities.

Zhang, X., & Zhu, F. (2012). Product reviews, information richness, and consumer purchasing behavior. Journal of Management Information Systems, 29(2), 7-36.

Hollebeek, L. D. (2011). Exploring customer brand engagement: Definition and themes. Journal of Strategic Marketing, 19(7), 555-573.

online-trust-scale technology-readiness-index tam-questionnaire elearning-satisfaction-scale


Social Media NLP

Social Media Text Analysis (NLP Pipeline)

Sosyal Medya Metin Analizi
social media text mining
Twitter NLP
short-text NLP

Community-established benchmark (SemEval shared tasks, Cardiff NLP group)

Social Media NLP is a specialised natural-language-processing pipeline designed for the short, noisy, and informal text that appears on platforms such as Twitter, Reddit, and comment sections. Unlike general-purpose NLP, this pipeline accounts for platform-specific conventions — hashtags, emojis, abbreviations, and code-switching — enabling tasks such as hashtag analysis, viral content detection, and public-opinion measurement. The benchmark tradition for this approach was established through the SemEval-2017 Task 4 shared task (Rosenthal et al., 2017) and the TweetEval unified benchmark (Barbieri et al., 2020).

NLP process pipeline for short, noisy social-media text

Raw tweets, Reddit posts, comments — short informal text

Rosenthal, S. et al. (2017). SemEval-2017 Task 4: Sentiment Analysis in Twitter. Proceedings of the 11th International Workshop on Semantic Evaluation (SemEval-2017). ACL.

Barbieri, F. et al. (2020). TweetEval: Unified Benchmark and Comparative Evaluation for Tweet Classification. Findings of the Association for Computational Linguistics: EMNLP 2020.

sentiment-analysis text-classification bert-embeddings tf-idf topic-modeling


Social Network Analysis

SNA
network analysis
sociometric analysis
relational analysis

1934 (sociometry); 1994 (modern formalization)

Moreno, J.L.; formalized by Wasserman & Faust

Social Network Analysis (SNA) is a structural method that maps and measures relationships and flows between people, groups, organizations, or other entities modeled as nodes connected by ties (edges). Rather than focusing on individual attributes, SNA reveals how the pattern of connections shapes behavior, influence, information flow, and outcomes within a system.

Relational (dyadic ties, adjacency matrices, edge lists)

Wasserman, S. & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press.

Scott, J. (2017). Social Network Analysis (4th ed.). SAGE Publications.

degree-centrality betweenness-centrality closeness-centrality modularity-analysis exponential-random-graph-model eigenvector-centrality


Social Provisions Scale

Cutrona & Russell Social Provisions Scale

social support and perceived social resources

The Social Provisions Scale is a widely used multidimensional instrument for measuring the degree to which individuals perceive their social relationships as providing essential emotional and practical support. Developed by Carolyn Cutrona and Daniel Russell in 1987, the SPS operationalizes the theory that healthy social support requires six provisions: attachment (emotional closeness), social integration (sense of belonging), reassurance of worth (feeling valued), reliable alliance (practical assistance), guidance (advice and direction), and opportunity for nurturance (ability to care for others). The SPS is used extensively in health psychology, gerontology, and stress and coping research.

Cutrona, C. E., & Russell, D. W. (1987). The provisions of social relationships and adaptation to stress. Advances in Personal Relationships, 1, 37-67.

Russell, D. W., & Cutrona, C. E. (2001). Social support, stress, and depressive symptoms among the elderly: Test of a process model. Psychology and Aging, 6(2), 190-201.


Social Role Participation Questionnaire

The Social Role Participation Questionnaire (SRPQ) is a brief, self-report instrument designed to measure the extent to which individuals participate in and derive meaning from key social roles (family member, friend, worker, volunteer, community member, leisure participant). Developed by Lyons, Sayer, and colleagues, SRPQ is used in traumatic brain injury, stroke, and other disability research to assess how completely a person has resumed their valued life roles post-injury or illness.

Lyons, K. S., & Sayer, A. G. (2005). How does loss matter? The experience of spouse loss among family caregivers of persons with Alzheimer's disease. American Journal of Alzheimer's Disease and Other Dementias, 20(5), 273–290.

Andruszkow, H., Chmielewski, C., Hoefer, J., Hildebrand, F., Lefering, R., & Frink, M. (2015). Severely injured patients with traumatic brain injury—does long-term outcome correlate with acute parameters? A retrospective analysis. Journal of Neurotrauma, 32(7), 531–538.

community-integration-questionnaire impact-participation-autonomy assessment-life-habits participation-scale craig-handicap-assessment


SODA

Strategic Options Development and Analysis (Cognitive Mapping)

Strategic Options Development and Analysis (SODA) is a facilitated, qualitative method for structuring complex organisational problems. Developed by Colin Eden in 1988, it uses cognitive maps — directed graphs of causal constructs — to capture and integrate the subjective views of multiple stakeholders. SODA is most valuable when decision makers face ill-defined, wicked problems where shared understanding must be built before any quantitative analysis can begin.

Context: Group strategic decision-making

Eden, C. (1988). Cognitive mapping. European Journal of Operational Research, 36(1), 1–13.


Sequential Organ Failure Assessment Score

Sequential Organ Failure Assessment (SOFA) Score

SOFA
Sepsis-related Organ Failure Assessment

The Sequential Organ Failure Assessment (SOFA) score, introduced by Vincent and Moreno in 1996, is a 24-point daily assessment tool that quantifies organ dysfunction across six physiological systems in critically ill patients. It was adopted into the 2016 Sepsis-3 definitions and is now the international standard for identifying and grading sepsis-related organ failure.

Vincent, J. L., Moreno, R., Takala, J., et al. (1996). The SOFA (Sepsis-related Organ Failure Assessment) score to describe organ dysfuncti on/failure. Intensive Care Medicine, 22(7), 707-710.

Singer, M., Deutschman, C. S., Seymour, C. W., et al. (2016). The Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3). JAMA, 315(8), 801-810.


Soft Set Theory

Soft Sets
Parameterized Family of Sets
Molodtsov Soft Sets
Yumuşak Küme Teorisi

Soft Set Theory is a mathematical framework for handling uncertainty and imprecision through parameterized families of sets. Introduced by Dmitriy Molodtsov in 1999, it provides an approximate description of objects in a universe by mapping each parameter in a chosen parameter set to a crisp subset of that universe. Unlike probability theory or fuzzy sets, soft sets require no membership function or probability distribution, making the framework free from the inadequacy of existing uncertainty tools when sufficient data are unavailable.

Parameterized uncertainty representation framework

Uses an approximate description via a set-valued map over a parameter set

Crisp (binary) within each parameter-indexed subset

Molodtsov, D. (1999). Soft set theory—first results. Computers & Mathematics with Applications, 37(4–5), 19–31.


Soft Systems Methodology

SSM
Checkland's SSM
Soft Systems Analysis
Yumuşak Sistemler Metodolojisi

Soft Systems Methodology (SSM) is an interpretive, action-research approach for structuring and managing complex, ill-defined ('soft') problem situations involving human activity. Developed by Peter Checkland at Lancaster University throughout the 1970s and formally presented in 1981, SSM guides practitioners through iterative cycles of inquiry that move from an unstructured problem situation to purposeful action through structured learning rather than optimization.

Cyclic; repeated until consensus or accommodation

Checkland, P. (1981). Systems Thinking, Systems Practice. Wiley.


Software Complexity Metrics

Software Complexity Metrics and Measurement

code complexity analysis
complexity measurement

Software complexity metrics quantify the structural and operational difficulty of code through numerical measurements. Introduced by Thomas McCabe in 1976, cyclomatic complexity became the foundational approach. These metrics assess maintainability, testability, and defect risk, enabling teams to identify problematic code regions and guide refactoring efforts.

McCabe, T. J. (1976). A complexity measure. IEEE Transactions on Software Engineering, 2(4), 308–320.

Chidamber, S. R., & Kemerer, C. F. (1994). A metrics suite for object-oriented design. IEEE Transactions on Software Engineering, 20(6), 476–493.

Halstead, M. H. (1977). Elements of Software Science. Elsevier.

defect-prediction-model code-coverage-analysis static-code-analysis technical-debt-measurement


Software-Defined Networking

network virtualization
programmable networks

Software-Defined Networking (SDN) is a network architecture paradigm that decouples the control plane (routing decisions) from the data plane (packet forwarding). Introduced by McKeown et al. (2008) with OpenFlow, SDN enables network programmability by centralizing control logic in software-based controllers that direct forwarding behavior of simple programmable switches. SDN has transformed network operations, enabling rapid service deployment, traffic engineering, and cloud integration. It is now foundational in data centers and service provider networks.

McKeown, N., Anderson, T., Balakrishnan, H., et al. (2008). OpenFlow: enabling innovation in campus networks. ACM SIGCOMM Computer Communication Review, 38(2), 69-74.

Doria, A., Hellstein, H., Haas, R., et al. (2013). Forwarding and Control Element Separation (ForCES) Protocol Specification. RFC 5810.

network-function-virtualization mpls bgp ospf


Software Reliability Model

Software Reliability Modeling and Growth Analysis

reliability growth model
failure rate prediction
SRGM

Software reliability models predict the behavior of failure rates during testing and operation, estimating when software achieves required reliability targets. Introduced by Goel and Okumoto (1979), these stochastic models capture how defect discovery declines as testing progresses. Organizations use reliability models to forecast release readiness, estimate testing duration, and validate quality achievement.

Goel, A. L., & Okumoto, K. (1979). Time-dependent error-detection rate model for software reliability and other performance measures. IEEE Transactions on Reliability, 28(3), 206–211.

Musa, J. D., Iannino, A., & Okumoto, K. (1987). Software Reliability: Measurement, Prediction, Application. McGraw-Hill.

Yamada, S., Ohera, H., & Narihisa, H. (1984). Software reliability growth with a Weibull test-effort: A model and application. IEEE Transactions on Reliability, 33(2), 117–123.

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


Equivalence Partitioning Testing

Equivalence Class Partitioning and Boundary Value Testing

equivalence partitioning
BVA
boundary value analysis

Equivalence partitioning divides input domains into equivalence classes—sets of inputs expected to behave identically—then selects test cases from each class. Introduced by Myers (1979), this technique reduces test cases while maintaining effectiveness. Boundary value analysis (BVA) complements partitioning by testing values at partition boundaries where failures often occur.

Myers, G. J. (1979). The Art of Software Testing. John Wiley & Sons.

Beizer, B. (1990). Software Testing Techniques (2nd ed.). International Thomson Computer Press.

Coppit, D., & Leavens, G. T. (2003). Practical implications of simpler, more scalable path-sensitive data flow analyses. ACM Transactions on Software Engineering and Methodology, 12(3), 261–306.

code-coverage-analysis software-complexity-metrics defect-prediction-model static-code-analysis


Soil Fertility Management

Soil Fertility Assessment and Nutrient Recommendation System

Soil nutrient management
Fertility program design
Soil test interpretation

Soil fertility testing institutions (ICAR, CSREES, regional extension)

Soil Fertility Management is a diagnostic and prescriptive pipeline for assessing soil nutrient status via laboratory testing, interpreting results against crop-specific nutrient requirements, and recommending fertilizer or amendment rates. Formalized by soil testing institutions (ICAR, USDA-CSREES) and widely adopted globally, this method supports efficient nutrient application and cost-effective crop production.

Tandon, H. L. (1997). Phosphorus research and agricultural production in India. ICAR, New Delhi.

Kamprath, E. J., & Watson, M. E. (1980). Conventional soil and tissue tests for assessing the phosphorus status of soils. In The role of phosphorus in agriculture. American Society of Agronomy, Madison, WI.

nitrogen-use-efficiency crop-growth-simulation crop-yield-estimation irrigation-scheduling-etref precision-agriculture-ndvi


Soil Moisture Curve

Soil Water Retention Curve (Soil Moisture Characteristic Curve)

Water Retention Curve
pF Curve
Characteristic Curve
SWRC

Willard Robert Gardner, Rollin H. Brooks, Arthur T. Corey

The soil moisture curve (or soil water retention curve, SWRC) describes the relationship between soil water content and soil matric potential (water tension). It characterizes how tightly water is bound in pores of different sizes: large pores drain at low tensions (wet soils), while smaller pores retain water at high tensions (dry soils). Quantifying this relationship is essential for water balance modeling, unsaturated flow prediction, and assessing plant-available water.

Gardner, W. R. (1956). Representation of soil aggregate-size distribution by a logarithmic-normal distribution. Soil Science Society of America Journal, 20(2), 151-153.

Brooks, R. H., & Corey, A. T. (1964). Hydraulic properties of porous media. Hydrology Papers No. 3, Colorado State University, Fort Collins.

van Genuchten, M. T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44(5), 892-898.


Soil Remediation

In Situ and Ex Situ Soil Contamination Treatment Technologies

soil cleanup
contaminated land treatment
remedial technologies
soil restoration

Soil remediation encompasses a suite of technologies and strategies to treat contaminated soil at sites with elevated levels of organic compounds, heavy metals, radionuclides, or other hazardous substances. Systematized by the US EPA in the 1980s following industrial accidents and legacy contamination discoveries, soil remediation methods range from in situ (biological, chemical, thermal) to ex situ (excavation, treatment, off-site disposal) approaches. The selection process integrates site characterization, contaminant bioavailability, regulatory risk thresholds, and cost-benefit analysis.

technology selection and design pipeline

Twardowska, I., Allen, H. E., Häggblom, M. M., & Stefaniak, S. (Eds.). (2004). Soil and Water Pollution Monitoring, Protection and Remediation (3rd ed.). Springer.

Margesin, R., & Schinner, F. (Eds.). (2005). Manual for Soil Analysis – Monitoring and Assessing Soil Bioremediation. Springer.

US Environmental Protection Agency. (2012). Remediation Technologies Screening Matrix and Reference Guide (4th ed.). EPA 542-B-12-001.


Soil Respiration Measurement

Soil Respiration Measurement (Soil CO2 Efflux Quantification)

soil CO2 efflux measurement
soil carbon flux measurement
belowground respiration measurement
soil surface CO2 flux measurement

Mid-20th century (chamber methods formalised ~1950s–1970s; automated systems ~1990s)

Soil respiration measurement quantifies the rate at which CO2 is released from the soil surface to the atmosphere, integrating contributions from root respiration and microbial decomposition of organic matter. It is a fundamental technique in agronomy, ecology, and climate science, providing insight into belowground carbon cycling, soil biological activity, and ecosystem carbon balance. Measurements are typically made using static or dynamic chambers placed on the soil surface.

Gas concentration readings (CO2 ppm), temperature, moisture

Hanson, P. J., Edwards, N. T., Garten, C. T., & Andrews, J. A. (2000). Separating root and soil microbial contributions to soil respiration: A review of methods and observations. Biogeochemistry, 48(1), 115–146.

Davidson, E. A., Savage, K. E., Verchot, L. V., & Navarro, R. (2002). Minimizing artifacts and biases in chamber-based measurements of soil respiration. Agricultural and Forest Meteorology, 113(1–4), 21–37.

carbon-stock-estimation microbial-biomass-carbon eddy-covariance litter-decomposition soil-enzyme-activity greenhouse-gas-flux


Soil-Structure Interaction

SSI analysis
Foundation compliance
Dynamic foundation analysis

Soil-structure interaction (SSI) analysis accounts for the dynamic coupling between a structure and its supporting foundation soil, recognizing that the soil is not infinitely rigid. Formalized by Veletsos in 1974, this approach reveals how foundation compliance, radiation damping, and kinematic effects modify the structure's seismic response compared to fixed-base assumptions.

Dynamic analysis of coupled soil-foundation-structure systems

Veletsos, A. S., & Meek, J. W. (1974). Dynamic behaviour of building-foundation systems. Earthquake Engineering & Structural Dynamics, 3(2), 121-138.

Wolf, J. P. (1997). Spring-Dashpot-Mass Systems for Foundation Vibrations. Journal of Engineering Mechanics, 123(5), 1031-1039.

Gazetas, G. (1991). Formulas for foundation vibration frequency and damping. Journal of Geotechnical Engineering, 117(9), 1373-1383.

terzaghi-consolidation modflow probabilistic-seismic-hazard-analysis incremental-dynamic-analysis


Soldier Adaptation Measure

The Soldier Adaptation Measure is a brief self-report instrument assessing psychological readiness and adaptation to military deployment. Developed by Bliese and colleagues in the context of military mental health surveillance, it measures dimensions of military motivation, unit cohesion, perceived leadership, and psychological well-being during deployment. It is used in pre-deployment, mid-deployment, and post-deployment screening to identify service members struggling with psychological adjustment and to inform unit support and individual intervention.

Bliese, P. D., Wright, K. M., Adler, A. B., Thomas, J. L., & Hoge, C. W. (2007). Validating the Primary Care PTSD Screen in military and veteran populations. Psychological Assessment, 19(2), 176-180.

Adler, A. B., Bliese, P. D., McGurk, D., Hoge, C. W., & Castro, C. A. (2009). Resilience and the signature wound of the military. Military Medicine, 174(10), 1012-1023.

deployment-risk-resilience post-deployment-reintegration military-identity-scale pcl-military


Solid Dispersion

solid solution
amorphous dispersion
polymer-based formulation

Solid dispersion is a formulation technique where a poorly soluble drug is molecularly dispersed in a hydrophilic polymer matrix, improving aqueous solubility and bioavailability. Introduced by Chiou and Riegelman in 1971, solid dispersions remain a key strategy for overcoming solubility-limited absorption.

Chiou, W. L., Riegelman, S. (1971). Pharmaceutical applications of solid dispersions. Journal of Pharmaceutical Sciences, 60(9), 1281-1302.

Vasconcelos, T., Sarmento, B., & Costa, P. (2007). Solid dispersions as strategy to improve oral bioavailability of poorly water soluble drugs. Drug Discovery Today, 12(23-24), 1068-1075.


Solomon Four-Group Design

Solomon design
four-group design
Solomon four-group control design
S4GD

The Solomon Four-Group Design extends the classic pretest-posttest control-group design by adding two groups that receive no pretest, enabling researchers to detect whether the pretest itself alters participants' responses to the treatment. Introduced by Richard L. Solomon in 1949, it remains the gold standard for isolating the independent effect of a pretest and for obtaining unbiased estimates of treatment efficacy.

Continuous or ordinal outcome measures (pre- and post-test scores)

Solomon, R. L. (1949). An extension of control group design. Psychological Bulletin, 46(2), 137–150.

Campbell, D. T., & Stanley, J. C. (1963). Experimental and Quasi-Experimental Designs for Research. Rand McNally.

pretest-posttest-experimental-design control-group-experimental-design randomized-controlled-trial factorial-experiment analysis-of-variance quasi-experimental-design


Somatic Cell Count

SCC
mastitis indicator
milk quality assessment

Somatic Cell Count (SCC) is a quantitative measure of the concentration of white blood cells and epithelial cells in milk, used as a primary indicator of udder health and the presence of mastitis in lactating cattle. Standardized by veterinary regulatory agencies worldwide, SCC serves as a non-invasive, cost-effective screening tool in dairy herd management and milk quality assessment.

Philippidis, G. P., Frey, H. R., & Klug, C. (2016). Somatic cell count and milk production in dairy cattle. Journal of Dairy Science, 99(2), 1419-1427.

Pyörälä, S. (2003). Indicators of inflammation in the diagnosis of mastitis. Veterinary Research, 34(5), 565-578.

FAO Animal Production and Health Division (2019). Milk quality and livestock standards. Food and Agriculture Organization of the United Nations.


Somatic Symptom Scale-8

The Somatic Symptom Scale-8 is a brief eight-item self-report instrument designed by Bernd Gierk and colleagues to assess the severity and burden of somatic (bodily) symptoms. Published in JAMA Internal Medicine in 2014, the SSS-8 is derived from the longer Somatic Symptom Disorder-B Criteria Scale and serves as a rapid screening tool for somatic symptom disorder and medically unexplained symptoms. It is widely used in primary care, general medicine, and psychiatry to identify patients whose physical complaints may warrant psychological or behavioral intervention.

Gierk, B., Kohlmann, S., Kroenke, K., Spangenberg, L., Zhan, Y., Scherer, M., & Herzberg, P. Y. (2014). The Somatic Symptom Scale-8 (SSS-8): a brief measure of somatic symptom burden. JAMA Internal Medicine, 174(3), 399–407.

Kroenke, K., Spitzer, R. L., Williams, J. B., & Löwe, B. (2010). The Patient Health Questionnaire Somatic, Anxiety, and Depressive Symptom Scales: a systematic review. General Hospital Psychiatry, 32(4), 345–359.

Toussaint, A., Murray, A. M., Voigt, K., Gierk, B., Kroenke, K., Scherer, M., & Lowe, B. (2016). Development and validation of the Somatic Symptom Disorder-B Criteria Scale (SSD-12). Psychosomatic Medicine, 78(1), 5–12.


Somers' D

Somers' D (Asymmetric Ordinal Association Measure)

Somers D
Somers' delta
d_YX
asymmetric Kendall tau
ordinal association coefficient

Somers' D is an asymmetric ordinal association coefficient, introduced by Robert H. Somers in 1962, that quantifies how well one ordinal variable predicts another by measuring the excess of concordant over discordant pairs relative to all pairs that are not tied on the designated independent variable. It is the standard companion to Kendall's tau in ordinal regression and is central to ROC curve analysis and the c-statistic in logistic regression.

Asymmetric ordinal association coefficient

Somers, R. H. (1962). A new asymmetric measure of association for ordinal variables. American Sociological Review, 27(6), 799–811.

Agresti, A. (2010). Analysis of Ordinal Categorical Data (2nd ed.). Wiley.

Harrell, F. E. (2001). Regression Modeling Strategies. Springer.

kendall-tau-b kendall-tau-c goodman-kruskal-gamma spearman-rho mann-whitney-u wilcoxon-rank-sum


Sonar Equation

Sonar Equation for Underwater Acoustic Detection and Localization

active sonar equation
passive sonar equation
underwater detection
acoustic range equation

The sonar equation is a fundamental framework for predicting the detection range and performance of active and passive sonar systems in underwater environments. Systematized by Robert Urick in his seminal 1983 work, the sonar equation quantifies the acoustic signal-to-noise ratio (SNR) needed for detection, accounting for source level, propagation loss, noise characteristics, and receiver sensitivity. It is the cornerstone of underwater acoustic system design, naval detection systems, marine research, and subsea communication.

Urick, R. J. (1983). Principles of Underwater Sound (3rd ed.). McGraw-Hill.

Burdic, W. S. (1984). Underwater Acoustic System Analysis (2nd ed.). Prentice Hall.

Medwin, H., & Clay, C. S. (1992). Fundamentals of Acoustical Oceanography. Academic Press.

beamforming acoustic-ray-tracing room-impulse-response fxlms-active-noise-control speech-intelligibility


Sorensen-Dice Coefficient

Dice coefficient
Czekanowski index
F1 similarity

Set similarity and presence-absence index

Sorensen-Dice coefficient, also called Dice coefficient or Czekanowski index, measures the similarity between two sets or samples based on presence and absence of attributes. Introduced independently by Thorvald Sorensen (1948) and Lee Dice (1945), this index ranges from 0 (completely dissimilar) to 1 (identical). It is particularly well-suited for binary presence-absence data and is the symmetric counterpart to the Bray-Curtis dissimilarity for abundance data.

Binary and compositional similarity measure

Sorensen, T. (1948). A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons. Biologiske Skrifter, 5, 1-34.

Dice, L. R. (1945). Measures of the amount of ecologic association between species. Ecology, 26(3), 297-302.


Sound Transmission Class

Sound Transmission Class (STC) Rating and Measurement

STC
sound transmission loss
acoustic isolation

Sound Transmission Class (STC) is a single-number rating used to describe how well building elements (walls, doors, windows) reduce sound transmission between adjacent spaces. Standardized by ASTM International and ISO, STC is calculated from sound transmission loss (STL) measurements across the speech frequency range (125 Hz–4 kHz). It is the primary metric used in building codes, product specifications, and acoustic design to ensure privacy, noise control, and occupant comfort.

ASTM E413-16 (2016). Classification for Rating Sound Insulation. American Society for Testing and Materials.

ISO 717-1 (1996). Rating of Sound Insulation for Buildings and Building Elements. International Organization for Standardization.

ASTM E2179-16 (2016). Standard Test Method for Measuring Sound Transmission Loss of Building Partitions by the Reverberation Method. American Society for Testing and Materials.

acoustic-ray-tracing impedance-tube bem-acoustics room-impulse-response psychoacoustic-masking


SOWA

SOWA (Spatial Ordered Weighted Averaging) is a ranking multi-criteria decision-making (MCDM) method introduced by Makropoulos, C. K.; Butler, D. in 2003/2006. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Zone-stratified OWA — order weights λ_k vary per spatial zone, encoding spatially heterogeneous risk attitudes (ORness) while criterion weights w_k remain global

Makropoulos, C. K., Butler, D. (2006). Spatial ordered weighted averaging: incorporating spatially variable attitude towards risk in spatial multi-criteria decision-making. Environmental Modelling & Software

ahp anp bwm critic entropy swara fucom merec


Sowing Date Optimization

Crop Sowing Date Decision Framework and Timing Optimization

Planting date optimization
Sowing time selection
Phenological timing

Sowing Date Optimization is a decision support pipeline for determining optimal crop planting dates that align phenological development with favorable environmental windows, maximizing yield and reducing climate risk. Developed by crop modelers (Aggarwal, Semenov) in the 2000s, this method combines crop simulation, climate data, and risk analysis to identify safe, profitable sowing windows.

Aggarwal, P. K., Kalra, N., Chander, S., & Pathak, H. (2006). InfoCrop: A decision support system for crop planning and resource management at farm level. Agricultural Systems, 88(1), 56-77.

Semenov, M. A., & Porter, J. R. (2000). Climatic variability and the modelling of crop yields. Agricultural and Forest Meteorology, 100(2-3), 149-167.

crop-growth-simulation phenological-observation crop-yield-estimation irrigation-scheduling-etref nitrogen-use-efficiency


Soxhlet Extraction

Soxhlet Extraction is a continuous solvent extraction method developed by Franz Soxhlet in 1879 for determining fat and lipid content in foods. Using a specialized glassware apparatus, Soxhlet repeatedly cycles hot solvent through a food sample, extracting lipids with high efficiency. It remains the official standard method for fat determination in numerous food standards and is widely used in food analysis and quality control.

Soxhlet, F. von (1879). Die Gewichtsbestimmung des Kaffein-Alkaloides. Dingler's Polytechnisches Journal, 232, 461-464.

Rüdiger, H. W. (2011). Extraction and determination of fats. In S. S. Nielsen (Ed.), Food analysis (4th ed., pp. 153-167). Springer.


Space Syntax Analysis

Space Syntax Analysis for Spatial Configuration Assessment

spatial configuration analysis
graph-based space analysis

Space Syntax Analysis is a quantitative method for assessing spatial configuration in buildings and urban environments through graph-based representations. Developed by Bill Hillier and Julienne Hanson in the 1980s, it quantifies how spatial layout affects human movement, visibility, and social interaction.

Hillier, B. (1984). The Social Logic of Space. Cambridge University Press.

Hillier, B. (1996). Space is the Machine: A Configurational Theory of Architecture. Cambridge University Press.

Turner, A. (2001). Depthmap: A Program to Perform Visibility Graph Analysis. Proceedings of the 3rd International Symposium on Space Syntax.


Space Syntax

Space syntax is a quantitative method that analyzes the spatial configuration of buildings and settlements to understand social organization and movement patterns. Developed by Bill Hillier and Julienne Hanson in the 1980s, space syntax measures how open or segregated spaces are, and how these properties relate to social behavior and cultural values. The method reveals distinctions between public and private spaces, movement corridors, and the degree of accessibility within architectural layouts.

Hillier, B., & Hanson, J. (1984). The Social Logic of Space. Cambridge University Press.

Bafna, S. (2003). Space syntax: a brief introduction to its logic and analytical techniques. Environment and Behavior, 35(1), 17-29.


Space-Time Geary's C

space-time local spatial autocorrelation

Geary (1954); extended to space-time by Anselin and others

Space-Time Geary's C extends the classical Geary contiguity ratio to panel or longitudinal spatial data, measuring autocorrelation across both geographic neighbors and adjacent time periods simultaneously. Values below 1 indicate positive space-time clustering; values above 1 indicate dispersion, and a value near 1 suggests random arrangement across the space-time lattice.

Georeferenced panel data (areal or point data across repeated time periods)

Geary, R. C. (1954). The Contiguity Ratio and Statistical Mapping. The Incorporated Statistician, 5(3), 115-145.

Anselin, L. (2019). A Local Indicator of Multivariate Spatial Association: Extending Geary's C. Geographical Analysis, 51(2), 133-150.


Space-Time Getis-Ord Gi*

Space-Time Getis-Ord Gi* Hot Spot Statistic

space-time local autocorrelation statistic

1992 (Gi*); space-time extension ~2000s–2010s

Getis & Ord (seminal); space-time extension developed in GIS literature and ArcGIS Emerging Hot Spot Analysis

The Space-Time Getis-Ord Gi* statistic extends the classic Gi* local hot spot measure into three dimensions — two spatial and one temporal — revealing not only where concentrations of high or low values cluster, but how those clusters evolve, intensify, or diminish over time. It is widely used in crime analysis, epidemiology, ecology, and urban studies.

Local spatial statistic (space-time extension)

Georeferenced point or areal count data observed at multiple time periods

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

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


Space-Time Hot Spot Analysis

Space-Time Hot Spot Analysis (Emerging Hot Spot Analysis)

emerging hot spot analysis
space-time cube hot spot
spatiotemporal hot spot detection
STHA

Kulldorff (spatial scan statistic); operationalized for time-series bins by Esri (Emerging Hot Spot Analysis)

Space-Time Hot Spot Analysis extends the classic Getis-Ord Gi* statistic across repeated time slices organised in a space-time cube. By testing each location-time bin for statistically significant clustering of high or low values, then examining the sequence of results over time, it identifies whether clusters are new, intensifying, persistent, sporadic, or diminishing — giving analysts a dynamic picture of how hot and cold spots evolve.

Georeferenced time-series counts or rates aggregated into a space-time cube

Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics: Theory and Methods, 26(6), 1481–1496.

Emerging Hot Spot Analysis. ArcGIS Pro Documentation. Esri Inc., 2021.


Space-Time Kernel Density Estimation

spatiotemporal kernel density estimation

2010 (space-time extension); 1956 (KDE origin)

Nakaya & Yano (space-time formulation); KDE foundation by Rosenblatt and Parzen

Space-Time Kernel Density Estimation extends classical KDE into three dimensions — two spatial and one temporal — to reveal how the intensity of point events (crimes, accidents, disease cases) varies continuously across both geographic space and time. It produces a smooth probabilistic surface that highlights where and when events concentrate most densely.

Point event data with timestamps and coordinates

Nakaya, T., & Yano, K. (2010). Visualising crime clusters in a space-time cube: An exploratory data-analysis approach using space-time kernel density estimation and scan statistics. Transactions in GIS, 14(3), 223-239.


Space-Time Kriging

spatiotemporal kriging
ST-kriging
space-time geostatistical interpolation
kriging in space-time

Space-Time Kriging is a geostatistical interpolation method that predicts an unknown variable at any location and time by borrowing strength from nearby observations in both space and time simultaneously. It models the joint spatial-temporal covariance structure through a space-time variogram, then uses optimal linear weights to produce predictions with quantified uncertainty.

Georeferenced time-series observations (point or areal data with timestamps)

Cressie, N., & Huang, H.-C. (1999). Classes of nonseparable, spatio-temporal stationary covariance functions. Journal of the American Statistical Association, 94(448), 1330-1340.

Kyriakidis, P. C., & Journel, A. G. (1999). Geostatistical space-time models: A review. Mathematical Geology, 31(6), 651-684.


spatiotemporal local indicators of spatial association

1995 (LISA); space-time extensions developed 2000s–2010s

Extension of Anselin (1995) LISA framework to the space-time domain

Space-Time Local Indicators of Spatial Association (ST-LISA) extend the classic LISA framework of Anselin (1995) into the temporal dimension, identifying locations that exhibit statistically significant spatial clustering or spatial outlier behavior consistently or intermittently across multiple time periods. They decompose global space-time autocorrelation into local contributions, revealing where and when spatial clusters emerge, persist, or dissolve.

Georeferenced panel or time-series data with spatial coordinates

Anselin, L. (1995). Local indicators of spatial association — LISA. Geographical Analysis, 27(2), 93–115.

Cheng, T., Haworth, J., & Wang, J. (2012). Spatio-temporal autocorrelation of road network data. Journal of Geographical Systems, 14(4), 389–413.

local-indicators-of-spatial-association local-morans-i space-time-spatial-autocorrelation space-time-morans-i hot-spot-analysis local-getis-ord-gi-star


Space-Time Moran's I

space-time autocorrelation index
ST Moran's I
spatiotemporal Moran's I
space-time I statistic

Cliff & Ord (extended to space-time domain)

Space-Time Moran's I extends the classic Moran's I statistic into the spatiotemporal domain, measuring whether observations that are close in both space and time tend to be more similar than those that are distant. It detects clustering, dispersion, or randomness across a combined space-time weight matrix, making it a foundational tool in epidemiology, criminology, and environmental monitoring.

Georeferenced time-series data (panel or repeated cross-sections)

Cliff, A. D., & Ord, J. K. (1981). Spatial Processes: Models and Applications. Pion.

Kulldorff, M., & Nagarwalla, N. (1997). Spatial disease clusters: detection and inference. Statistics in Medicine, 14(8), 799–810.

morans-i local-morans-i space-time-geary-c space-time-getis-ord-gi-star local-indicators-of-spatial-association space-time-spatial-autocorrelation


ST-NBA
space-time network analysis
spatiotemporal network analysis
network-based space-time analysis

Torsten Hägerstrand (time-geography foundation); extended by Harvey J. Miller and others for network contexts

Space-Time Network-Based Spatial Analysis integrates network topology with temporal constraints to model how people, goods, or phenomena move through geographic networks over time. Rooted in Hägerstrand's time-geography, it evaluates accessibility, interaction potential, and movement patterns along real-world infrastructure networks while respecting both spatial distance and time budgets.

Movement trajectories, GPS tracks, network-linked event data with timestamps

Hägerstrand, T. (1970). What about people in regional science? Papers of the Regional Science Association, 24(1), 7–21.

Miller, H. J. (2005). A measurement theory for time geography. Geographical Analysis, 37(1), 17–45.

space-time-cube network-kernel-density-estimation temporal-gis spatial-interaction-model geographically-weighted-regression trajectory-clustering


Space-Time Ordinary Kriging

STOK
spatio-temporal ordinary kriging
ordinary space-time kriging
ST-OK

Kyriakidis & Journel (seminal review); Cressie & Huang (covariance models)

Space-Time Ordinary Kriging (STOK) is a geostatistical interpolation method that predicts a spatially and temporally varying phenomenon at unsampled space-time locations by combining the ordinary kriging assumption of an unknown, locally constant mean with a joint space-time covariance (or variogram) structure. It produces optimal, unbiased predictions along with associated estimation uncertainty.

Georeferenced observations with timestamps (point or areal, continuous variable)

Kyriakidis, P. C., & Journel, A. G. (1999). Geostatistical space-time models: a review. Mathematical Geology, 31(6), 651-684.

Gräler, B., Pebesma, E., & Heuvelink, G. (2016). Spatio-temporal interpolation using gstat. The R Journal, 8(1), 204-218.

ordinary-kriging space-time-kriging space-time-universal-kriging space-time-co-kriging kriging space-time-spatial-autocorrelation


multi-temporal remote sensing classification

Woodcock, Zhu, and remote sensing community

Space-Time Remote Sensing Classification extends standard image classification to multi-temporal satellite or aerial imagery, enabling analysts to track land cover change, phenological cycles, and environmental dynamics across both space and time. By incorporating the temporal dimension, classifiers achieve higher accuracy and can detect transitions that a single-date analysis would miss.

Satellite imagery time series, multi-temporal raster data

Zhu, Z. (2017). Change detection using landsat time series: A review of frequencies, preprocessing, algorithms, and applications. ISPRS Journal of Photogrammetry and Remote Sensing, 130, 370-384.

Woodcock, C. E., et al. (2008). Free access to Landsat imagery. Science, 320(5879), 1011-1011.


Space-Time Spatial Autocorrelation

Space-Time Spatial Autocorrelation Analysis

STSA
spatiotemporal autocorrelation
space-time Moran's I
temporal spatial dependence

Cliff & Ord; extended by Anselin and others

Space-Time Spatial Autocorrelation extends classic spatial autocorrelation measures — most notably Moran's I — to data that vary across both geographic units and time periods. It detects whether nearby locations that are also temporally close tend to share similar attribute values, revealing clusters, trends, or anomalies that purely spatial or purely temporal analyses would miss.

Georeferenced panel / longitudinal spatial data

Clifford, P., Richardson, S., & Hemon, D. (1989). Assessing the significance of the correlation between two spatial processes. Biometrics, 45(1), 123–134.

Anselin, L., & Getis, A. (1992). Spatial statistical analysis and geographic information systems. The Annals of Regional Science, 26(1), 19–33.

global-morans-i local-morans-i spatial-lag-model geographically-weighted-regression kriging spatial-panel-model


Space-Time Spatial Durbin Model

ST-SDM
spatiotemporal Durbin model
spatial Durbin panel model
space-time SDM

LeSage & Pace; extended to space-time by Elhorst

The Space-Time Spatial Durbin Model extends the cross-sectional Spatial Durbin Model to panel data, simultaneously capturing spatial spillovers in both the dependent variable and the explanatory variables across space and over time. It is the most general and flexible specification in the spatial panel family, nesting the spatial lag and spatial error models as special cases.

Georeferenced panel (repeated observations across spatial units over time)

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

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

spatial-durbin-model spatial-lag-model spatial-error-model space-time-spatial-lag-model space-time-spatial-error-model panel-spatial-durbin-model


Space-Time Spatial Error Model

SEM panel
spatial error panel model
space-time SEM
spatiotemporal error model

1988 (SEM); 2003 (panel/space-time extension)

Anselin (1988); panel extension by Elhorst (2003, 2014)

The Space-Time Spatial Error Model (space-time SEM) is a spatial panel regression technique that accounts for spatial dependence confined to the error term across geographic units and time periods. It corrects biased inference caused by spatially correlated disturbances while estimating covariate effects on a panel of spatial observations.

Spatial panel data (multiple units observed over multiple time periods)

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

spatial-error-model space-time-spatial-lag-model space-time-spatial-durbin-model panel-spatial-error-model geographically-weighted-regression space-time-spatial-regression


Space-Time Spatial Lag Model

Space-Time Spatial Autoregressive Lag Model

ST-SAR
spatial-temporal lag model
spatiotemporal autoregressive model
space-time SAR model

The Space-Time Spatial Lag Model extends the classic spatial autoregressive (SAR) lag model to panel data, capturing how the outcome in each location at each time point is influenced by the contemporaneous outcomes of neighboring locations, while also controlling for unit-specific and time-specific fixed effects.

Georeferenced panel data (cross-sectional units observed over time)

Anselin, L., Le Gallo, J., & Jayet, H. (2008). Spatial Panel Econometrics. In L. Matyas & P. Sevestre (Eds.), The Econometrics of Panel Data (pp. 625-660). Springer.

spatial-lag-model space-time-spatial-error-model space-time-spatial-durbin-model panel-spatial-lag-model geographically-weighted-regression spatial-autocorrelation


Space-Time Spatial Panel Model

ST-SPM
spatiotemporal panel model
space-time panel econometrics
dynamic spatial panel model

The Space-Time Spatial Panel Model extends standard spatial panel econometrics to jointly account for cross-sectional spatial dependence, temporal autocorrelation, and unit-level heterogeneity. It allows outcomes in one location and time period to be influenced by outcomes in neighboring locations and by the location's own past, making it the canonical framework for dynamic spatiotemporal panel data analysis.

Georeferenced panel data (multiple units observed over multiple time periods)

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

spatial-lag-model spatial-error-model spatial-durbin-model panel-spatial-panel-model geographically-weighted-regression space-time-spatial-lag-model


Space-Time Spatial Regression

spatio-temporal regression
spatial panel regression
space-time regression
ST spatial regression

Anselin, LeSage, Pace and colleagues in spatial econometrics

Space-Time Spatial Regression extends classical spatial regression to panel settings where georeferenced units are observed across multiple time periods. By embedding a spatial weights matrix into a panel regression framework, it simultaneously controls for spatial dependence among cross-sectional units and temporal dynamics, yielding unbiased and consistent estimates in spatio-temporal data.

Georeferenced panel data (cross-sectional units observed over multiple time periods)

spatial-lag-model spatial-error-model spatial-durbin-model panel-spatial-regression geographically-weighted-regression space-time-kriging


Space-Time Universal Kriging

STUK
spatiotemporal universal kriging
space-time kriging with trend
universal kriging in space-time

Kyriakidis & Journel (1999); foundations in Matheron's geostatistics

Space-Time Universal Kriging (STUK) is a geostatistical method that interpolates a continuously varying phenomenon across both space and time while explicitly modelling a deterministic trend component. It generalises Universal Kriging to the joint space-time domain, producing unbiased optimal predictions and associated uncertainty estimates at unobserved space-time locations.

Continuous georeferenced observations with timestamps

Kyriakidis, P. C., & Journel, A. G. (1999). Geostatistical space-time models: A review. Mathematical Geology, 31(6), 651-684.

Graler, B., Pebesma, E., & Heuvelink, G. (2016). Spatio-temporal interpolation using gstat. The R Journal, 8(1), 204-218.

space-time-ordinary-kriging ordinary-kriging universal-kriging space-time-kriging geographically-weighted-regression kriging


Ashworth Scale for Spasticity

MAS
Modified Ashworth
spasticity assessment

The Modified Ashworth Scale (MAS) is a clinical rating scale for assessing muscle spasticity, quantifying the resistance to passive movement on a 0-4 scale plus an additional grade. Originally developed by B. Ashworth in 1964 and refined by Bohannon and Smith in 1987, the MAS is the most widely used bedside tool for evaluating spasticity in stroke survivors, individuals with cerebral palsy, multiple sclerosis, and spinal cord injury.

Ashworth, B. (1964). Preliminary trial of carisoprodol in multiple sclerosis. Practitioner, 192, 540-542.

Bohannon, R. W., & Smith, M. B. (1987). Interrater reliability of a modified Ashworth scale of muscle spasticity. Physical Therapy, 67(2), 206-207.


likelihood-free Bayesian spatial inference

2002 (spatial extensions from mid-2000s)

Diggle & Gratton (implicit statistical models, 1984); Beaumont, Zhang & Balding (ABC formalization, 2002)

Spatial Approximate Bayesian Computation (Spatial ABC) is a likelihood-free Bayesian inference framework for spatial data models whose likelihood function is intractable or too expensive to evaluate. It draws candidate parameters from a prior, simulates spatially structured datasets under those parameters, and accepts only the draws whose simulated spatial summary statistics closely match the observed data, thereby building an approximate posterior over model parameters.

georeferenced / areal / point-process spatial data

Beaumont, M. A., Zhang, W., & Balding, D. J. (2002). Approximate Bayesian computation in population genetics. Genetics, 162(4), 2025–2035.

Diggle, P. J., & Gratton, R. J. (1984). Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society: Series B, 46(2), 193–212.

approximate-bayesian-computation sequential-monte-carlo spatial-bayesian-inference spatial-mcmc gaussian-process-regression spatial-bayesian-hierarchical-model


Spatial Autocorrelation

spatial dependence
geographic autocorrelation
spatial clustering measure
SA

P. A. P. Moran (global measure, 1950); Roy Geary (Geary's C, 1954); Luc Anselin (LISA, 1995)

Spatial autocorrelation quantifies the degree to which a variable's values at nearby locations resemble each other more (positive autocorrelation) or less (negative autocorrelation) than expected by chance. Global indices such as Moran's I summarise the pattern across the entire study area, while local variants reveal clusters and outliers at the level of individual observations.

Spatial statistic / exploratory spatial data analysis

Georeferenced areal or point data with a continuous or count attribute

Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37(1/2), 17–23.

morans-i gearys-c local-indicators-of-spatial-association local-getis-ord-gi-star geographically-weighted-regression kriging


Spatial Bayesian Inference

Bayesian spatial analysis
Bayesian geostatistics
spatial Bayesian modeling
Bayesian areal modeling

Besag, York & Mollie (CAR prior, 1991); Gelfand & colleagues (Bayesian geostatistics, 1990s)

Spatial Bayesian inference applies Bayesian hierarchical modeling to data indexed by geographic location. By placing structured spatial priors on location-specific random effects, the model borrows information from neighboring regions or nearby points, producing smooth, uncertainty-quantified maps of any spatially varying outcome — disease rates, pollution levels, species abundance, or environmental risk.

areal, point-referenced, or point-process spatial data

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

Besag, J., York, J. & Mollie, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43(1), 1-20.

hierarchical-bayesian-inference spatial-mcmc kriging conditional-autoregressive-model gaussian-process-regression spatial-particle-filter


Spatial Bayesian Model Averaging

Bayesian model averaging with spatial effects

LeSage & Fischer (building on Raftery et al. BMA framework, 1997)

Spatial Bayesian model averaging (spatial BMA) extends classical BMA to settings where observations are georeferenced and spatial dependence must be modelled. Rather than selecting a single spatial regression model — which spatial weight matrix to use, which regressors to include, which spatial lag or error structure to adopt — it averages the predictions and parameter estimates across all candidate models, weighting each by its posterior probability given the data.

Bayesian model combination with spatial structure

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

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

Fernandez, C., Ley, E. & Steel, M. F. J. (2001). Benchmark priors for Bayesian model averaging. Journal of Econometrics, 100(2), 381-427.

bayesian-model-averaging spatial-bayesian-inference spatial-metropolis-hastings hierarchical-bayesian-inference spatial-variational-inference bayesian-regression


Spatial Bootstrap Simulation

spatial block bootstrap
spatial resampling
geostatistical bootstrap
bootstrap for spatial data

Lahiri and others, building on Efron's bootstrap (1979)

Spatial bootstrap simulation is a resampling technique designed for spatially dependent data. By resampling contiguous spatial blocks rather than independent observations, it preserves the local autocorrelation structure of the data and yields valid estimates of sampling variability for statistics computed on geographic or lattice observations.

Spatially indexed observations (point-referenced or areal)

Lahiri, S. N. (2003). Resampling Methods for Dependent Data. Springer.

Efron, B. & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman & Hall/CRC.

spatial-mcmc spatial-bayesian-inference sequential-monte-carlo kalman-filter spatial-particle-filter robust-bootstrap-simulation


Spatial Causal Impact Analysis

spatial causal inference
geo-causal analysis
spatial treatment effect estimation
spatial impact evaluation

Delgado & Florax (spatial DiD); Halleck Vega & Elhorst (SLX model); broader lineage in spatial econometrics (Anselin, 1988)

Spatial causal impact analysis estimates the causal effect of a spatially-targeted intervention — a policy, shock, or treatment applied to particular locations — while explicitly accounting for geographic spillovers between treated and untreated units. By combining quasi-experimental designs such as difference-in-differences or regression discontinuity with spatial econometric models, it separates the direct local effect of a treatment from indirect effects that diffuse to neighbouring areas.

Quasi-experimental causal inference with spatial data

Geo-referenced panel or cross-sectional data with treatment and control units across space

Delgado, M. S., & Florax, R. J. G. M. (2015). Difference-in-differences techniques for spatial data: Local autocorrelation and spatial interaction. Economics Letters, 137, 123-126.

Halleck Vega, S., & Elhorst, J. P. (2015). The SLX Model. Journal of Regional Science, 55(3), 339-363.

difference-in-differences spatial-regression-discontinuity synthetic-control-method spatial-econometrics geographically-weighted-regression propensity-score-matching


Spatial Coarsened Exact Matching

Spatial Coarsened Exact Matching Estimator

Spatial CEM
Geographic CEM
Spatial exact matching
CEM with spatial covariates

2012 (CEM foundation); spatial extension in applied literature 2015-present

Iacus, King & Porro (CEM foundation, 2012); extended to spatial contexts by applied spatial econometricians

Spatial Coarsened Exact Matching applies the Coarsened Exact Matching framework to study designs involving geographic units — neighbourhoods, census tracts, municipalities, or grid cells. Covariates are coarsened into discrete bins and units are matched exactly on those bins, with spatial attributes (location, adjacency, geographic characteristics) incorporated as matching dimensions to control for spatial confounding.

Quasi-experimental matching estimator with spatial covariates

Cross-sectional or panel data with geographic unit identifiers and spatial covariates

Iacus, S. M., King, G., & Porro, G. (2012). Causal Inference without Balance Checking: Coarsened Exact Matching. Political Analysis, 20(1), 1-24.

Anselin, L., & Rey, S. J. (Eds.) (2014). Modern Spatial Econometrics in Practice: A Guide to GeoDa, GeoDaSpace and PySAL. GeoDa Press.

coarsened-exact-matching spatial-propensity-score-matching spatial-doubly-robust-estimation propensity-score-matching spatial-regression-discontinuity-design difference-in-differences


SCIE
spatial CIE
place-based counterfactual evaluation
regional counterfactual analysis

Cerqua, Pellegrini, and regional-science scholars building on counterfactual econometrics

Spatial Counterfactual Impact Evaluation (SCIE) is a family of quasi-experimental methods that estimate the causal effect of geographically targeted policies — such as EU Cohesion Funds, enterprise zones, or place-based subsidies — by constructing a spatial counterfactual: what outcomes the treated region would have experienced without the intervention, inferred from comparable untreated regions or from discontinuities at policy boundaries.

Spatial panel or cross-sectional data with geographic treatment assignment

Cerqua, A., & Pellegrini, G. (2014). Do subsidies to private capital boost firms' growth? A multiple regression discontinuity design approach. Journal of Public Economics, 109, 114-126.

Pellegrini, G., Terribile, F., Tarola, O., Muccigrosso, T., & Busillo, F. (2013). Measuring the effects of European Regional Policy on economic growth: A regression discontinuity approach. Papers in Regional Science, 92(1), 217-233.

difference-in-differences regression-discontinuity-design synthetic-control-method propensity-score-matching geographically-weighted-regression instrumental-variables


Spatial Difference-in-Differences

Difference-in-Differences with Spatial Autocorrelation

Spatial Difference-in-Differences (Spatial DiD) extends the classical DiD estimator to settings where observations are geo-referenced and outcomes may be spatially autocorrelated or subject to spillover effects. Introduced by Delgado and Florax (2015), the method augments the standard two-way fixed-effects DiD regression with a spatial lag or spatial error term, yielding unbiased treatment-effect estimates even when policy shocks propagate across geographic units. It is used by economists, regional scientists, and urban planners evaluating place-based interventions such as infrastructure investment, environmental regulations, or zoning reforms.

Parallel trends corrected for spatial dependence

Delgado, M. S., & Florax, R. J. G. M. (2015). Difference-in-differences techniques for spatial data: Local autocorrelation and spatial interaction. Economics Letters, 126, 35–40.


Spatial Doubly Robust Estimation

Spatial DR
Spatial AIPW
Spatial augmented IPW
Doubly robust spatial causal estimation

Extension of Robins, Rotnitzky & Zhao (1994) doubly robust framework to spatial settings; developed in spatial epidemiology and econometrics literature

Spatial doubly robust estimation is a semiparametric causal inference method that combines propensity score weighting with outcome regression modeling — providing protection against misspecification of either component — while explicitly accounting for spatial autocorrelation among units. It extends the classical augmented inverse probability weighting (AIPW) estimator to settings where treatment assignment and outcomes are geographically clustered or spatially dependent.

Geo-referenced observational data with spatially correlated units

Papadogeorgou, G., Mealli, F., & Zigler, C. M. (2019). Causal inference with interfering units for cluster and population level treatment allocation programs. Biometrics, 75(3), 778-787.

Kennedy, E. H. (2016). Semiparametric theory and empirical processes in causal inference. In H. He, P. Wu, & D.-G. Chen (Eds.), Statistical Causal Inferences and Their Applications in Public Health Research (pp. 141-167). Springer.

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


Spatial Durbin Model

SDM
spatial mixed model
uzamsal durbin modeli

The Spatial Durbin Model is a general spatial regression model that includes a spatial lag of both the dependent variable (ρWy) and the explanatory variables (WXθ). Introduced as the recommended starting point by LeSage and Pace (2009), it nests the spatial autoregressive (SAR) and spatial error (SEM) models as special cases.

Maximum likelihood (Bayesian MCMC alternative for small samples)

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

Elhorst, J. P. (2010). Applied Spatial Econometrics: Raising the Bar. Spatial Economic Analysis, 5(1), 9–28.

spatial-panel-model geographically-weighted-regression mgwr-model ols-regression kriging-interpolation


Spatial Entropy Balancing

Spatial Entropy Balancing for Causal Inference

Extension of Hainmueller (2012) entropy balancing to spatial settings; spatial adaptations developed in geographic epidemiology and spatial econometrics literature

Spatial entropy balancing extends standard entropy balancing to observational settings where units are embedded in geographic space, incorporating spatial structure into the reweighting process so that balance is achieved while respecting spatial proximity, clustering, or spillover dependencies between units.

Observational cross-sectional or panel data with geographic coordinates or spatial identifiers

Hainmueller, J. (2012). Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies. Political Analysis, 20(1), 25-46.

entropy-balancing spatial-propensity-score-matching spatial-inverse-probability-weighting spatial-doubly-robust-estimation propensity-score-weighting spatial-matching-estimator


Spatial Error Model

Uzamsal Hata Modeli (SEM / Spatial Error)

The Spatial Error Model, developed within Anselin's spatial econometrics framework (1988), is a regression model that assumes spatial dependence enters through the error term: the disturbances of neighbouring units are correlated. It is used when unobserved shared factors make the errors of nearby observations move together, and it is estimated by maximum likelihood or GMM rather than ordinary least squares.

Spatial regression (spatially autocorrelated errors)

Maximum likelihood (ML) or generalized method of moments (GMM)

cross-sectional with geographic coordinates

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

spatial-lag-model spatial-durbin-model spatial-panel-model ols-regression mgwr-model


Spatial Event Study Design

spatial event study
geographic event study
spatial dynamic DiD
place-based event study

Developed across applied spatial economics literature; canonical applications in Autor, Dorn & Hanson (2013) and related regional economics studies

Spatial event study design estimates the dynamic causal effects of a geographically concentrated shock or policy by plotting how outcomes in affected locations evolve relative to unaffected locations across time periods, while explicitly accounting for spatial spillovers and autocorrelation across geographic units. It is widely used in regional and urban economics to evaluate place-based policies, trade shocks, and local labour market interventions.

Quasi-experimental causal inference with spatial structure

Panel data with geographic identifiers (regions, commuting zones, counties)

Autor, D. H., Dorn, D., & Hanson, G. H. (2013). The China Syndrome: Local Labor Market Effects of Import Competition in the United States. American Economic Review, 103(6), 2121-2168.

Kline, P. (2012). The Impact of Juvenile Curfew Laws on Arrests of Youth and Adults. American Law and Economics Review, 14(1), 44-67.

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


Spatial Fuzzy Regression Discontinuity

Spatial Fuzzy RD
Geographic Fuzzy RDD
Spatial Fuzzy RDD
Geo-Fuzzy RD

Keele & Titiunik (2015); fuzzy extension of geographic RDD building on Imbens & Lemieux (2008)

Spatial Fuzzy Regression Discontinuity Design (Spatial Fuzzy RDD) estimates a local average treatment effect when a geographic boundary determines treatment eligibility but some units on either side of the boundary fail to comply with their assigned status. It combines the spatial running-variable logic of geographic RDD with the instrumental-variable correction for imperfect compliance used in fuzzy RDD.

Quasi-experimental causal inference / IV-based spatial design

Geo-coded observational data with continuous spatial running variable and imperfect boundary compliance

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

Imbens, G., & Lemieux, T. (2008). Regression Discontinuity Designs: A Guide to Practice. Journal of Econometrics, 142(2), 615-635.

fuzzy-regression-discontinuity regression-discontinuity-design spatial-regression-discontinuity-design spatial-instrumental-variables geographic-regression-discontinuity instrumental-variables


Spatial Gibbs Sampling

Spatial Gibbs Sampling for Markov Random Fields and Geostatistical Models

Gibbs sampler for spatial models
MRF Gibbs sampling
spatial MCMC via Gibbs
conditional field simulation

Spatial Gibbs sampling applies the Gibbs sampler — a coordinate-wise Markov chain Monte Carlo algorithm — to models where observations are arranged in space and nearby locations are statistically dependent. By exploiting the conditional independence implied by a spatial neighbourhood structure, each site is updated one at a time given its neighbours, making posterior inference tractable for Markov random fields, Gaussian random fields, and hierarchical geostatistical models.

MCMC sampling algorithm for spatial models

spatially indexed continuous or discrete observations, lattice data, geostatistical data

Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721–741.

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

gibbs-sampling metropolis-hastings spatial-bayesian-inference bayesian-hierarchical-model spatial-mcmc markov-random-field