Hamilton Depression Rating Scale

Hamilton Depression Rating Scale (17-item HDRS or HAM-D)

HAM-D
HDRS
Hamilton Rating Scale for Depression

The Hamilton Depression Rating Scale, published by Max Hamilton in 1960, is a clinician-administered interview assessment of depressive symptom severity. The most common version contains 17 items (HAM-D-17), though 21-item and 24-item versions exist. It is considered the gold standard outcome measure in antidepressant drug trials and remains the most cited depression rating scale in the psychiatric literature. Unlike self-report measures, HAM-D requires clinician judgment and observation, making it particularly valuable in research settings where standardized measurement by trained raters is essential.

Hamilton, M. (1960). A rating scale for depression. Journal of Neurology, Neurosurgery & Psychiatry, 23(1), 56–62.

Bagby, R. M., Ryder, A. G., Schuller, D. R., & Marshall, M. B. (1997). The Hamilton Depression Rating Scale: has the gold standard become a lead weight? American Journal of Psychiatry, 161(12), 2163–2177.

Williams, J. B. (1988). A structured interview guide for the Hamilton Depression Rating Scale. Archives of General Psychiatry, 45(8), 742–747.

phq-9 bdi-ii montgomery-asberg-depression quick-inventory-depressive clinical-global-impressions-scale


Hamilton-Jacobi-Bellman Equation

HJB Equation
Bellman Equation
Dynamic Programming

The Hamilton-Jacobi-Bellman (HJB) equation is a partial differential equation characterizing the optimal cost-to-go function in dynamic programming. Developed by Bellman in 1957, HJB provides both necessary and sufficient conditions for optimality, enabling elegant theoretical analysis and numerical solutions for optimal control problems. HJB is fundamental to reinforcement learning, approximate dynamic programming, and real-time control.

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

Kirk, D. E. (2004). Optimal Control Theory: An Introduction (2nd ed.). Dover Publications.


Hamiltonian Monte Carlo with Measurement Error

Hamiltonian Monte Carlo for Bayesian Measurement Error Models

HMC measurement error model
Bayesian errors-in-variables with HMC
HMC latent variable measurement error
Hamiltonian MCMC with covariate error

Neal (2011) for HMC; Carroll et al. (2006) for measurement error framework

Hamiltonian Monte Carlo (HMC) with measurement error is a Bayesian computational strategy for fitting models where one or more covariates are observed with noise. HMC samples jointly from the posterior over model parameters and the unobserved true covariate values, using gradient-based proposals that explore the high-dimensional posterior efficiently and avoid the slow random-walk behaviour of standard Metropolis sampling.

Bayesian sampling algorithm for latent-variable models

continuous or categorical outcomes with error-prone continuous covariates

Carroll, R. J., Ruppert, D., Stefanski, L. A., & Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective (2nd ed.). Chapman and Hall/CRC.

Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. Jones, & X.-L. Meng (Eds.), Handbook of Markov Chain Monte Carlo (pp. 113-162). CRC Press.


Hamiltonian Monte Carlo with Missing Data Imputation

HMC with missing data
HMC data augmentation
Bayesian HMC imputation
HMC with data augmentation

Radford M. Neal (HMC, 1996/2011); missing-data treatment via Bayesian data augmentation (Tanner & Wong, 1987)

Hamiltonian Monte Carlo with missing data extends the gradient-based HMC sampler to handle incomplete observations by treating missing values as additional unknown parameters. The posterior over model parameters and missing values is sampled jointly in one efficient pass, exploiting gradient information to explore the high-dimensional joint space with far fewer rejected proposals than random-walk MCMC.

continuous, mixed, or incomplete multivariate data with MAR or MCAR missingness

Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. Jones & X.-L. Meng (Eds.), Handbook of Markov Chain Monte Carlo (pp. 113-162). CRC Press.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. Chapter 18: Missing-data imputation.

hamiltonian-monte-carlo mcmc-with-missing-data gibbs-sampling-with-missing-data bayesian-inference-with-missing-data multiple-imputation variational-inference-with-missing-data


Hamiltonian Monte Carlo

HMC
Hybrid Monte Carlo
NUTS
No-U-Turn Sampler
gradient-based MCMC

Hamiltonian Monte Carlo (HMC) is a gradient-based Markov chain Monte Carlo algorithm that uses the geometry of the log-posterior surface to make large, informed jumps through parameter space instead of the small random steps of classical MCMC. Originally introduced for lattice field theory by Duane, Kennedy, Pendleton, and Roweth (1987) under the name Hybrid Monte Carlo, and brought into mainstream statistics by Radford Neal's authoritative 2011 chapter, HMC is today the default sampler in Stan and PyMC and is widely regarded as the state-of-the-art engine for Bayesian posterior inference in high-dimensional models.

Gradient-based Markov chain Monte Carlo sampler

Duane, Kennedy, Pendleton & Roweth (1987); popularised for statistics by Neal (2011)

Draw samples from high-dimensional posterior distributions efficiently

Posterior samples, posterior means, credible intervals, convergence diagnostics

Stan (default engine), PyMC, NumPyro, TensorFlow Probability

Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.

Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. L. Jones, & X.-L. Meng (Eds.), Handbook of Markov Chain Monte Carlo (pp. 116–162). Chapman and Hall/CRC.

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

bayesian-regression mcmc metropolis-hastings variational-inference hierarchical-bayes


Hamming Loss

Hamming Loss (Multi-label Classification)

Information theory and multi-label learning

Hamming loss measures the fraction of labels that are incorrectly predicted in multi-label classification. It counts the number of label mistakes divided by the total number of labels, providing a simple metric for multi-label problems.

Schapire, R. E., & Singer, Y. (2000). BoosTexter: A boosting-based system for text categorization. Machine Learning, 39(2-3), 135-168.

Tsoumakas, G., & Katakis, I. (2007). Multi-label classification: An overview. International Journal of Data Warehousing and Mining, 3(3), 1-13.


HAQ Disability Index

HAQ-DI
Health Assessment Questionnaire
Disability Index

James Fries and colleagues at Stanford University

The Health Assessment Questionnaire Disability Index (HAQ-DI) is a 20-item self-report measure of functional disability developed by Fries and colleagues at Stanford University in 1980. Originally designed for rheumatoid arthritis, the HAQ-DI has become the gold-standard functional assessment instrument across diverse rheumatic diseases and chronic conditions.

Functional disability measurement for arthritis and chronic disease

Bruce, B., & Fries, J. F. (1989). The Stanford Health Assessment Questionnaire: a review of its history, issues, progress, and documentation. Journal of Rheumatology, 16(8), 1055–1064.

Fries, J. F., Spitz, P., Kraines, R. G., & Holman, H. R. (1980). Measurement of patient outcome in arthritis. Arthritis & Rheumatism, 23(2), 137–145.

Pincus, T., Swearingen, C., & Wolfe, F. (2011). Toward a multidimensional Health Assessment Questionnaire (MDHAQ): assessment of advanced activities of daily living and psychological well-being. Seminars in Arthritis and Rheumatism, 30(2), 10–17.


HAR-RV Model

Heterogeneous Autoregressive Model of Realized Volatility

heterogeneous autoregressive realized volatility

HAR-RV Modeli (Heterogeneous Autoregressive Realized Volatility)

The HAR-RV model, introduced by Fulvio Corsi in 2009, forecasts realized volatility by decomposing it into daily, weekly, and monthly components. It is a simple linear regression that mirrors how market participants with different investment horizons react to volatility, and it naturally captures the long-memory behaviour of volatility.

Linear time-series regression for volatility

Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174–196.

ols-regression garch-model regime-switching-finance tail-risk-measures wavelet-finance


Hardy Cross Method

Hardy Cross Method for Pipe Network Analysis

Cross method
Moment distribution method
Iterative balancing

The Hardy Cross method is an iterative technique for solving steady-state flow distribution in pipe networks, originally developed for water distribution systems. Introduced by Hardy Cross in 1936, this method balances flow continuity and pressure head constraints through successive iterations, making it ideal for hand calculations and gaining physical insight into network behavior.

Iterative method for pipe network flow distribution

Cross, H. (1936). Analysis of flow in networks of conduits or conductors. University of Illinois Bulletin, 34(17), 3-29.

Duffy, A., Malone, D., & O'Neill, J. (1987). The Hardy Cross Method for Water Distribution Networks. Water Research Centre.

Jeppson, R. W. (1976). Analysis of Flow in Pipe Networks. Ann Arbor Science Publishers.


Harmful Algal Bloom Monitoring

Harmful algal bloom (HAB) monitoring is an integrated approach combining satellite remote sensing, in situ observations, and predictive modeling to detect, track, and forecast toxic algal outbreaks in marine and freshwater systems. HAB monitoring has become essential for public health protection, as certain algal species produce potent toxins that accumulate in shellfish and pose severe health risks to consumers and marine life.

Davidson, K., Miller, P., Wilding, T. A., & Shutler, J. (2016). Harmful algal bloom risk assessment in the context of climate change. Harmful Algae, 53, 34-41.

Glibert, P. M., Allen, J. I., Bouwman, A. F., et al. (2010). Modeling of harmful algal blooms. Journal of Marine Systems, 83(3-4), 261-271.


Harmonic Analysis in Music

Harmonic Analysis and Harmonic Function Identification Algorithm

functional harmony analysis
harmonic progression detection
tonal function estimation

Harmonic analysis is the computational study of chord progressions, harmonic function, and tonal relationships in music. Formalized for audio by Pardo and Birmingham (2002), it goes beyond simple chord identification to interpret harmonic role and structure. Harmonic analysis is essential for music theory education, compositional understanding, and music generation systems. It requires understanding both the chords themselves and their functional relationships within a tonal context.

Harmonic function and progression analysis

Pardo, B., & Birmingham, W. P. (2002). Algorithms for chordal analysis. Computer Music Journal, 26(4), 27-49.

Pauwels, G., Salamon, J., Gómez, E., & Ryckebusch, P. (2015). Automatic chord estimation from audio using a Deep Neural Network trained on music theory. In Proceedings of the International Society for Music Information Retrieval Conference.

Chen, T. P., Tan, A. H., & Zhu, S. (2012). Speech emotion recognition using robust temporal dynamics-based feature extraction methods. In Proceedings of the International Conference on Neural Information Processing.

chord-recognition key-detection-music pitch-detection-algorithm melody-extraction music-segmentation


Harmonic Distortion Analysis

Harmonic Analysis and Total Harmonic Distortion Measurement

harmonic content analysis
THD analysis
Fourier harmonic decomposition

Harmonic distortion analysis quantifies the deviation of voltage or current waveforms from sinusoidal shape due to nonlinear loads. Using Fourier decomposition, engineers separate the waveform into its fundamental frequency and harmonic components (integer multiples of 50 or 60 Hz). Harmonic analysis is critical for assessing power quality and designing filters in modern power systems with high penetration of nonlinear devices.

IEEE Std 519-1992: IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems.

Arrillaga, J., Watson, N. R., & Chen, S. (2003). Power System Quality Assessment. Wiley.

Dugan, R. C., McGranaghan, M. F., Santoso, S., & Beaty, H. W. (2012). Electrical Power Systems Quality (3rd ed.). McGraw-Hill.

power-quality-assessment power-flow-analysis load-forecasting smart-grid-state-estimation


Harmony Search

HS algorithm
Harmoni Araması (Harmony Search)
music-inspired optimization

Zong Woo Geem, Joong Hoon Kim, G. V. Loganathan

Harmony Search (HS) is a population-based metaheuristic optimization algorithm introduced by Geem, Kim, and Loganathan in 2001. It mimics the improvisation process of jazz musicians seeking a perfect state of harmony, using three operators — memory consideration, pitch adjustment, and random selection — to generate candidate solutions. The algorithm applies to both continuous and discrete variables and has found wide use in engineering design, water distribution network optimization, and combinatorial problems.

HMS (harmony memory size), HMCR (harmony memory consideration rate), PAR (pitch adjustment rate)

Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A New Heuristic Optimization Algorithm: Harmony Search. Simulation, 76(2), 60–68.

Mahdavi, M., Fesanghary, M., & Damangir, E. (2007). An Improved Harmony Search Algorithm for Solving Optimization Problems. Applied Mathematics and Computation, 188(2), 1567–1579.

genetic-algorithm particle-swarm-optimization simulated-annealing differential-evolution ant-colony-optimization


Harris Corner Detection

Harris Corner Detector
Harris-Stephens Detector
Plessey Operator

The Harris corner detector, introduced by Chris Harris and Mike Stephens in 1988, is a foundational method for identifying corners and interest points in digital images. Harris corners are points where two edges meet at a significant angle, making them stable and repeatable features for image analysis, matching, and 3D reconstruction.

Harris, C., & Stephens, M. (1988). A combined corner and edge detector. Alvey Vision Conference, 147–152.

Förstner, W., & Gülch, E. (1987). A fast operator for detection and precise localization of distinct points, corners and centres of circular features. ISPRS Intercommission Conference on Fast Processing of Photogrammetric Data, 281–305.

sift-feature-detection orb-feature-descriptor blob-detection scale-space-theory image-morphology


Harris Hawks Optimization

Harris Hawks Optimization (HHO) is a metaheuristic algorithm introduced by Heidari et al. in 2019, inspired by the hunting strategies of Harris's hawks. The algorithm models the cooperative hunting behavior and escape strategies of these raptors to solve complex optimization problems. HHO balances exploration through perching and exploitation through dynamic pursuit, making it effective for multimodal and high-dimensional optimization.

Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., & Chen, H. (2019). Harris hawks optimization: Algorithm and applications. Future Generation Computer Systems, 97, 849-872.

slime-mould-algorithm aquila-optimizer particle-swarm-optimization grey-wolf-optimizer whale-optimization-algorithm


Hartree-Fock Method

The Hartree-Fock (HF) method is a foundational self-consistent field approach for solving the many-electron Schrödinger equation. Developed independently by Douglas Hartree and Vladimir Fock in the late 1920s, it approximates the ground state by assuming electrons move in an average field generated by all other electrons, enabling tractable quantum chemistry calculations.

Fock, V. (1930). Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Zeitschrift für Physik, 61, 126–148.

Hartree, D. R. (1928). The wave mechanics of an atom with a non-coulomb central field. Mathematical Proceedings of the Cambridge Philosophical Society, 24, 89–110.

Szabo, A., Ostlund, N. S. (2012). Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publications.

density-functional-theory moller-plesset-perturbation-theory coupled-cluster-ccsd quantum-monte-carlo


Harvey-Bradshaw Index

Harvey-Bradshaw Index for Crohn's Disease Activity

The Harvey-Bradshaw Index (HBI) is a simple, clinician-administered tool for assessing disease activity in Crohn's disease. Developed in 1980, it measures five clinical parameters including abdominal pain, stool frequency, and extraintestinal manifestations. The HBI is widely used in clinical practice and research for monitoring disease progression and treatment response.

Harvey, R. F., & Bradshaw, J. M. (1980). A simple index of Crohn's-disease activity. Lancet, 315(8167), 514.

cdai-crohns mayo-score-uc sccai ibdq-short child-pugh-score


Hate Speech Detection

offensive language detection
toxic content detection
Nefret Söylemi Tespiti

Hate speech detection is a natural-language-processing task that automatically identifies hateful, offensive, or harmful text on social media and online platforms. The task was sharpened by Davidson and colleagues (2017), who showed why separating genuine hate speech from merely offensive language is a hard, distinct classification problem rather than a single toxicity score.

Feature-based machine learning / fine-tuned transformer models

Output: Class label (hate speech / offensive / neither)

Davidson, T., Warmsley, D., Macy, M. & Weber, I. (2017). Automated Hate Speech Detection and the Problem of Offensive Language. ICWSM, 11(1), 512-515.

Fortuna, P. & Nunes, S. (2018). A Survey on Automatic Detection of Hate Speech in Text. ACM Computing Surveys, 51(4), 1-30.

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


Hatemi-J Asymmetric Causality

Hatemi-J Asymmetric Causality Test
Asymmetric Causality Test
Positive and Negative Causality Test
Asimetrik Nedensellik Testi

The Hatemi-J asymmetric causality test, introduced by Abdulnasser Hatemi-J in 2012, extends the Granger causality framework to allow causal relationships between the positive and negative components of integrated time series to differ. By decomposing each series into cumulative positive and negative partial sums and embedding the Toda-Yamamoto approach within a VAR, the test enables researchers to distinguish whether positive shocks, negative shocks, or both drive causation between economic variables.

Hatemi-J, A. (2012). Asymmetric causality tests with an application. Empirical Economics, 43(1), 447–456.


Hatemi-J Cointegration Test

Hatemi-J Cointegration Test with Two Regime Shifts

Hatemi-J İki Kırılmalı Eşbütünleşme Testi

The Hatemi-J cointegration test, introduced by Abdulnasser Hatemi-J in 2008, tests for a long-run equilibrium relationship between integrated time series while allowing for up to two unknown structural breaks in the cointegrating vector. It extends earlier single-break approaches by permitting both the intercept and slope coefficients of the cointegrating regression to shift at two endogenously determined breakpoints, making it particularly suited for economic and financial data spanning periods of major institutional or policy change.

Residual-based cointegration test with two structural breaks

Hatemi-J, A. (2008). Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empirical Economics, 35(3), 497–505.


Hausman Test

Hausman Specification Test (Fixed Effects vs Random Effects)

Hausman specification test
FE vs RE test
Durbin-Wu-Hausman test
Hausman Spesifikasyon Testi (FE vs RE)

The Hausman test is a specification test, introduced by Jerry A. Hausman in 1978, that decides between the fixed-effects (FE) and random-effects (RE) estimators in panel data models. The null hypothesis is that the random-effects estimator is consistent and efficient and should be preferred; the alternative is that random effects is inconsistent and fixed effects is required because the unit-specific effects are correlated with the explanatory variables.

Specification test for panel data models

Wald-type quadratic form comparing FE and RE coefficient vectors

Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica, 46(6), 1251–1271.

panel-fixed-effects panel-random-effects ols-regression fmols-estimator panel-cointegration


Haversine Distance

Haversine distance measures the great-circle distance between two points on a sphere given their latitude and longitude coordinates. Popularized by Roger Sinnott in 1984, this formula computes the shortest distance between two points on Earth's surface, accounting for the planet's spherical geometry. It ranges from 0 (identical locations) to half the Earth's circumference. Haversine is essential for geographic information systems (GIS), location-based services, and spatial analysis.

Sinnott, R. W. (1984). Virtues of the haversine. Sky and Telescope, 68(2), 159.

Tobler, W. (1980). Numerical map generalization. In Proceedings of the Ninth International Cartographic Association Conference (pp. 280-286).


Historical Clinical Risk Management-20 version 3

Kevin S. Douglas, Stephen D. Hart, Christopher D. Webster, et al.

The HCR-20v3 is a structured professional judgment framework developed by Douglas, Hart, and colleagues for the assessment of risk for violence among adolescents and adults in mental health, criminal justice, and forensic settings. Published in 2013, it represents the third version of one of the most widely validated risk assessment instruments in forensic psychology, synthesizing clinical judgment with empirical evidence of violence risk factors.

Douglas, K. S., Hart, S. D., Webster, C. D., Belfrage, H., Guy, L. S., & Wilson, C. M. (2013). HCR-20v3: Assessing risk for violence. Simon Fraser University Mental Health Law Program.

Webster, C. D., Douglas, K. S., Eaves, D., & Hart, S. D. (1997). HCR-20: Assessing risk for violence (Version 2). Simon Fraser University Mental Health Law Program.

violence-risk-appraisal-guide saprof static-99 beck-hopelessness-scale level-of-service-inventory


HDBSCAN

HDBSCAN
Hierarchical DBSCAN
hierarchical density-based clustering
HDBSCAN*

Campello, R. J. G. B.; Moulavi, D.; Sander, J.

HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering algorithm introduced by Campello, Moulavi, and Sander in 2013. It extends DBSCAN by building a full hierarchy of density-based clusters across all density scales and then extracting a stable flat partition, making it robust to datasets where cluster densities vary substantially across regions.

Unsupervised clustering, outlier detection

Campello, R. J. G. B., Moulavi, D., & Sander, J. (2013). Density-Based Clustering Based on Hierarchical Density Estimates. In J. Pei et al. (Eds.), Advances in Knowledge Discovery and Data Mining. PAKDD 2013. Lecture Notes in Computer Science, vol. 7819 (pp. 160–172). Springer, Berlin, Heidelberg.

Campello, R. J. G. B., Moulavi, D., Zimek, A., & Sander, J. (2015). Hierarchical Density Estimates for Data Clustering, Visualization, and Outlier Detection. ACM Transactions on Knowledge Discovery from Data, 10(1), Article 5.

McInnes, L., Healy, J., & Astels, S. (2017). hdbscan: Hierarchical density based clustering. Journal of Open Source Software, 2(11), 205.

dbscan kmeans gaussian-mixture-model optics spectral-clustering


Head-Related Transfer Function

Head-Related Transfer Function (HRTF) for 3D Spatial Audio

The Head-Related Transfer Function (HRTF) describes how the human head, ears, and torso filter sound from different directions. HRTFs capture the acoustical changes that occur as sound travels around the head to reach each ear, enabling the perception of sound location in 3D space. Measured or modeled HRTFs are essential for creating convincing 3D audio through headphones in virtual reality, spatial games, and immersive audio applications.

Frequency-dependent spatial filtering function

Wightman, F. L., & Kistler, D. J. (1989). Headphone simulation of free-field listening. I: Stimulus synthesis. The Journal of the Acoustical Society of America, 85(2), 858-867.

Blauert, J. (1997). Spatial Hearing: The Psychophysics of Human Sound Localization. The MIT Press.

Møller, H., Sørensen, M. F., Hammershøi, D., & Jensen, C. B. (1995). Head-related transfer functions of human subjects. Journal of the Audio Engineering Society, 43(5), 300-321.


The HIT-6 is a brief, validated measure of headache impact on daily functioning and quality of life. Developed by Mark Kosinski and colleagues in 2003, this 6-item questionnaire quantifies how headache (migraine or other types) affects work, social activities, sleep, and emotional well-being. It is widely used in headache research, clinical trials, and practice to assess disease burden and treatment benefit.

Self-report functional impact questionnaire

Kosinski, M., Bayliss, M. S., Bjorner, J. B., Ware, J. E., Garber, W. H., Batenhorst, A., & Tepper, S. (2003). A six-item short-form survey for measuring headache impact: The HIT-6. Quality of Life Research, 12(8), 963-974.

Yang, M., Rendas-Baum, R., Varon, S. F., & Kosinski, M. (2011). Validation of the Headache Impact Test (HIT-6) across episodic and chronic migraine. Cephalalgia, 31(3), 357-367.

Lipton, R. B., Dodick, D. W., Silberstein, S. D., Saper, J. R., Aurora, S. K., Pearlman, S. H., ... & Goadsby, P. J. (2007). Topiramate for episodic migraine prevention: A randomized, double-blind, placebo-controlled trial. Headache, 47(2), 170-180.


Health Anxiety Inventory

Paul M. Salkovskis, Karina A. Rimes, Helen M. Warwick, David M. Clark

The Health Anxiety Inventory (HAI) is a 14-item self-report questionnaire designed to measure health anxiety and health-related worry, including concerns about having serious illness, fear of dying, and preoccupation with bodily symptoms. Developed by Salkovskis, Rimes, Warwick, and Clark in 2002, the HAI has become a standard instrument for assessing health anxiety in clinical and research settings, particularly valuable for distinguishing health anxiety from general anxiety or depression.

Salkovskis, P. M., Rimes, K. A., Warwick, H. M., & Clark, D. M. (2002). The Health Anxiety Inventory: Development and validation of scales for the measurement of health anxiety and illness worry. Psychological Medicine, 32(5), 843-853.


Health Anxiety Questionnaire

Mark P. Lucock, Steve M. Gillespie, and colleagues

The Health Anxiety Questionnaire (HAQ) is a self-report measure assessing the preoccupation, worry, and avoidance behaviors related to health concerns. Developed by Lucock and colleagues in 2007, the HAQ measures the cognitive and behavioral dimensions of health anxiety (formerly called hypochondriasis). It is used to screen for and assess illness anxiety disorder and to monitor treatment response in cognitive-behavioral interventions targeting health-focused worry and illness avoidance.

Lucock, M. P., Gillespie, S. M., Perera, S., & Goodwin, K. (2008). Health Anxiety: A viable diagnosis and differential diagnosis in primary care. British Journal of General Practice, 58(556), 763–768.


Health App Usability Scale

System Usability Scale for Health Applications (SUS-Health)

The System Usability Scale (SUS) is a rapid, validated tool for measuring perceived usability of digital products, widely adapted for health applications. Developed by John Brooke in 1996 and extensively validated by Bangor and colleagues, the 10-item SUS generates a single composite score reflecting users' subjective perception of ease of use, learnability, and overall system quality. Its simplicity and robustness have made it the de facto standard for usability assessment in health technology research.

Brooke, J. (1996). SUS—A quick and dirty usability scale. In P. W. Jordan, B. Weerdmeester, A. Thomas, & I. L. McClelland (Eds.), Usability evaluation in industry (pp. 189–194). Taylor & Francis.

Bangor, A., Kortum, P. T., & Miller, J. T. (2008). An empirical evaluation of the System Usability Scale. International Journal of Human-Computer Interaction, 24(6), 574–594.


Health Belief Model Scale

The Health Belief Model (HBM) is a foundational psychological framework developed by Marshall Rosenstock in 1966 to predict and explain preventive health behavior. Based on the central premise that people take health action to avoid illness when they perceive susceptibility to a health threat and believe that taking action will reduce that threat at an acceptable cost, the HBM measures four core constructs: Perceived Susceptibility, Perceived Severity, Perceived Benefits, and Perceived Barriers. The model also incorporates 'Cues to Action' (external triggers) and 'Self-Efficacy' (added later). HBM is extensively used in research on disease prevention, health screening uptake, medication adherence, and vaccine acceptance.

Rosenstock, I. M. (1966). Why people use health services. Milbank Memorial Fund Quarterly, 44(3), 94-127.

Champion, V. L., & Skinner, C. S. (2008). The Health Belief Model. In K. Glanz, B. K. Rimer, & K. Viswanath (Eds.), Health Behavior and Health Education: Theory, Research, and Practice (4th ed., pp. 45-65). Jossey-Bass.


Health Literacy Scale

Health Literacy Scale - Functional and Interactive Dimensions

Health communication and patient comprehension

Health literacy scales are validated self-report instruments designed to measure the capacity of individuals to access, understand, appraise, and communicate health information to maintain or improve health. The Rapid Estimate of Adult Literacy in Medicine (REALM) and Test of Functional Health Literacy in Adults (TOFHLA) are commonly used variants assessing functional health literacy in clinical populations. Health literacy measurement identifies patients at risk for poor health outcomes and guides communication simplification.

Osborn, C. Y., Weiss, B. D., Davis, T. C., & Skripkauskas, S. (2007). Literacy and health outcomes: a systematic review. Journal of Health Communication, 12(4), 371-383.

Baker, D. W., Williams, M. V., Parker, R. M., Gazmararian, J. A., & Nurss, J. (1999). Development of a brief test to measure functional health literacy. Patient Education and Counseling, 38(1), 33-42.

Berkman, N. D., Sheridan, S. L., Donahue, K. E., Halpern, D. J., & Crotty, K. (2011). Low health literacy and health outcomes: an updated systematic review. Annals of Internal Medicine, 155(2), 97-107.


Barbara S. Wallston, Kenneth A. Wallston, and Robert DeVellis

The Multidimensional Health Locus of Control Scale (MHLC) is an 18-item measure developed by Wallston, Wallston, and DeVellis (1978) to assess individual differences in health-related beliefs about the locus of control—that is, to whom or what people attribute responsibility for their health. The MHLC measures three dimensions: Internal control (belief that health is determined by one's own actions and responsibility), Powerful Others control (belief that health is determined by healthcare providers, family, or powerful authority figures), and Chance control (belief that health is determined by fate, luck, or uncontrollable events). These beliefs profoundly influence health behavior engagement, treatment adherence, and response to health information. The MHLC is widely used in health behavior research, patient education evaluation, and clinical practice to understand how beliefs about health control shape behavior and to tailor communication styles.

Wallston, B. S., Wallston, K. A., & DeVellis, R. (1978). Development of the Multidimensional Health Locus of Control (MHLC) Scales. Health Education Monographs, 6(2), 160-170.


Health-Promoting Lifestyle Profile II

Health-Promoting Lifestyle Profile II Scale

Susan Noble Walker, Karen Sechrist, and Nola J. Pender

The Health-Promoting Lifestyle Profile II (HPLP-II) is a 52-item self-report instrument developed by Walker, Sechrist, and Pender in 1987 to assess and measure health-promoting behaviors across multiple life domains. Based on Pender's Health Promotion Model, the HPLP-II evaluates six dimensions of positive health behavior: Health Responsibility, Physical Activity, Nutrition, Spiritual Growth, Interpersonal Relations, and Stress Management. Unlike disease-focused instruments, the HPLP-II captures a comprehensive picture of wellness-oriented lifestyle practices. It is widely used in nursing research, health promotion program evaluation, population health assessment, and clinical practice to identify health strengths and areas for behavior change counseling.

Walker, S. N., Sechrist, K. R., & Pender, N. J. (1987). The Health-Promoting Lifestyle Profile: development and psychometric characteristics. Nursing Research, 36(2), 76-81.

Walker, S. N., Pender, N. J., Sechrist, K. R., & Frank-Stromborg, M. (1995). A Spanish language version of the Health-Promoting Lifestyle Profile. Nursing Research, 44(5), 268-273.


Health Protective Behavior Scale

The Health Protective Behavior Scale (HPBS) assesses self-reported engagement in preventive behaviors during infectious disease outbreaks, including hand hygiene, respiratory etiquette, isolation, and vaccination. Developed from literature review and behavioral theory by Bish and Michie, and refined through implementation research by Conner and colleagues, it measures adherence to public health guidance. The HPBS is widely used in pandemic surveillance research and behavioral intervention trials to track population adoption of protective measures.

Bish, A., & Michie, S. (2010). Demographic and attitudinal determinants of protective behaviours during a pandemic: A review. British Journal of Health Psychology, 15(4), 797–824.

Conner, M., Godin, G., Norman, P., & Sheeran, P. (2011). Using the question-behavior effect to promote disease prevention behaviours: Two randomized controlled trials. Health Psychology, 30(3), 300–309.


Health Technology Assessment

Health Technology Assessment for Evidence-Based Healthcare Decision Making

Health economics, Evidence-based decision making

International HTA organizations, National Institutes of Health

Health Technology Assessment (HTA) is a structured, multidisciplinary approach to evaluating the clinical, economic, and societal effects of healthcare technologies (devices, drugs, procedures, systems). HTA synthesizes evidence from clinical trials, observational studies, and economic analyses to support decision-makers in adoption and reimbursement determinations.

Goodman, C. S. (2004). HTA 101: Introduction to Health Technology Assessment (Version 1.0). National Library of Medicine, National Institutes of Health.

Husereau, D., Drummond, M., Petrou, S., Carswell, C., Moher, D., Greenberg, D., & Sculpher, M. (2013). Consolidated Health Economic Evaluation Reporting Standards (CHEERS) statement. BMJ, 346, f1049.

Drummond, M. F., Sculpher, M. J., Claxton, K., Stoddart, G. L., & Torrance, G. W. (2015). Methods for the Economic Evaluation of Health Care Programmes (4th ed.). Oxford University Press.

cost-effectiveness-analysis-hta balanced-scorecard-healthcare dea-hospital-efficiency clinical-audit staffing-ratio-analysis


Healthcare Team Vitality Instrument

Metersky, M. L., and colleagues; based on organizational team cohesion research

The Healthcare Team Vitality Instrument (HTVI) is a brief, 5-item survey designed to measure healthcare team cohesion, communication quality, and shared purpose—dimensions of team "vitality" that are associated with effective teamwork and patient safety. Developed by Metersky and colleagues and validated in intensive care units and surgical units, the HTVI assesses whether team members perceive themselves as a cohesive unit with clear goals, good communication, and mutual respect. The instrument is particularly valued for its brevity (takes <2 minutes) and its ability to rapidly assess team dynamics in clinical settings where administrative burden is a barrier to survey completion.

Metersky, M. L., Garman, A., Li, X., & Teplitsky, M. (2015). Cohesion and teamwork in the ICU: Validation of the Health Care Team Vital Instrument. American Journal of Medical Quality, 30(1), 44–52.

Neily, J., Mills, P. D., Young-Xu, Y., Carney, B. T., West, P., Berger, D. H., Mazzia, L. M., Paull, D. E., & Bagian, J. P. (2010). Association between implementation of a medical team training program and surgical mortality. JAMA, 304(15), 1693–1700.

Seys, D., Klinglmueller, F., Wu, A. W., Aerts, B., Vermeir, P., Meersseman, W., De Pauw, R., Voet, S., & Claes, N. (2013). Healthcare professional–patient communication of adverse events. Best Practice & Research Clinical Anaesthesiology, 25(2), 161–173.

teamstepps-perceptions safety-attitudes-questionnaire patient-safety-climate-scale clinical-handover-quality


The Healthcare Worker COVID-19 Burnout Scale (HWCBS) measures occupational burnout specific to pandemic-era healthcare work, including emotional exhaustion, depersonalization, and reduced personal accomplishment under pandemic stress. Adapted from the Maslach Burnout Inventory (MBI) by Lan and colleagues for COVID-19 contexts, it captures the compounded burden of patient care, infection risk, resource scarcity, and social isolation affecting frontline workers. The HWCBS is widely used in occupational health surveillance and intervention trials targeting healthcare worker mental health and retention.

Lan, F. Y., Suharlim, C., Keparskis, K. A., Stokes, P., Tasavori, S., Yang, J., ... & Gould, M. K. (2020). Psychiatric symptoms and coping strategies among Chinese healthcare workers during the early stages of the COVID-19 pandemic. JAMA Network Open, 3(5), e203976.

Maslach, C., Jackson, S. E., & Leiter, M. P. (2016). Maslach Burnout Inventory Manual (4th ed.). Consulting Psychologists Press.


USDA/NCI Dietary Assessment Shared Resource; Krebs-Smith et al.

The HEI-2020 is a composite score measuring diet quality based on adherence to the 2020–2025 Dietary Guidelines for Americans. Developed by USDA and the National Cancer Institute, the HEI evaluates 13 dietary components: adequacy of fruit, vegetables, grains, protein foods, dairy; moderation of saturated fat, added sugars, and sodium; and appropriate whole grain and polyunsaturated fat intakes. The HEI-2020 provides a single metric of overall diet quality suitable for population surveillance, research, and individual dietary assessment.

Calculated from dietary intake data (24-hour recall or FFQ)

Guenther, P. M., Casavale, K. O., Reedy, J., & Kirkpatrick, S. I. (2021). Update of the Healthy Eating Index: HEI-2015. Journal of the Academy of Nutrition and Dietetics, 113(4), 569–580.

Krebs-Smith, S. M., Pannucci, T. E., Subar, A. F., et al. (2018). Update of the Healthy Eating Index: HEI-2015. Journal of the Academy of Nutrition and Dietetics, 118(9), 1591–1602.


HHIA

Craig W. Newman, Barbara E. Weinstein, Gary P. Jacobson, and Gail A. Hug

The Hearing Handicap Inventory for Adults (HHIA) is a 25-item self-report questionnaire that quantifies the functional and emotional effects of hearing loss on daily life, work, and psychosocial well-being. Developed by Newman, Weinstein, Jacobson, and Hug in 1990, the HHIA is the most widely used hearing-specific quality-of-life measure in audiology and otolaryngology. It provides a patient-centered assessment of hearing handicap, distinct from audiometric measures alone, and is standard for baseline assessment, monitoring hearing aid benefit, and outcome evaluation in hearing conservation programs.

Newman, C. W., Weinstein, B. E., Jacobson, G. P., & Hug, G. A. (1990). The Hearing Handicap Inventory for Adults: Psychometric adequacy and audiometric correlates. Ear & Hearing, 11(6), 430-433.


Heart Failure Somatic Awareness Scale

heart failure symptom awareness and self-monitoring

The Heart Failure Somatic Awareness Scale (HFSAS) is a specialized measure that assesses heart failure patients' ability to recognize and accurately perceive early warning signs of disease worsening (somatic awareness), such as subtle changes in dyspnea, edema, weight, fatigue, or palpitations. Early recognition of decompensation signs enables prompt self-management action (diuretic adjustment, physician contact) and prevents costly hospitalizations. The HFSAS is essential in modern HF management, particularly with remote monitoring technologies and self-management support programs.

Steinhubl, S. R., Mehta, P. K., & Ebner, G. S. (2017). The digital health revolution and consumer empowerment. Current Cardiology Reports, 19(11), 105.

Riegel, B., Lee, C. S., Sochalski, J., & Jaarsma, T. (2007). Improving heart failure self-management through nurse-coaching: the HF-CARE trial. JACC Heart Failure, 3(5), 392–400.

minnesota-heart-failure kansas-city-cardiomyopathy new-york-heart-association-class duke-activity-status-index


Heart Rate Recovery

Heart Rate Recovery and Parasympathetic Reactivation Assessment

HRR
heart rate variability recovery
parasympathetic tone
autonomic recovery

Heart rate recovery (HRR) is the decline in heart rate during the first minutes following maximal or submaximal exercise, reflecting the reactivation of parasympathetic (vagal) tone. Introduced as a clinical predictor by Cole and colleagues (1999), HRR serves as a non-invasive biomarker of cardiac autonomic function and overall cardiovascular health. A rapid decline in heart rate after exertion indicates efficient parasympathetic reactivation and healthy autonomic nervous system balance. Conversely, blunted HRR (slow heart rate recovery) is associated with increased mortality risk, autonomic dysfunction, and poor exercise tolerance.

Cole, C. R., Blackstone, E. H., Pashkow, F. J., Snader, C. E., & Lauer, M. S. (1999). Heart-rate recovery immediately after exercise as a predictor of mortality. New England Journal of Medicine, 341(18), 1351-1357.

Lauer, M. S., & Okin, P. M. (2005). Heart rate response to exercise stress testing: a predictor of cardiovascular outcomes? Current Problems in Cardiology, 30(7), 357-387.

Jouven, X., Empana, J. P., Schwartz, P. J., Desnos, M., Courbon, D., & Ducimetière, P. (2005). Heart-rate profile during exercise as a predictor of sudden death. New England Journal of Medicine, 352(19), 1951-1958.

vo2-max respiratory-exchange-ratio critical-power epoc lactate-threshold


Heart Rate Variability

HRV
RR interval analysis
Cardiac variability

Task Force of European Society of Cardiology

Heart rate variability (HRV) analysis quantifies the variation in time intervals between consecutive heartbeats as a window into autonomic nervous system function and cardiovascular health. Formalized by the European Society of Cardiology Task Force in 1996, HRV metrics are now standard in cardiology, physiology, and sports science for assessing stress, recovery, and disease risk.

Time-series and frequency-domain analysis pipeline

Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. (1996). Heart rate variability: standards of measurement, physiological interpretation, and clinical use. Circulation, 93(5), 1043-1065.

Malik, M. (1996). Heart Rate Variability. Futura Publishing Company.


Heatmap and Scrollmap

Heatmaps and scrollmaps are behavioral analytics tools that visually represent user attention and interaction on web pages and screens. Click heatmaps show where users click most frequently, visualized as color-coded density overlays. Scrollmaps show how far down pages users scroll and where they typically stop. These passive tracking methods collect aggregate data from hundreds or thousands of real users, revealing attention patterns, engagement hotspots, and content visibility issues without requiring direct user interaction or controlled studies.

Passive behavior tracking for understanding user attention and engagement

Hotjar. (2021). The Complete Guide to Heatmaps. Hotjar White Paper.

Loranger, H., & Nielsen, J. (2017). Scrolling and Attention. Nielsen Norman Group Report.

first-click-testing eye-tracking tree-testing heuristic-evaluation


Heavy Metal Speciation

Characterization of Chemical Forms and Bioavailability of Metals in Environmental Matrices

metal speciation
metal partitioning
bioavailability assessment
speciation analysis

Environmental geochemistry and contaminant fate

Heavy metal speciation is the analytical and geochemical determination of the chemical forms (species) and partitioning of toxic metals (lead, cadmium, chromium, zinc, copper) in soil, sediment, and water. Metal bioavailability—the fraction accessible to organisms—depends critically on speciation: metal bound to soil organic matter or iron oxides is immobile and non-bioavailable; dissolved or exchangeable metal is highly bioavailable and toxic. Speciation assessment informs remediation design, risk assessment, and contaminant fate prediction.

analytical and geochemical modeling pipeline

Tessier, A., Campbell, P. G. C., & Bisson, M. (1979). Sequential Extraction Procedure for the Speciation of Particulate Trace Metals. Analytical Chemistry, 51(7), 844–851.

Allen, H. E. (2002). Bioavailability of Metals in Terrestrial Ecosystems: Importance of Partitioning for Bioavailability to Invertebrates, Microorganisms, and Plants. SETAC Press.

US Environmental Protection Agency. (2007). Bioavailability of Metals. EPA/540/R-04/016.


HEC-RAS

HEC-RAS (Hydrologic Engineering Center River Analysis System) is a hydraulic modeling software developed by the US Army Corps of Engineers that computes water surface elevation and velocity in open channels and floodplains, and depicts inundation extent and depth. Since its introduction in 1995, HEC-RAS has become the de facto standard for floodplain delineation, dam break analysis, and flood risk assessment for regulatory and engineering purposes.

1D/2D river hydraulics and flood inundation modeling

Brunner, G. W. (2010). HEC-RAS river analysis system hydraulic reference manual. US Army Corps of Engineers Hydrologic Engineering Center.

Dyhouse, G. R., Hatchett, J. L., & Barkau, R. L. (2003). Floodplain modeling using HEC-RAS. Haestad Press.


Heckman Selection Model

Heckman Sample Selection Model (Heckit / Tobit Type II)

Heckman Seçim Modeli (Heckit / Tobit II)

The Heckman selection model, introduced by James J. Heckman in 1979, is a two-step model that corrects sample selection bias when the outcome is only observed for a non-random subset of cases. A probit selection equation models who is observed, and the outcome equation then corrects for the resulting bias using the inverse Mills ratio.

Two-step (Heckit) or full maximum likelihood

continuous (observed only for the selected subsample)

Heckman, J. J. (1979). Sample Selection Bias as a Specification Error. Econometrica, 47(1), 153–161.

ols-regression logistic-regression tobit-regression panel-fixed-effects quantile-regression


Hedonic Pricing

Hedonic Regression
Characteristics Pricing Model

The hedonic pricing model, developed by Sherwin Rosen in 1974 and building on Kevin Lancaster's characteristics theory (1966), is an econometric method for valuing the implicit prices of product attributes by regressing market prices on observed characteristics. It reveals the trade-offs consumers are willing to make among product features and can be used to infer valuations of environmental amenities (e.g., air quality via house prices) and to adjust price indices for quality changes.

Rosen, S. (1974). Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition. Journal of Political Economy, 82(1), 34–55.

Lancaster, K. J. (1966). A New Approach to Consumer Theory. Journal of Political Economy, 74(2), 132–157.

Epple, D. (1987). Hedonic Prices and Implicit Markets: Estimating Demand and Supply Functions for Differentiated Products. Journal of Political Economy, 95(1), 59–80.


HEdPERF Higher Education Performance Scale

Higher Education Performance Scale (HEdPERF)

HEdPERF
Educational Service Quality Scale

HEdPERF is a 41-item scale designed specifically to measure service quality in higher education contexts, developed by Srikanthan and Dalrymple (2003). Extending SERVQUAL's framework to academic environments, HEdPERF captures unique dimensions of educational service: Academic Aspects (teaching quality, curriculum relevance), Non-Academic Aspects (administrative efficiency, physical facilities), Reputation (institutional prestige, employability), Access (availability of information, ease of enrollment), and Programme Issues (program content, skill development). The scale addresses the distinctive characteristics of educational services, which blend academic content delivery with student support and institutional experience.

Multi-dimensional higher education service quality scale

Srikanthan, G., & Dalrymple, J. F. (2003). Developing a Holistic Model for Quality in Higher Education. Quality in Higher Education, 9(2), 123-138.

O'Neill, M. A., & Palmer, A. (2003). An Exploratory Study of the Effect of Experience on Consumer Perceptions of the 'Service Quality' of Hairdressing Salons and Higher Education Institutions. Journal of Hospitality & Leisure Marketing, 10(3-4), 5-30.

servqual servperf customer-satisfaction-index e-servqual


Hellinger Distance

Hellinger distance is a symmetric, bounded metric that measures the difference between two probability distributions. Rooted in the work of Ernst Hellinger (1909) and later formalized in statistical divergence by Anil Bhattacharyya (1946), this distance ranges from 0 (identical distributions) to 1. It is a true metric satisfying all mathematical distance properties and is particularly well-suited for comparing probability distributions in a symmetric, numerically stable manner.

Symmetric metric for probability distributions

Hellinger, E. (1909). Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal für die Reine und Angewandte Mathematik, 136, 210-271.

Bhattacharyya, A. (1946). On a measure of divergence between two multinomial populations. Sankhya, 7, 401-406.


HELLWIG

HELLWIG (Hellwig's Method — Development Pattern) is a ranking multi-criteria decision-making (MCDM) method introduced by Hellwig, Z. in 1968. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Taxonomic distance-from-ideal (development measure)

Hellwig, Z. (1968). Zastosowanie metody taksonomicznej do typologicznego podziału krajów ze względu na poziom ich rozwoju oraz zasoby i strukturę kwalifikowanych kadr technicznych. Przegląd Statystyczny

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


Helpful Aspects of Therapy Form

The Helpful Aspects of Therapy (HAT) form is a semi-structured client feedback instrument designed to capture the client's perception of what was most beneficial or helpful in a therapy session or course of treatment. Developed by Llewellyn and refined by Elliott, the HAT combines open-ended narrative response with structured rating scales, enabling rich qualitative insight alongside quantitative comparison. It is used in qualitative outcome research and clinical feedback systems to understand mechanisms of change from the client's perspective.

Llewellyn, S. P., Foo, S., & Stam, H. J. (1988). Assessing psychotherapy outcome: Clients' perspectives. Canadian Journal of Counselling, 22(2), 191–206.

Elliott, R. (1985). Helpful and nonhelpful events in brief counseling interviews: An empirical taxonomy. Journal of Counseling Psychology, 32(3), 307–322.

session-rating-scale working-alliance-inventory common-factors-questionnaire outcome-rating-scale


Hemagglutination Inhibition Assay

HI assay
HAI test
haemagglutination inhibition test
HI test

The Hemagglutination Inhibition (HI) Assay is a classical serological test used to detect and quantify antibodies against hemagglutinating viruses — most notably influenza and Newcastle disease virus — in animal and human serum. Widely employed in veterinary diagnostics, vaccine efficacy evaluation, and epidemiological surveillance, it relies on the principle that specific antibodies in serum will block a known quantity of virus from agglutinating red blood cells.

Serum antibody titers (numeric, ordinal dilution series)

Hirst, G. K. (1942). The quantitative determination of influenza virus and antibodies by means of red cell agglutination. Journal of Experimental Medicine, 75(1), 49–64.

World Organisation for Animal Health (WOAH/OIE). (2021). Manual of Diagnostic Tests and Vaccines for Terrestrial Animals, Chapter 3.3.4 (Avian Influenza). WOAH.

hemagglutination-assay virus-neutralization-test elisa serum-neutralization agar-gel-immunodiffusion microneutralization-assay


Hemolysis Assay

Hemolysis Assay Red Blood Cell Toxicity Evaluation

RBC lysis assay
hemolytic compatibility test
hemolytic potential test

The hemolysis assay is a standard method for evaluating the blood compatibility of biomaterials by quantifying the extent to which a material or substance damages red blood cells (RBCs) and causes hemoglobin release. Codified in standards including ASTM F756 and ISO 10993-4, the hemolysis assay is essential for regulatory approval of blood-contacting devices such as stents, catheters, artificial heart valves, and hemodialysis membranes. The assay provides a simple, quantitative measure of hemolytic potential that correlates with clinical safety.

ASTM F756-17 (2017). Standard Practice for Assessment of Hemolytic Properties of Materials. ASTM International.

ISO 10993-4:2017. Biological Evaluation of Medical Devices. Part 4: Selection of tests for interactions with blood.

Tomos, M. S., Morrison, S., & Williams, D. F. (2012). Comparison of hemolytic methods for assessing the blood compatibility of biomaterials. Journal of Biomedical Materials Research, 105(7), 1926-1933.

mtt-mts-assay live-dead-assay cam-assay electrospinning


HEP Track Reconstruction

High-Energy Physics Track Reconstruction

tracking
charged particle reconstruction
trajectory fitting

Track reconstruction is the process of identifying and measuring the trajectories of charged particles through a detector, providing momentum and impact parameter information essential for particle identification, vertex reconstruction, and physics analysis in high-energy physics experiments.

Fruhwirth, R. (1987). Application of Kalman filtering to track and vertex fitting. Nuclear Instruments and Methods in Physics Research Section A, 262(2-3), 444–450.

Mankel, R. (2006). Pattern recognition and reconstruction. Nuclear Instruments and Methods in Physics Research Section A, 559(1), 88–91.

Aad, G., et al. (ATLAS Collaboration). (2010). The ATLAS inner detector commissioning. European Physical Journal C, 70(3), 787–821.


West Haven Criteria for Hepatic Encephalopathy Grading

Hepatic Encephalopathy Grading
HE Grade
West Haven Grade

West Haven Group (Parsons, Williams, Sherlock, Trey, Davidson)

The West Haven Criteria are the standard for grading hepatic encephalopathy (HE) severity, ranging from subclinical (Grade 0) to deep coma (Grade 4). Developed by Trey and Davidson in the 1960s and refined by the West Haven group, these criteria integrate mental status changes (confusion, asterixis, disorientation) and consciousness level to stage HE. The West Haven grade is a strong predictor of short-term prognosis in cirrhosis and guides urgency of intervention (lactulose, rifaxomicin, mannitol, intubation).

Parsons, P. L., Williams, R., & Sherlock, S. (1978). The role of plasma amino acids in hepatic encephalopathy and the effect of branched-chain amino acid infusion. Gut, 19(10), 969–978.

Trey, C., & Davidson, C. S. (1966). The management of fulminant hepatic failure. Progress in Liver Diseases, 2, 282–298.

child-pugh-score gcsi mayo-score-uc harvey-bradshaw-index


Herd Reproductive Performance

Herd Reproductive Performance Assessment and Management

fertility monitoring
reproductive efficiency evaluation
breeding performance analysis

Dairy Veterinarians and Herd Health Specialists

Herd reproductive performance assessment integrates multiple metrics to evaluate the efficiency of breeding programs and overall population fertility. Formalized in the 1990s-2000s by dairy veterinarians and herd health specialists, the method combines individual animal records (conception rates, calving intervals) with population-level indicators (age structure, open days, pregnancy rate) to identify reproductive constraints. Assessment is fundamental to dairy profitability and sustainability.

data analysis and performance assessment

Macmillan, K. L. (2002). Fertility and production in grazing dairy cattle. Veterinary Record, 150(9), 267-273.

Buckley, F., O'Sullivan, K., Mee, J. F., Evans, R. D., & Berry, D. P. (2003). Relationships among milk yield, body condition, cow welfare, and reproductive performance in spring-calving Irish dairy cows. Journal of Dairy Science, 86(7), 2308-2319.

Darwash, A. O., Lamming, G. E., & Woolliams, J. A. (2000). The fertility of dairy cattle in the United Kingdom as affected by calving season and service period fertility on subsequent performance. Journal of Dairy Science, 79(3), 453-463.


Hermeneutic Analysis

hermeneutics
hermeneutical interpretation
interpretive hermeneutics
philosophical hermeneutics

19th–20th century (Schleiermacher ~1819; Dilthey ~1883; Gadamer 1960; Ricoeur 1969)

Friedrich Schleiermacher; Wilhelm Dilthey; Hans-Georg Gadamer; Paul Ricoeur

Hermeneutic analysis is a qualitative interpretive method for uncovering the meaning of texts, documents, spoken discourse, or human actions. Rooted in 19th-century biblical and legal scholarship and systematised by Schleiermacher, Dilthey, Gadamer, and Ricoeur, it operates through the hermeneutic circle: the meaning of a part is understood through the whole, and the meaning of the whole is revised as parts are interpreted. The goal is not to measure or code, but to achieve a deepening, dialogic understanding of the object of interpretation.

Texts, documents, interviews, historical records

Gadamer, H.-G. (1975). Truth and Method (G. Barden & J. Cumming, Trans.). Seabury Press. (Original work published 1960 as Wahrheit und Methode).

Ricoeur, P. (1981). Hermeneutics and the Human Sciences: Essays on Language, Action and Interpretation (J. B. Thompson, Ed. & Trans.). Cambridge University Press.

phenomenology textual-criticism discourse-analysis narrative-analysis critical-discourse-analysis thematic-analysis


Hermeneutic Phenomenological Research in Education

van Manen phenomenology
pedagogical hermeneutics
lived-experience inquiry in education
human science pedagogy

Hermeneutic phenomenology in education research is a qualitative approach — developed principally by Max van Manen — that investigates the lived, meaning-laden dimensions of educational experience. Drawing on Heidegger's interpretive philosophy and Gadamer's hermeneutics, it asks what it is like, from the inside, to be a teacher, a learner, or a student navigating a formative moment, and renders that understanding through carefully crafted, evocative writing rather than through codes or statistics.

Qualitative interpretive research approach

In-depth interviews, field texts, anecdotes, journal entries, observations

van Manen, M. (1990). Researching Lived Experience: Human Science for an Action Sensitive Pedagogy. State University of New York Press.

van Manen, M. (2016). Phenomenology of Practice: Meaning-Giving Methods in Phenomenological Research and Writing. Routledge.

phenomenology interpretive-phenomenological-analysis hermeneutics narrative-inquiry case-study grounded-theory


Hermeneutic Phenomenology

Heideggerian phenomenology
interpretive phenomenology
hermeneutic inquiry
van Manen phenomenology

Philosophical roots 1927 (Heidegger); systematic research method from 1980s–1990s

Martin Heidegger (philosophical foundation); Max van Manen (methodological application)

Hermeneutic phenomenology is a qualitative research approach that investigates the interpreted meaning of lived experience from within the existential conditions that shape it. Rooted in Heidegger's ontology and developed as an empirical method by Max van Manen, it does not seek to bracket or suspend the researcher's understanding but instead treats that understanding as the very medium through which the meaning of experience can be disclosed. The approach is widely used in education, nursing, and social sciences to explore how people dwell in, and make sense of, their world.

In-depth interviews, field observations, written narratives, diaries, artefacts

Heidegger, M. (1962). Being and Time (J. Macquarrie & E. Robinson, Trans.). Harper & Row. (Original work published 1927).

phenomenology grounded-theory narrative-analysis ethnography discourse-analysis thematic-analysis


HERONIAN-MEAN

HERONIAN-MEAN (Heronian Mean (HM)) is a aggregation multi-criteria decision-making (MCDM) method introduced by Yu, D. in 2012. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Interrelationship-based aggregation — geometric pairwise interactions

Yu, D. (2012). Intuitionistic fuzzy geometric Heronian mean aggregation operators. Applied Soft Computing


Heterogeneous treatment effect Causal impact analysis

Heterogeneous Treatment Effect Causal Impact Analysis

HTE-CausalImpact
CATE causal impact
heterogeneous causal impact
subgroup causal impact analysis

Brodersen et al. (causal impact framework, 2015); Athey & Imbens (HTE estimation, 2016)

Heterogeneous treatment effect causal impact analysis extends the Bayesian structural time-series causal impact framework to estimate not just the average effect of an intervention but how that effect varies across subgroups or individual units. By combining counterfactual prediction with conditional average treatment effect (CATE) estimation, it reveals which groups benefit most or least from an intervention.

Causal inference / heterogeneous effects estimation

Time series, panel, or observational data with subgroup identifiers

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

Athey, S., & Imbens, G. (2016). Recursive partitioning for heterogeneous causal effects. Proceedings of the National Academy of Sciences, 113(27), 7353-7360.


Heterogeneous Treatment Effect Coarsened Exact Matching

Heterogeneous Treatment Effect Estimation via Coarsened Exact Matching

coarsened exact matching with effect heterogeneity

Iacus, King & Porro (CEM foundation, 2012); subgroup HTE extensions by Imai & colleagues

Heterogeneous treatment effect coarsened exact matching (HTE-CEM) extends the coarsened exact matching framework to estimate how treatment effects vary across subgroups or individual characteristics. After CEM creates balanced strata by coarsening continuous covariates into bins and exactly matching units within each bin, conditional average treatment effects (CATEs) are computed within or across these strata, revealing where treatment works, for whom, and by how much.

Matching-based causal inference with subgroup CATE estimation

Cross-sectional or panel; mixed continuous and categorical covariates

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

Imai, K., & Ratkovic, M. (2013). Estimating treatment effect heterogeneity in randomized program evaluation. Annals of Applied Statistics, 7(1), 443-470.


Heterogeneous treatment effect Counterfactual impact evaluation

subgroup counterfactual impact evaluation

Cerulli (2010) for CIE framework; Athey & Wager (2019) for causal forest-based CATE within CIE

Heterogeneous Treatment Effect Counterfactual Impact Evaluation (HTE-CIE) extends standard counterfactual impact evaluation by estimating how the causal effect of a policy or intervention varies across subgroups defined by pre-treatment characteristics. Rather than reporting a single average treatment effect, it maps the Conditional Average Treatment Effect (CATE) across the covariate space, revealing who benefits most or least from an intervention.

Quasi-experimental causal inference with subgroup heterogeneity

Cross-sectional or panel data with treatment indicator and moderating covariates

Cerulli, G. (2010). Modelling and measuring the effect of public subsidies on business R&D: A critical review of the econometric literature. Economic Record, 86(274), 421-449.

Athey, S., & Wager, S. (2019). Estimating treatment effects with causal forests: An application. Observational Studies, 5(2), 37-51.


Heterogeneous Treatment Effect Difference-in-Differences Estimator

HTE-DiD
heterogeneous DiD
CATT estimator
group-time ATT

HTE-DiD extends the classic Difference-in-Differences estimator to settings where treatment effects vary across units, time periods, or treatment cohorts. Developed formally by Callaway and Sant'Anna (2021) and Sun and Abraham (2021), it avoids the biases that arise when a conventional two-way fixed-effects regression is used with staggered adoption or effect heterogeneity, by estimating cohort-and-time-specific average treatment effects that can then be aggregated flexibly.

Panel or repeated cross-sections with staggered or simultaneous treatment

Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-Differences with multiple time periods. Journal of Econometrics, 225(2), 200-230.

Sun, L., & Abraham, S. (2021). Estimating dynamic treatment effects in event studies with heterogeneous treatment effects. Journal of Econometrics, 225(2), 175-199.

difference-in-differences dynamic-difference-in-differences panel-data-difference-in-differences staggered-difference-in-differences event-study-design synthetic-control-method


Heterogeneous treatment effect Doubly robust estimation

Doubly Robust Estimation of Heterogeneous Treatment Effects

DR-HTE
augmented IPW for HTE
doubly robust CATE estimation
semiparametric HTE estimation

Kennedy (2023); building on Robins, Rotnitzky & Zhao (1994) and Chernozhukov et al. (2018)

Doubly robust estimation of heterogeneous treatment effects (HTE) estimates how the causal effect of a treatment varies across subgroups or individual covariate values. By combining an outcome model and a propensity score model, it retains consistency if either model is correctly specified, and supports flexible machine learning nuisance estimators through cross-fitting to produce valid conditional average treatment effect (CATE) estimates.

Observational cross-sectional or panel data with continuous or binary treatment and outcome

Kennedy, E. H. (2023). Towards optimal doubly robust estimation of heterogeneous causal effects. Electronic Journal of Statistics, 17(2), 3008-3049.

Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1-C68.


Heterogeneous Treatment Effect Estimation with Entropy Balancing

HTE entropy balancing
CATE with entropy balancing
heterogeneous effects EB
subgroup entropy balancing

Hainmueller (2012) for entropy balancing; Athey & Imbens (2016) for heterogeneous effect estimation

Heterogeneous Treatment Effect Entropy Balancing combines entropy balancing — a preprocessing step that reweights control units to match the treatment group on covariate moments — with methods that estimate how the treatment effect varies across subgroups or individuals. It produces covariate-balanced weights without parametric propensity models, then uses those weights to estimate conditional average treatment effects (CATEs) across moderating variables.

Causal inference / heterogeneous effect estimation

Observational cross-sectional or panel data with a binary treatment

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.

Athey, S., & Imbens, G. W. (2016). Recursive partitioning for heterogeneous causal effects. Proceedings of the National Academy of Sciences, 113(27), 7353-7360.


HTE event study
heterogeneous effects event study
group-time ATT event study
dynamic HTE design

Sun & Abraham (2021); Callaway & Sant'Anna (2021)

Heterogeneous Treatment Effect Event Study Design is a causal-inference framework that uses event study regression to estimate how treatment effects vary across groups, cohorts, or time relative to a treatment event. Unlike classical two-way fixed-effects event studies — which assume a homogeneous effect — this approach explicitly models and recovers group-time average treatment effects (ATTs), addressing the contamination bias that arises when effects differ across treated units.

Panel data with staggered or simultaneous treatment timing

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


Heterogeneous Treatment Effect Fuzzy Regression Discontinuity

Heterogeneous Treatment Effect Estimation in Fuzzy Regression Discontinuity Design

HTE-Fuzzy RDD
heterogeneous LATE at threshold
subgroup fuzzy RD
fuzzy RD with effect heterogeneity

Hahn, Todd & Van der Klaauw (2001); extensions by Calonico, Cattaneo & Titiunik (2014)

Heterogeneous Treatment Effect Fuzzy RDD extends the standard fuzzy regression discontinuity design — where treatment probability, not treatment status itself, jumps at a threshold — by examining whether the Local Average Treatment Effect (LATE) estimated at the threshold differs systematically across subgroups defined by covariates such as gender, socioeconomic status, or prior ability. It combines the instrumental-variable logic of fuzzy RDD with structured heterogeneity analysis.

Quasi-experimental causal inference / heterogeneity analysis

Observational panel or cross-sectional with a running variable and threshold

Hahn, J., Todd, P., & Van der Klaauw, W. (2001). Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design. Econometrica, 69(1), 201-209.

Calonico, S., Cattaneo, M. D., & Titiunik, R. (2014). Robust Nonparametric Confidence Intervals for Regression-Discontinuity Designs. Econometrica, 82(6), 2295-2326.


Heterogeneous treatment effect Instrumental variables

Instrumental Variables Estimation with Heterogeneous Treatment Effects

HTE-IV
LATE estimator
IV with effect heterogeneity
local average treatment effect IV

Heterogeneous treatment effect IV applies instrumental variables estimation while explicitly acknowledging and modelling that the treatment effect differs across units. Rather than recovering a single average effect, it focuses on the Local Average Treatment Effect (LATE) — the causal effect for compliers, the subpopulation whose treatment status is actually shifted by the instrument — and extends analysis to variation in that effect across observed subgroups.

Causal inference / IV with effect heterogeneity

Cross-sectional or panel; continuous or binary outcome; binary or multi-valued instrument

Imbens, G. W., & Angrist, J. D. (1994). Identification and Estimation of Local Average Treatment Effects. Econometrica, 62(2), 467-475.

Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.


Heterogeneous Treatment Effect Interrupted Time Series Analysis

HTE-ITS
Subgroup ITS
Effect-modifier ITS
Segmented ITS with interaction

Extensions of Shadish, Cook & Campbell (2002) ITS framework; HTE formulation developed by Lopez Bernal and colleagues

Heterogeneous Treatment Effect Interrupted Time Series extends the standard ITS design to detect whether an intervention's effect on a time series differs systematically across subgroups or in response to unit-level moderators. Where ordinary ITS yields a single level-change and slope-change estimate, HTE-ITS adds interaction terms for a moderating variable, revealing who benefits more or less from the intervention and by how much.

Quasi-experimental segmented regression with subgroup moderation

Longitudinal / time-series, continuous or count outcomes with a defined intervention point

Lopez Bernal, J., Cummins, S., & Gasparrini, A. (2017). Interrupted time series regression for the evaluation of public health interventions: a tutorial. International Journal of Epidemiology, 46(1), 348-355.

Kontopantelis, E., Doran, T., Springate, D. A., Buchan, I., & Reeves, D. (2015). Regression based quasi-experimental approach when randomisation is not an option: interrupted time series analysis. BMJ, 350, h2750.


Heterogeneous Treatment Effect Inverse Probability Weighting

Heterogeneous Treatment Effect Estimation via Inverse Probability Weighting

HTE-IPW
CATE-IPW
heterogeneous IPW
conditional effect IPW

Hirano, Imbens & Ridder; further developed by Abrevaya, Hsu & Lieli

HTE-IPW extends standard inverse probability weighting to recover how causal effects vary across subgroups or covariate values. By reweighting each observation by the inverse of its estimated treatment probability, the method creates a pseudo-population in which treatment is independent of background characteristics, and then estimates conditional average treatment effects (CATEs) as a function of those characteristics.

Observational panel or cross-sectional data with a binary or multi-valued treatment

Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity score. Econometrica, 71(4), 1161-1189.

Abrevaya, J., Hsu, Y.-C., & Lieli, R. P. (2015). Estimating conditional average treatment effects. Journal of Business and Economic Statistics, 33(4), 485-505.


effect-modified marginal structural model

Robins, Hernan & Brumback (foundational MSM framework, 2000); heterogeneous-effect extensions developed throughout 2000s–2010s

The Heterogeneous Treatment Effect Marginal Structural Model extends the classic MSM framework of Robins, Hernan, and Brumback to estimate how treatment effects vary across subgroups or individual-level moderators. By weighting observations with inverse probability of treatment weights (IPTW) and interacting the treatment with effect modifiers in the weighted outcome model, the approach produces subgroup-specific or continuous causal effect estimates from observational data.

Causal inference / weighted regression with effect modification

Observational longitudinal or cross-sectional data with time-varying or static treatments and potential confounders

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

Hernan, M. A., & Robins, J. M. (2020). Causal Inference: What If. Chapman & Hall/CRC.


Heterogeneous Treatment Effect Matching Estimator

HTE matching
subgroup matching estimator
conditional matching estimator
CATE matching

Heckman, Ichimura & Todd; Abadie & Imbens

The Heterogeneous Treatment Effect (HTE) Matching Estimator extends standard matching to recover how treatment impacts differ across subgroups or covariate values. Rather than reporting a single average treatment effect, it pairs treated and control units on observed characteristics and then estimates the conditional average treatment effect (CATE) as a function of those characteristics — revealing who benefits most, least, or not at all.

Causal inference / nonparametric matching

Observational cross-sectional or panel; continuous or binary outcome

Heckman, J. J., Ichimura, H., & Todd, P. E. (1997). Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme. Review of Economic Studies, 64(4), 605-654.

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


Heterogeneous treatment effect Panel event study

Heterogeneous Treatment Effect Panel Event Study

HTE panel event study
heterogeneous effects event study
staggered panel event study
CATT event study

A heterogeneous treatment effect panel event study estimates how treatment impacts vary across units and over time in a panel setting, allowing each cohort of treated units to have its own dynamic response. Seminal contributions by Sun and Abraham (2021) and Callaway and Sant'Anna (2021) showed that standard two-way fixed-effects event studies mask sign-reversing treatment heterogeneity across cohorts, motivating cohort-specific estimation followed by flexible aggregation.

Panel data with multiple pre- and post-treatment periods

Sun, L., & Abraham, S. (2021). Estimating dynamic treatment effects in event studies with heterogeneous treatment effects. Journal of Econometrics, 225(2), 175-199.

Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2), 200-230.


Heterogeneous treatment effect Placebo test

Placebo Test for Heterogeneous Treatment Effects

HTE placebo test
heterogeneous-effect placebo check
subgroup placebo test
CATE placebo validation

Rosenbaum (placebo test concept); Athey & Imbens (HTE estimation framework)

A placebo test for heterogeneous treatment effects is a falsification strategy used to validate whether estimated variation in treatment effects across subgroups or covariate values is genuine rather than an artifact of model specification, overfitting, or coincidental patterns. By applying the same estimation procedure to pseudo-treatments, fake outcomes, or subgroups that logically should not differ, researchers check that observed heterogeneity reflects real causal variation.

Panel, cross-sectional, or experimental data with subgroup or covariate information

Imbens, G. W., & Rubin, D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press.

Athey, S., & Imbens, G. (2016). Recursive partitioning for heterogeneous causal effects. Proceedings of the National Academy of Sciences, 113(27), 7353-7360.


Heterogeneous Treatment Effect Estimation via Propensity Score Matching

conditional average treatment effect matching

Rosenbaum & Rubin (PSM foundation, 1983); Athey & Imbens (HTE extensions, 2016)

Heterogeneous Treatment Effect Propensity Score Matching extends standard PSM to estimate how treatment effects vary across subgroups or individual characteristics. Rather than reporting a single average treatment effect, it uses the matched sample to estimate conditional average treatment effects (CATE), revealing which types of units benefit most or least from a treatment.

Causal inference / matching with effect heterogeneity

Observational cross-sectional or panel data with binary treatment and covariates

Athey, S., & Imbens, G. W. (2016). Recursive Partitioning for Heterogeneous Causal Effects. Proceedings of the National Academy of Sciences, 113(27), 7353-7360.

Rosenbaum, P. R., & Rubin, D. B. (1983). The Central Role of the Propensity Score in Observational Studies for Causal Effects. Biometrika, 70(1), 41-55.


Heterogeneous Treatment Effect Regression Discontinuity Design

HTE-RDD
heterogeneous RDD
subgroup RDD
effect heterogeneity RD

Dong & Lewbel (2015); Chiang, Hsu & Sasaki (2019)

Heterogeneous Treatment Effect RDD extends the classic regression discontinuity framework to detect and estimate how the causal effect of crossing an assignment cutoff varies across subgroups or along covariates. Rather than reporting a single local average treatment effect at the threshold, HTE-RDD maps how treatment impact differs by individual characteristics, enabling richer policy conclusions about who benefits most or least from a threshold-based intervention.

Quasi-experimental causal inference with effect heterogeneity

Cross-sectional or panel data with a continuous running variable and a cutoff

Dong, Y., & Lewbel, A. (2015). Identifying the Effect of Changing the Policy Threshold in Regression Discontinuity Models. Review of Economics and Statistics, 97(5), 1081-1092.

Chiang, H. D., Hsu, Y.-C., & Sasaki, Y. (2019). Causal Inference by Quantile Regression Kink Designs. Journal of Econometrics, 210(2), 405-433.


Heterogeneous Treatment Effect Sensitivity Analysis for Causality

Sensitivity Analysis for Causality under Heterogeneous Treatment Effects

sensitivity analysis with effect heterogeneity

Rosenbaum (sensitivity analysis framework); extended to heterogeneous effects by Crump, Imbens, and others

Heterogeneous Treatment Effect Sensitivity Analysis examines how robust subgroup-specific causal estimates are to unobserved confounding. Rather than testing a single average treatment effect, it asks whether the estimated variation in treatment effects across units or subgroups could be explained away by hidden bias, and at what level of hidden bias the causal conclusions for each subgroup would break down.

Observational data with treatment and outcome variables; panel or cross-section

Rosenbaum, P. R. (2002). Observational Studies (2nd ed.). Springer.

Crump, R. K., Hotz, V. J., Imbens, G. W., & Mitnik, O. A. (2008). Nonparametric tests for treatment effect heterogeneity. Review of Economics and Statistics, 90(3), 389-405.


HTE-SCM
heterogeneous SCM
heterogeneous synthetic control
SCM with HTE

Abadie, Diamond & Hainmueller (SCM foundation); Ben-Michael, Feller & Rothstein (augmented/HTE extensions)

The Heterogeneous Treatment Effect Synthetic Control Method (HTE-SCM) extends the classical synthetic control framework by allowing the causal effect of an intervention to vary across time periods, subgroups, or outcome dimensions rather than collapsing it to a single average estimate. It combines the counterfactual donor-pool matching logic of Abadie et al. (2010) with modern heterogeneous-effects machinery to recover time-varying or subgroup-specific treatment paths.

Aggregate time-series panel (donor pool + treated unit)

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

Ben-Michael, E., Feller, A., & Rothstein, J. (2021). The Augmented Synthetic Control Method. Journal of the American Statistical Association, 116(536), 1789-1803.


Heterogeneous Treatment Effects

Heterogeneous Treatment Effects (CATE / Meta-Learners)

Heterojen Tedavi Etkileri (CATE / Meta-Learners)

Wager & Athey (causal forest); Künzel et al. (meta-learners)

Heterogeneous Treatment Effects is a machine-learning framework that estimates how a treatment effect varies across individuals — the conditional average treatment effect (CATE). It bundles meta-learner strategies such as the T-Learner, S-Learner, X-Learner and R-Learner alongside the causal forest of Wager and Athey (2018) and Künzel et al. (2019).

Meta-learners (T/S/X/R) and causal forest with cross-fitting

Wager, S. & Athey, S. (2018). Estimation and Inference of Heterogeneous Treatment Effects using Random Forests. Journal of the American Statistical Association.

Künzel, S. R., Sekhon, J. S., Bickel, P. J. & Yu, B. (2019). Metalearners for Estimating Heterogeneous Treatment Effects using Machine Learning. Proceedings of the National Academy of Sciences (PNAS).

propensity-score-matching iv-2sls causal-discovery frontdoor-adjustment regression-discontinuity


Heteroscedasticity-Consistent (HC) Standard Errors

Heterokedastisiteye Robust Standart Hatalar (HC)

Eicker; Huber; White (1980); MacKinnon & White (1985)

Heteroscedasticity-robust standard errors are a correction to the covariance matrix of an OLS regression that yields valid inference when the error variance is not constant. Introduced by Halbert White in 1980 and refined into the finite-sample variants HC1-HC4 by MacKinnon and White in 1985, they leave the coefficient estimates unchanged but rebuild the standard errors so that t and F tests remain trustworthy under heteroscedasticity.

Robust covariance estimator for linear regression

Sandwich (Huber-Eicker-White) covariance matrix, HC0-HC4

White, H. (1980). A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica, 48(4), 817-838.

MacKinnon, J. G. & White, H. (1985). Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties. Journal of Econometrics, 29(3), 305-325.

ols-regression cluster-robust-se wild-bootstrap quantile-regression weighted-least-squares


Heuristic Evaluation

HE
Expert Evaluation
Nielsen's Heuristics

Heuristic Evaluation is a usability inspection method in which small teams of expert evaluators examine an interface and judge its compliance with established usability principles (heuristics). Developed by Jakob Nielsen and Rolf Molich in 1990, this method is rapid and low-cost, identifying 60–90% of usability problems with as few as 3–5 evaluators. Nielsen's Ten Usability Heuristics—visibility of system status, match between system and real world, user control and freedom, consistency and standards, error prevention and recovery, recognition over recall, flexibility and efficiency, aesthetic and minimalist design, error recovery, and documentation—form the basis of most evaluations.

Expert-based inspection using established design principles

Nielsen, J. (1994). Heuristic evaluation of user interfaces. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 249–256).

Nielsen, J., & Molich, R. (1990). Heuristic evaluation of user interfaces. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 249–256).

cognitive-walkthrough pluralistic-walkthrough think-aloud-protocol system-usability-scale


HF-AHP

HF-AHP (Hesitant Fuzzy AHP (AHP-Hesitant Group Decision Making via HMPM)) is a weight subjective multi-criteria decision-making (MCDM) method introduced by Zhu, B., Xu, Z. in 2014. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant multiplicative pairwise comparison (HMPR) — linear-programming prioritisation (HMPM)

Zhu, B., Xu, Z. (2014). Analytic hierarchy process-hesitant group decision making. European Journal of Operational Research

ahpsort aras cobra cocoso codas copras edas gra


HF-ARAS

HF-ARAS (Hesitant Fuzzy Additive Ratio Assessment) is a ranking multi-criteria decision-making (MCDM) method introduced by Mishra, A. R., Rani, P., Krishankumar, R., Ravichandran, K. S., Kar, S. in 2021. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy utility-degree ranker (P_i / P_0 against ideal alternative row)

Mishra, A. R., Rani, P., Krishankumar, R., Ravichandran, K. S., Kar, S. (2021). A multi-criteria framework for evaluating the sustainable drug selection for COVID-19 patients using hesitant fuzzy information and ARAS method. Applied Soft Computing Journal


HF-CODAS

HF-CODAS (Hesitant extension of HF-CODAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Torra, V. in 2010. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant outranking/ranking — Hesitant Fuzzy Element (HFE: set of possible membership degrees)

Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems


HF-COPRAS

HF-COPRAS (Hesitant Fuzzy Complex Proportional Assessment) is a ranking multi-criteria decision-making (MCDM) method introduced by Mishra, A.R., Rani, P., Pardasani, K.R. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy benefit/cost proportional ranking

Mishra, A.R., Rani, P., Pardasani, K.R. (2018). Multiple-criteria decision-making for service quality selection based on Shapley COPRAS method under hesitant fuzzy sets. Granular Computing


HF-DFT

HF-DFT (Hesitant Fuzzy Decision Field Theory (Song-Xu 2021)) is a ranking multi-criteria decision-making (MCDM) method introduced by Song, C. Zhang, Y. Xu, Z. S. Hao, Z. Wang, X. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant Fuzzy Decision Field Theory (HFDFT): hesitant fuzzy momentary preference function drives dynamic preference accumulation; feedback matrix governs evolution; group decision making via consensus aggregation of HFEs; predicts deliberation effects.

Song, C., Zhang, Y., Xu, Z. S., Hao, Z., Wang, X. (2019). Route Selection of the Arctic Northwest Passage Based on Hesitant Fuzzy Decision Field Theory. IEEE Access


HF-EDAS

HF-EDAS (Hesitant Fuzzy EDAS (Evaluation Based on Distance from Average Solution)) is a ranking multi-criteria decision-making (MCDM) method introduced by Kutlu Gündoğdu, F.; Kahraman, C.; Civan, H. (HF-EDAS); Keshavarz Ghorabaee, M. et al. 2015 (base EDAS); Yu, D. 2014 (TFHFS value-space) in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant outranking/ranking — Triangular Fuzzy Hesitant Fuzzy Set (TFHFS, Yu 2014): each cell is a finite set of triangular fuzzy numbers in [0,1]^3

Kutlu Gündoğdu, F., Kahraman, C., Civan, H. N. (2018). A novel hesitant fuzzy EDAS method and its application to hospital selection. Journal of Intelligent & Fuzzy Systems


HF-ELECTRE-I

HF-ELECTRE-I (HF-ELECTRE I — Hesitant Fuzzy ELECTRE I (Chen-Xu-Xia 2015)) is a outranking multi-criteria decision-making (MCDM) method introduced by Chen, N. Xu, Z. S. Xia, M. M. in 2015. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Concordance/discordance outranking for Hesitant Fuzzy Elements; constructs HF concordance and discordance indices based on score function and deviation degree; derives credibility matrix for choice selection.

Chen, N., Xu, Z. S., Xia, M. M. (2015). The ELECTRE I multi-criteria decision making method based on hesitant fuzzy sets. International Journal of Information Technology & Decision Making


HF-ELECTRE-II

HF-ELECTRE-II (HF-ELECTRE II — Hesitant Fuzzy ELECTRE II (Chen-Xu 2015)) is a outranking multi-criteria decision-making (MCDM) method introduced by Chen, N. Xu, Z. S. in 2015. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Two-pass outranking ranking (ascending/descending distillation extended) for Hesitant Fuzzy Elements; strong/weak outranking relations via HF concordance indices; produces final ranking by intersection of two pre-orders.

Chen, N., Xu, Z. S. (2015). Hesitant fuzzy ELECTRE II approach: A new way to handle multi-criteria decision making problems. Information Sciences


HF-GRA

HF-GRA (Hesitant Fuzzy Grey Relational Analysis) is a ranking multi-criteria decision-making (MCDM) method introduced by Li, X., Wei, G. in 2014. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy reference-based grey relational ranking (TOPSIS-like closeness)

Li, X., Wei, G. (2014). GRA method for multiple criteria group decision making with incomplete weight information under hesitant fuzzy setting. Journal of Intelligent & Fuzzy Systems


HF-MABAC

HF-MABAC (Hesitant Fuzzy Multi-Attributive Border Approximation area Comparison) is a ranking multi-criteria decision-making (MCDM) method introduced by Mishra, A.R., Saha, A., Rani, P., Pamucar, D., Dutta, D., Hezam, I.M. in 2022. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy border-approximation distance ranking

Mishra, A.R., Saha, A., Rani, P., Pamucar, D., Dutta, D., Hezam, I.M. (2022). Sustainable supplier selection using HF-DEA-FOCUM-MABAC technique: a case study in the Auto-making industry. Soft Computing


HF-MARCOS

HF-MARCOS (Hesitant Fuzzy MARCOS) is a ranking multi-criteria decision-making (MCDM) method introduced by Li, G., Geng, X., Yuan, Y. in 2020 crisp; 2023 variant applicator. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant Fuzzy compromise ranking — MARCOS extended via Hesitant Fuzzy Elements (HFE)

Li, G., Geng, X., Yuan, Y. (2023). An integrated MCDM method based on hesitant fuzzy MARCOS for supplier evaluation under sustainability requirements. Journal of Intelligent & Fuzzy Systems


HF-MAXSCORE-PORT

HF-MAXSCORE-PORT (HF-MaxScore-Portfolio — Hesitant Fuzzy Maximum-Score Portfolio Selection (Zhou-Xu 2018)) is a portfolio multi-criteria decision-making (MCDM) method introduced by Zhou, W. Xu, Z. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy portfolio selection model for general investors. Maximises the aggregated score s(⊗_i w_i h_i) of the hesitant fuzzy portfolio, where ⊗_i w_i h_i is the HFE-power-weighted combination of per-stock aggregated HFEs. Output is optimal investment weight vector W = (w_1,...,w_n) summing to 1. Equivalent to the hesitant fuzzy version of Markowitz's maximum-return portfolio (no risk constraint).

Zhou, W., Xu, Z. (2018). Portfolio selection and risk investment under the hesitant fuzzy environment. Knowledge-Based Systems


HF-MOORA

HF-MOORA (Hesitant Fuzzy Multi-Objective Optimization by Ratio Analysis) is a ranking multi-criteria decision-making (MCDM) method introduced by Li, Z.-H. in 2014. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy ratio system ranker (benefit-vs-non-beneficial net score on vector-normalised defuzzified matrix)

Li, Z.-H. (2014). An Extension of the MULTIMOORA Method for Multiple Criteria Group Decision Making Based upon Hesitant Fuzzy Sets. Journal of Applied Mathematics


HF-QUALIFLEX

HF-QUALIFLEX (Hesitant Fuzzy extension of QUALIFLEX) is a outranking multi-criteria decision-making (MCDM) method introduced by Zhang, Z. X. Xu, Z. S. in 2015. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant Fuzzy concordance outranking — Hesitant Fuzzy Set (HFS: multiple μ values) with signed distance comparison

Zhang, Z. X., Xu, Z. S. (2015). Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis. Expert Systems with Applications

ahp anp bwm critic entropy merec swara fucom


HF-SAW

HF-SAW (Hesitant extension of HF-SAW) is a ranking multi-criteria decision-making (MCDM) method introduced by Torra, V. in 2010. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.


HF-TODIM

HF-TODIM (Hesitant Fuzzy TODIM via new measure function Z_δ (Zhang-Xu 2016 ITOR)) is a ranking multi-criteria decision-making (MCDM) method introduced by Zhang, Y., Xu, Z. in 2016. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Prospect-theory pairwise dominance (Gomes-Lima 1992) extended to Hesitant Fuzzy Elements (HFE ⊂ [0,1]) via the parametric Z_δ measure function (Zhang-Xu 2016)

Zhang, Y., Xu, Z. (2016). Efficiency evaluation of sustainable water management using the HF-TODIM method. International Transactions in Operational Research


HF-TOPSIS

HF-TOPSIS (Hesitant Fuzzy TOPSIS with optional incomplete weight information (Xu-Zhang 2013 KBS)) is a ranking multi-criteria decision-making (MCDM) method introduced by Xu, Z., Zhang, X. in 2013. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Distance-to-ideal ranking (Hwang-Yoon 1981) extended to Hesitant Fuzzy Elements (HFE ⊂ [0,1]) via the hesitant normalised Euclidean distance d_1 (Xu-Xia 2011b); supports three weight-information modes: fully specified, completely unknown (Eq.(22) maximizing deviation closed-form), and partly known (Model M-2 linear programme).

Xu, Z., Zhang, X. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems


HF-TRADEOFF-PORT

HF-TRADEOFF-PORT (HF-TradeOff-Portfolio — Hesitant Fuzzy Score-Deviation Trade-Off Portfolio Selection (Zhou-Xu 2018)) is a portfolio multi-criteria decision-making (MCDM) method introduced by Zhou, W. Xu, Z. in 2018. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Hesitant fuzzy portfolio selection for risk-aware investors. Two dual formulations: (A) max-score with deviation upper bound D (Model 3.16) and (B) min-deviation with score lower bound S (Model 3.18). D and S are calibrated per investor risk type (risk-seeker / neutral / risk-averse) via deviation trisection or score trisection approaches (Definitions 3.1-3.2). Generalises HF-MaxScore-Portfolio by incorporating a risk (deviation) constraint.


HF-VIKOR

HF-VIKOR (Hesitant Fuzzy VIKOR (Liao-Xu 2013)) is a ranking multi-criteria decision-making (MCDM) method introduced by ? in 2013. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Compromise ranking on Hesitant Fuzzy Elements; Manhattan L_p-metric defuzzification; S/R/Q measures with compromise-solution conditions

Liao, H., Xu, Z. (2013). A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optimization and Decision Making


HF-WASPAS

HF-WASPAS (Hesitant Fuzzy Weighted Aggregated Sum Product Assessment) is a ranking multi-criteria decision-making (MCDM) method introduced by Mishra, A.R., Rani, P., Pardasani, K.R., Mardani, A. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Mishra, A.R., Rani, P., Pardasani, K.R., Mardani, A. (2019). A novel hesitant fuzzy WASPAS method for assessment of green supplier problem based on exponential information measures. Journal of Cleaner Production


HFEA

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

DEA extension to Hesitant Fuzzy Sets — efficiency measured as weighted score-to-deviation ratio m_e = Σp_i·s_{ie} / Σq_i·d_{ie}; LP-solved in linearised DHFEA (deviation-normalised) or SHFEA (score-normalised) form; provides both ranking and improvement schedules for inefficient alternatives.

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