Markov Chain Monte Carlo

Markov Chain Monte Carlo (MCMC — Metropolis-Hastings, Gibbs Sampling)

Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)

1953 (Metropolis-Hastings); 1984 (Gibbs)

Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)

Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.

Simulation-based Bayesian inference / numerical integration

Metropolis-Hastings (general proposal); Gibbs (full conditional distributions)

Gelman-Rubin R̂ statistic (target R̂ < 1.05)

Required — early chain iterations discarded before stationarity

Optional — retaining every k-th sample to reduce autocorrelation

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

Brooks, S., Gelman, A., Jones, G.L. & Meng, X.-L. (Eds.) (2011). Handbook of Markov Chain Monte Carlo. Chapman & Hall/CRC.

monte-carlo-simulation bayesian-regression approximate-bayesian-computation latin-hypercube-sampling bootstrap-simulation


Markov Model in Health Economics

Markov Chain Model for Health Economic Evaluation

Markov model
state transition model
cohort simulation

Beck & Pauker (medical decision analysis, Massachusetts General Hospital)

A Markov model is a decision-analytic tool that simulates disease progression through defined health states over time, calculating cumulative costs and quality-adjusted life years (QALYs) to enable cost-effectiveness analysis. Developed by Beck and Pauker in 1983, Markov models are now the standard framework for projecting long-term outcomes of health interventions, especially chronic diseases where patients transition between clinical states (treatment response, disease progression, remission, death). Used by health technology assessment bodies and pharmaceutical companies to predict intervention value beyond trial duration.

Beck, J. R., & Pauker, S. G. (1983). The Markov Process in Medical Prognosis. Medical Decision Making, 3(4), 419-458.

Sonnenberg, F. A., & Beck, J. R. (1993). Markov Models in Medical Decision Making: A Practical Guide. Medical Decision Making, 13(4), 322-338.

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: Oxford University Press.

cost-effectiveness-analysis cost-benefit-analysis quality-adjusted-life-year decision-analytic-modeling budget-impact-analysis


Markov Model

Markov Chain
Discrete-Time Markov Chain
DTMC
Markov Process

A Markov Model represents a system as a finite set of states and specifies the probability of moving from one state to another at each time step. By capturing only the current state — not the full history — it enables tractable analysis of complex dynamic processes across health economics, engineering reliability, operations research, and social-science modeling.

Discrete or continuous state sequences; transition probability matrices

Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge.

monte-carlo-simulation queueing-simulation stochastic-markov-model discrete-event-simulation hidden-markov-model dynamic-programming


Markov-Switching Multifractal

The Markov-Switching Multifractal (MSM) model is a flexible framework for capturing time-varying volatility and long-memory effects in financial time series. Developed by Calvet and Fisher (2004), it combines Markov chain theory with multifractal scaling principles to generate volatility that exhibits multiple frequency components, each switching between high and low regimes. This approach is particularly effective for modeling asset returns with realistic fat tails and clustered volatility.

Calvet, L. E., & Fisher, A. J. (2004). How to forecast long-run volatility: regime-switching and the estimation of multifractal processes. Journal of Financial Econometrics, 2(1), 49–83.

Calvet, L. E., & Fisher, A. J. (2008). Multifractal Volatility: Theory, Forecasting, and Pricing. Academic Press.

Lux, T. (2008). The Markov-switching multifractal model of asset returns: GMM estimation and linear forecasting of volatility. Journal of Business & Economic Statistics, 26(2), 194–210.

garch-model vector-autoregression kalman-filter hidden-markov-model


Markov-Switching Model

Markov Regime-Switching Model (MS-AR / MS-VAR)

Markov Rejim Değiştirme Modeli (MS-AR / MS-VAR)

The Markov regime-switching model lets the parameters of a time series change probabilistically across hidden regimes governed by a Markov chain. Introduced by Hamilton (1989) and developed further by Kim and Nelson (1999), it automatically detects business-cycle phases such as expansions and contractions.

Maximum likelihood via the Hamilton filter (or Gibbs sampling)

Hamilton, J. D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57(2), 357-384.

Kim, C. J. & Nelson, C. R. (1999). State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. MIT Press.

arima vector-autoregression garch egarch ols-regression


MARS

Multivariate Adaptive Regression Splines (MARS)

multivariate adaptive regression splines

çok değişkenli uyarlamalı regresyon spline'ları

Multivariate adaptive regression splines, introduced by Jerome Friedman in 1991, is a flexible nonparametric regression method that automatically models nonlinearities and interactions by combining piecewise-linear 'hinge' functions. It builds the model in a forward stagewise pass that adds basis functions where they help most, then prunes back the overgrown model, yielding an interpretable additive-plus-interaction form that adapts its complexity to the data.

Nonlinearities and interactions automatically

Forward addition + backward pruning (GCV)

Friedman, J. H. (1991). Multivariate adaptive regression splines. The Annals of Statistics, 19(1), 1–67.

regression-splines generalized-additive-model decision-tree gradient-boosting


Marx Activity Rating Scale

Russell G. Marx, T. J. Stump, E. C. Jones, T. L. Wickiewicz, R. F. Warren

The Marx Activity Rating Scale (MARS) is a 4-item patient-reported instrument that quantifies the frequency of high-demand athletic activities performed in the past four weeks. Developed by Marx and colleagues in 2001 and published in the American Journal of Sports Medicine, the MARS focuses specifically on quantifying participation in running, cutting, decelerating, and pivoting—the high-impact, multi-directional activities that demand the most from the knee and ankle. The MARS is widely used in orthopedic research to classify patients by activity level and to assess return to activity following surgery.

Marx RG, Stump TJ, Jones EC, Wickiewicz TL, Warren RF. Development and evaluation of an activity rating scale for disorders of the knee. Am J Sports Med. 2001;29(2):213-218.

ikdc-subjective-knee-form acl-return-to-sport-scale lower-extremity-functional-scale patient-specific-functional-scale


Marxan MPA Planning

Marxan is a decision-support system that uses optimization algorithms to design cost-effective marine protected area (MPA) networks that achieve conservation targets while minimizing socioeconomic costs. Developed by Ian Ball and Hugh Possingham in 2000, Marxan has become the global standard tool for systematic conservation planning in marine environments. The software enables planners to explore trade-offs between conservation effectiveness and economic feasibility.

Possingham, H. P., Ball, I., & Andelman, S. (2000). Mathematical methods for identifying representative reserve networks. In S. Ferson & M. Burgman (Eds.), Quantitative Methods for Conservation Biology (pp. 291-306). Springer-Verlag.

Ball, I. R., Possingham, H. P., & Watts, M. (2009). Marxan and relatives: software for spatial conservation prioritisation. In A. Moilanen, K. A. Wilson, & H. P. Possingham (Eds.), Spatial Conservation Prioritisation: Quantitative Methods and Computational Tools (pp. 185-195). Oxford University Press.


Mask R-CNN

Mask Region-based Convolutional Neural Network

Mask R-CNN is a deep learning framework for instance segmentation introduced by Kaiming He, Georgia Gkioxari, Piotr Dollár, and Ross Girshick at Facebook AI Research (FAIR) in 2017. It extends Faster R-CNN by adding a parallel branch that predicts a binary pixel-level mask for each detected object instance, enabling simultaneous object detection, classification, and fine-grained segmentation in a single forward pass.

Instance segmentation deep neural network

Output: Bounding box + class label + pixel-level binary mask per instance

He, K., Gkioxari, G., Dollár, P., & Girshick, R. (2017). Mask R-CNN. IEEE International Conference on Computer Vision (ICCV), 2980–2988.


Masked Autoencoders

Masked Autoencoders are Scalable Vision Learners

Masked Autoencoders (MAE) is a self-supervised learning approach introduced by He et al. in 2021 that masks random patches of an image and trains a model to reconstruct the missing content. Adapting the masked language modeling paradigm from NLP to vision, MAE learns rich visual representations by solving a challenging reconstruction task without requiring labels.

He, K., Chen, X., Xie, S., Li, Y., Dollár, P., & Girshick, R. (2022). Masked autoencoders are scalable vision learners. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 16000-16009).

swin-transformer vision-transformer latent-diffusion-models simclr


Maslach Burnout Inventory

Maslach Burnout Inventory — Human Services Survey

The Maslach Burnout Inventory (MBI) is the most widely used instrument for measuring occupational burnout—a syndrome of emotional exhaustion, depersonalization, and reduced personal accomplishment in response to chronic workplace stress. Developed by Christina Maslach and Susan Jackson in the early 1980s, the MBI has become the standard reference for burnout assessment in research, occupational health, and clinical practice across helping professions and other high-stress occupations.

Maslach, C., & Jackson, S. E. (1981). The measurement of experienced burnout. Journal of Organizational Behavior, 2(2), 99–113.

Maslach, C. (1982). Burnout: The cost of caring. Prentice Hall.

Schaufeli, W. B., Leiter, M. P., & Maslach, C. (2009). Burnout: 35 years of research and practice. Career Development International, 14(3), 204–220.


Matched case-control study

matched case-referent study
individually matched case-control
pair-matched case-control
matched case-control design

Brian MacMahon and others; systematised by Schlesselman (1982)

A matched case-control study is an observational epidemiological design in which each case (a person with the disease or outcome of interest) is paired with one or more controls (persons without the outcome) who share one or more characteristics — such as age, sex, or clinical setting — to control confounding. Exposure history is then compared between cases and their matched controls to estimate the odds ratio of the exposure-disease association.

Categorical and continuous exposure / covariate data; binary outcome (case/control status)

Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins.

Schlesselman, J. J. (1982). Case-Control Studies: Design, Conduct, Analysis. Oxford University Press.

case-control-study nested-case-control cohort-study propensity-score-matching conditional-logistic-regression case-crossover-design


Matched Case-Crossover Design

Matched Case-Crossover Epidemiological Design

matched case-crossover study
time-matched case-crossover
bidirectional case-crossover
symmetric bidirectional design

1991 (base design); matched variant refined ~1998–2000

Malcolm Maclure (case-crossover); time-matched variant developed by Navidi (1998) and Lumley & Levy (2000)

The matched case-crossover design is a self-controlled observational study in which each case serves as its own control. A short hazard window immediately before the acute event is compared with one or more matched control windows — selected to have the same day of week, season, or other time-varying covariate — making the design robust to stable individual confounders and calendar-time trends simultaneously.

Time-stamped individual-level event and exposure data

Maclure, M. (1991). The case-crossover design: a method for studying transient effects on the risk of acute events. American Journal of Epidemiology, 133(2), 144–153.

Lumley, T., & Levy, D. (2000). Bias in the case-crossover design: implications for studies of air pollution. Environmetrics, 11(6), 689–704.

case-crossover-design nested-case-control matched-case-control-study case-time-control-design self-controlled-case-series conditional-logistic-regression


Matched case report

matched case write-up
case report with matched comparator
matched single-case report
comparator-matched case report

Late 20th century (widely used from 1990s onward in pharmacovigilance and rare-disease literature)

Evolved from standard clinical case reporting practice; no single originator

A matched case report is a structured clinical case write-up in which the index patient is compared against one or more systematically selected matched comparators — typically patients with similar demographics, comorbidities, or clinical settings who did not experience the same unusual outcome. The matched comparator contextualises the index case, strengthening causal inference beyond what a conventional single case report can support, and is used particularly in pharmacovigilance, rare-disease documentation, and novel-intervention reporting.

Observational descriptive design with comparator

Clinical data from one index case and one or more systematically matched reference patients

Gagnier, J. J., Kienle, G., Altman, D. G., Moher, D., Sox, H., & Riley, D. (2013). The CARE guidelines: consensus-based clinical case reporting guideline development. Journal of Medical Case Reports, 7, 223.

van Walraven, C., & Rokosh, E. (1999). What is necessary for high-quality case reports? Journal of Clinical Epidemiology, 52(6), 525-532.

case-report case-series matched-case-control-study case-crossover-design n-of-1-trial cohort-study


Matched Cohort Study

matched follow-up study
paired cohort study
propensity-matched cohort
matched prospective study

Mid-20th century; propensity-score variant 1983

Established practice; propensity-score matching formalized by Rosenbaum & Rubin (1983)

A matched cohort study is an observational design in which each exposed participant is paired with one or more unexposed counterparts who share key characteristics — such as age, sex, or comorbidity status — before both groups are followed forward in time to compare incident outcomes. Matching controls for measured confounders at the design stage, reducing bias that would otherwise require statistical adjustment alone.

Individual-level longitudinal data (time-to-event, binary, or continuous outcomes)

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.

cohort-study case-control-study nested-case-control propensity-score-matching prospective-cohort-study competing-risks-analysis


Matched Competing Risks Analysis

Matched Competing Risks Survival Analysis

matched Fine-Gray analysis
propensity-matched competing risks
matched cause-specific hazard analysis
matched subdistribution hazard analysis

1999 (Fine-Gray model); extended to matched designs ~2010s

Fine & Gray (subdistribution hazard model); Austin, Lee & Fine (matched competing risks framework)

Matched competing risks analysis combines subject-level matching (e.g., propensity-score matching) with competing risks survival methods to estimate the cause-specific or subdistribution hazard of an event of interest while accounting for competing events that preclude the occurrence of that event. It is widely used in clinical and epidemiological observational studies where patients may die from causes other than the primary outcome of interest, and where treatment groups differ on baseline confounders.

Observational survival analysis with matching and competing events

Time-to-event data with multiple mutually exclusive event types; matched pairs from observational cohorts

Fine, J. P., & Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94(446), 496–509.

Austin, P. C., Lee, D. S., & Fine, J. P. (2016). Introduction to the analysis of survival data in the presence of competing risks. Circulation, 133(6), 601–609.

competing-risks-analysis propensity-score-matching cause-specific-hazard kaplan-meier-estimator cox-proportional-hazards inverse-probability-weighting


Matched Cox Proportional Hazards

Stratified Cox Proportional Hazards Regression for Matched Designs

stratified Cox regression
conditional Cox model
matched survival analysis
Cox model for matched pairs

1972 (Cox model); matched extension widely adopted 1970s–1980s

D. R. Cox (Cox model, 1972); stratification extension for matched designs by subsequent methodologists including D. C. Thomas

Matched Cox proportional hazards is a survival analysis method that extends the Cox regression model to appropriately handle data arising from matched study designs — matched cohorts or matched case-control studies with time-to-event outcomes. By stratifying the partial likelihood by matched set, the method eliminates confounding from matching factors without estimating their baseline hazard, yielding valid hazard ratio estimates that are free from matching-induced bias.

Semi-parametric survival regression for matched data

Time-to-event (survival) data from matched cohort or matched case-control studies

Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187–202.

Thomas, D. C. (1977). Addendum to: Methods of cohort analysis: Appraisal by application to asbestos mining. Journal of the Royal Statistical Society: Series A, 140(4), 483–485.

cox-proportional-hazards matched-cohort-study matched-case-control survival-analysis kaplan-meier-analysis competing-risks-analysis


Matched Cross-Sectional Epidemiological Study

matched cross-sectional survey
matched prevalence study
matched cross-sectional design
frequency-matched cross-sectional study

Mid-to-late 20th century (formalized ~1970s–1990s)

Developed within the tradition of observational epidemiology; matching principles codified by Greenland, Rothman, and Kelsey in modern epidemiology texts

A matched cross-sectional epidemiological study is an observational design that measures exposure and outcome simultaneously in a population sample while applying matching to control for one or more confounding variables. By pairing or grouping participants on key characteristics such as age, sex, or socioeconomic status before or during analysis, the design reduces confounding bias without requiring longitudinal follow-up, making it efficient for estimating prevalence and cross-sectional associations.

Observational epidemiological study design

Cross-sectional survey data with individual or frequency matching on confounders

Kelsey, J. L., Whittemore, A. S., Evans, A. S., & Thompson, W. D. (1996). Methods in Observational Epidemiology (2nd ed.). Oxford University Press.


Matched Diagnostic Accuracy Study

matched DAS
paired diagnostic accuracy study
matched test accuracy study
matched sensitivity-specificity study

1990s–2000s (formalised with STARD 2003)

Evolved from matched case-control methodology; STARD standards formalised by Bossuyt et al. (2003)

A matched diagnostic accuracy study evaluates how well an index test correctly identifies a target condition in study participants who have been matched on key characteristics — such as age, sex, or disease severity — to control for confounding. By pairing diseased and non-diseased subjects on relevant factors before administering the test, the design isolates the test's own discriminative performance from variation attributable to imbalanced covariates, yielding cleaner estimates of sensitivity, specificity, and related accuracy measures.

Diagnostic / clinical epidemiology study design

Paired or matched binary/ordinal test results vs. reference standard

Bossuyt, P. M., Reitsma, J. B., Bruns, D. E., Gatsonis, C. A., Glasziou, P. P., Irwig, L. M., Lijmer, J. G., Moher, D., Rennie, D., & de Vet, H. C. W. (2003). Towards complete and accurate reporting of studies of diagnostic accuracy: The STARD initiative. BMJ, 326(7379), 41–44.

Pepe, M. S. (2003). The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press.


Matched dose-response analysis

Matched Dose-Response Analysis in Epidemiology

exposure-response analysis with matching

Developed within the matched case-control framework; formalized by Breslow and Day (1980) and Rothman and colleagues

Matched dose-response analysis evaluates whether increasing levels of exposure are associated with proportionally increasing (or decreasing) risk of an outcome, within a study where cases and controls — or exposed and unexposed individuals — have been deliberately matched on key confounders such as age, sex, or study site. Matching controls residual confounding structurally, while the dose-response component tests whether the exposure-outcome relationship follows a biologically plausible gradient, strengthening causal inference.

Matched pairs or sets with ordinal/continuous exposure data

Rothman, K.J., Greenland, S., & Lash, T.L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins.

Breslow, N.E., & Day, N.E. (1980). Statistical Methods in Cancer Research, Vol. 1: The Analysis of Case-Control Studies. IARC Scientific Publications No. 32. International Agency for Research on Cancer.

dose-response-analysis matched-case-control-study case-control-study conditional-logistic-regression cohort-study exposure-assessment


Matched ecological study

matched ecologic study
geographically matched ecological study
area-matched ecological design
matched aggregate study

Extension of classical ecological study design; matching principles formalized in 20th-century epidemiology

A matched ecological study is an observational epidemiological design in which aggregate units — such as geographic areas, communities, or time periods — are systematically paired or matched on key characteristics before comparing exposure and outcome rates. Matching at the group level controls for area-level confounders and improves comparability between exposed and unexposed units, producing more credible estimates of ecological associations than an unmatched counterpart.

Aggregate / group-level data (area statistics, population counts, environmental measurements)

Morgenstern, H. (1998). Ecologic studies in epidemiology: Concepts, principles, and methods. Annual Review of Public Health, 16, 61–81.

ecological-study cohort-study matched-cohort-study case-control-study matched-case-control-study cross-sectional-epidemiological-study


Matched Filter

Correlation Detector
Optimal Filter Detection
Template Matching

The matched filter is an optimal signal detector that maximizes the signal-to-noise ratio (SNR) for detecting a known signal in additive Gaussian noise. Developed by D. O. North during World War II for radar applications, the matched filter represents the optimal linear filter for signal detection and remains the foundation for detection theory and digital communications.

North, D. O. (1943). An Analysis of the Factors Which Determine Signal/Noise Discrimination in Pulsed Carrier Systems. RCA Laboratories, Technical Report PTM-946.

Oppenheim, A. V., Schafer, R. W., & Buck, J. R. (1999). Discrete-Time Signal Processing (2nd ed.). Prentice Hall.

wiener-filter kalman-filter-signal fir-filter-design adaptive-lms-filter


Matched Kaplan-Meier Analysis

Matched Cohort Kaplan-Meier Survival Analysis

KM analysis in matched cohorts
propensity-matched survival curves
matched survival analysis
paired Kaplan-Meier

1958 (KM); matched application formalized 1980s–2000s

Kaplan & Meier (KM method, 1958); matching extensions developed through propensity score methods (Rosenbaum & Rubin, 1983)

Matched Kaplan-Meier analysis estimates and compares survival functions in groups that have been pre-balanced through individual or propensity-score matching. By applying the Kaplan-Meier product-limit estimator to matched cohorts or matched pairs, investigators can visualize time-to-event outcomes while controlling for confounders that would otherwise distort treatment or exposure comparisons in observational data.

Nonparametric survival analysis with observational confounder control

Time-to-event data with censoring in matched pairs or matched cohorts

Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457-481.

Austin, P. C. (2014). Pointwise confidence intervals for restricted mean survival time in a propensity-matched analysis. Statistics in Medicine, 33(14), 2659-2671.

kaplan-meier-analysis matched-cohort-study matched-case-control-study cox-proportional-hazards propensity-score-matching survival-analysis


Matched nested case-control

matched NCC study
nested case-control with matching
matched risk-set sampling
incidence density matched case-control

Mantel (1973), Thomas (1977); formalized by Breslow & Day (1980)

A matched nested case-control study is an efficient observational design embedded within a defined cohort. When a participant develops the outcome of interest (a case), a small number of controls are sampled from those still at risk at that moment and matched to the case on key variables such as age, sex, or calendar time. This design preserves the temporal structure of the underlying cohort while sharply reducing the cost of exposure measurement.

Longitudinal cohort records, biobank samples, time-to-event data

Thomas, D.B. (1977). Methodology for assessing interaction in epidemiological studies of matched pairs. Biometrics, 33(3), 463-470.

nested-case-control case-control-study matched-case-control-study cohort-study propensity-score-matching incidence-density-sampling


Matched Phase II clinical trial

matched Phase II trial
historically matched Phase II study
propensity-matched Phase II trial
externally controlled Phase II trial

1960s–1980s (formalized with Simon optimal designs, 1989)

Gehan (1961) for Phase II designs; matching frameworks adapted from case-control methodology

A matched Phase II clinical trial is a single-arm or small-controlled early-efficacy study in which treated patients are paired with matched controls — drawn from historical databases, registries, or concurrent external cohorts — on key prognostic variables such as age, disease stage, and performance status. This design allows preliminary efficacy assessment without a concurrent randomized arm, trading randomization for feasibility while partially controlling for confounding through the matching process.

Patient-level clinical data (treatment outcomes, covariates for matching)

Gehan, E. A. (1961). The determination of the number of patients required in a preliminary and a follow-up trial of a new chemotherapeutic agent. Journal of Chronic Diseases, 13(4), 346–353.

Simon, R. (1989). Optimal two-stage designs for phase II clinical trials. Controlled Clinical Trials, 10(1), 1–10.

phase-ii-clinical-trial matched-case-control-study propensity-score-matching randomized-clinical-trial single-arm-trial matched-cohort-study


Matched Phase III Clinical Trial

matched controlled Phase III trial
Phase III matched-pair trial
matched confirmatory trial
matched late-phase RCT

Mid-20th century (matching in RCTs formalized ~1950s–1970s)

Fisher, R. A. (matching principles); adapted into confirmatory trial design over mid-20th century

A matched Phase III clinical trial is a confirmatory, late-stage controlled study in which each participant assigned to the experimental treatment is paired with one or more controls who share key prognostic characteristics — such as age, disease stage, or comorbidities — before treatment allocation. By ensuring baseline comparability at the level of matched pairs, the design reduces confounding and improves statistical efficiency in settings where simple randomization alone may produce imbalanced groups or where full randomization is logistically or ethically constrained.

Controlled confirmatory clinical trial with matching

Continuous, binary, or time-to-event outcome data from matched treatment-control pairs

Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins.

randomized-controlled-trial phase-iii-clinical-trial matched-cohort-study propensity-score-matching adaptive-phase-iii-clinical-trial parallel-group-design


Matched Phase IV Study

matched post-marketing surveillance study

1980s–1990s (formalized in post-marketing regulatory frameworks)

Regulatory tradition (FDA, EMA); matching methodology from Rosenbaum & Rubin (1983)

A Matched Phase IV study is a post-marketing observational design in which patients who received an approved drug (or intervention) are matched to comparable non-exposed patients — or patients on an alternative therapy — to evaluate real-world safety, effectiveness, or long-term outcomes. Conducted after regulatory approval, it combines the epidemiological rigour of matching with the breadth of post-authorization pharmacovigilance, generating evidence that randomized trials are rarely powered or timed to provide.

Longitudinal patient records, claims databases, electronic health records

Strom, B. L., & Kimmel, S. E. (Eds.). (2005). Textbook of Pharmacoepidemiology. Wiley.

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.

propensity-score-matching case-control-study cohort-study pharmacovigilance inverse-probability-weighting interrupted-time-series


Matched Randomized Clinical Trial

matched RCT
matched-pair randomized trial
matched randomized controlled trial
covariate-matched RCT

Mid-20th century concept; methodological formalization circa 2000–2010

Developed formally in biostatistics literature; Greevy, Imai and colleagues advanced modern frameworks in the 2000s

A matched randomized clinical trial pairs participants (or clusters) on key baseline characteristics before randomization, then allocates one member of each pair to treatment and the other to control. This design combines the causal validity of randomization with the covariate balance of matching, increasing statistical efficiency and reducing confounding from known prognostic variables without sacrificing the internal validity of a controlled experiment.

Baseline covariate data, randomized allocation records, continuous or binary outcome measures

Imai, K., King, G., & Nall, C. (2009). The essential role of pair matching in cluster-randomized experiments, with application to the Mexican universal health insurance evaluation. Statistical Science, 24(1), 29–53.

Greevy, R., Lu, B., Silber, J. H., & Rosenbaum, P. R. (2004). Optimal multivariate matching before randomization. Biostatistics, 5(2), 263–275.

randomized-clinical-trial prospective-randomized-clinical-trial matched-case-control-study adaptive-randomized-clinical-trial pragmatic-randomized-clinical-trial multicenter-randomized-clinical-trial


Matched Screening Test Evaluation

Matched Design Screening Test Evaluation

matched diagnostic accuracy study
paired screening evaluation
matched-pair test performance study
matched screening assessment

1980s–2000s (formalized alongside diagnostic accuracy methodology)

Methodological synthesis from matched case-control and diagnostic accuracy traditions (Pepe, Zhou, and others)

Matched screening test evaluation assesses the sensitivity, specificity, and predictive values of a screening or diagnostic test using a matched design, in which disease-positive cases are paired with one or more disease-free controls selected to share key characteristics such as age, sex, or clinical setting. Matching controls for confounders before measuring test performance produces more precise and less biased estimates of diagnostic accuracy, and enables direct paired comparisons of competing tests within the same subjects.

Observational diagnostic study with matched design

Binary or ordinal test results, disease status, matched subject pairs or sets

Zhou, X.-H., Obuchowski, N. A., & McClish, D. K. (2011). Statistical Methods in Diagnostic Medicine (2nd ed.). Wiley.

diagnostic-accuracy-study screening-test-evaluation matched-case-control-study case-control-study nested-case-control roc-analysis


Matched Survival Analysis

matched time-to-event analysis
propensity-matched survival analysis
matched Kaplan-Meier analysis
paired survival analysis

1983 (propensity-score matching); applied to survival outcomes throughout 1990s–2000s

Building on Kaplan & Meier (1958) and Cox (1972); matching framework formalised in observational study design literature (Rosenbaum & Rubin, 1983)

Matched survival analysis combines a matching design — typically propensity score matching or exact matching on key covariates — with time-to-event methods such as Kaplan-Meier estimation and the Cox proportional hazards model. By pairing treated and control subjects who are similar on observed confounders before estimating survival curves or hazard ratios, the approach reduces confounding bias in non-randomised studies and produces more credible comparisons of event-free survival between exposure groups.

Time-to-event data with censoring; matched pairs or matched sets from cohort or registry data

Austin, P. C. (2014). Graphical assessments of the balance of propensity score matched samples: A SAS macro. Journal of Statistical Software, 58(7), 1-29. Also see Austin, P. C. (2017). A tutorial on multilevel survival analysis: Methods, models and applications. International Statistical Review, 85(2), 185-203.

Collett, D. (2015). Modelling Survival Data in Medical Research (3rd ed.). CRC Press.

kaplan-meier-estimator cox-proportional-hazards propensity-score-matching competing-risks-analysis log-rank-test time-to-event-analysis


Matching Estimator

Nonparametric Matching Estimator for Average Treatment Effects

nearest-neighbor matching
NNM
matching on covariates
covariate matching

Rubin (1973); large-sample theory by Abadie & Imbens (2006)

The matching estimator identifies the causal effect of a treatment by pairing each treated unit with one or more untreated units that have similar observed characteristics. Formalised by Rubin (1973) and given rigorous large-sample theory by Abadie and Imbens (2006), it constructs a credible control group from observational data without requiring a parametric model for the outcome.

Nonparametric matching / causal inference

Cross-sectional or panel; continuous or binary outcome; multi-dimensional covariates

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

Rubin, D. B. (1973). Matching to Remove Bias in Observational Studies. Biometrics, 29(1), 159-183.

propensity-score-matching propensity-score-weighting coarsened-exact-matching difference-in-differences inverse-probability-weighting doubly-robust-estimation


Matching Methods

General Matching Methods (CEM / Optimal / Genetic)

Genel Eşleştirme Yöntemleri (CEM / Optimal / Genetic)

Iacus, King & Porro (CEM); Hansen (optimal/full matching)

Matching Methods are a family of causal-inference techniques beyond propensity-score matching that pair treated and control units with similar covariates so that a treatment effect can be read off the balanced sample. The family includes Coarsened Exact Matching (Iacus, King & Porro, 2012), optimal matching, and genetic matching.

Treatment effect on matched/balanced samples

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

Hansen, B. B. (2004). Full Matching in an Observational Study of Coaching for the SAT. Journal of the American Statistical Association, 99(467), 609-618.

propensity-score-matching inverse-probability-weighting sensitivity-analysis-observational local-average-treatment-effect heterogeneous-treatment-effects


Material Flow Analysis

Substance Flow Analysis
Bulk-MFA
Material Flux Analysis
Malzeme Akış Analizi

Material Flow Analysis (MFA) is a systematic method for quantifying the flows and stocks of materials within a defined system boundary over a specified time period. Introduced comprehensively by Paul H. Brunner and Helmut Rechberger in their 2004 handbook, MFA applies mass-balance principles to track how raw materials, products, wastes, and emissions move through industrial, urban, or national metabolisms, enabling evidence-based resource management and waste policy.

Output: Stocks and flows of materials within a defined system boundary

Brunner, P. H., & Rechberger, H. (2004). Practical Handbook of Material Flow Analysis. Lewis Publishers.


Material Requirements Planning

Material Requirements Planning (MRP) is a computerized system developed by Joseph Orlicky in the 1970s that calculates material requirements based on master production schedules and bill-of-materials data. MRP determines what materials to buy, how much to order, and when to order them to meet production demand while minimizing inventory carrying costs. It became a foundational technology for manufacturing planning and later evolved into manufacturing resource planning (MRP II) and enterprise resource planning (ERP) systems.

Orlicky, J. (1975). Material requirements planning: The new way of life in production and inventory management. New York: McGraw-Hill.

APICS (2020). APICS Dictionary (16th ed.). Chicago: APICS.

aggregate-planning kanban job-shop-scheduling inventory-routing scor-model


MDQI

Bodnar, Matus, Simhan; University of Pittsburgh

The Maternal Diet Quality Index (MDQI) is a composite measure of maternal nutrition that evaluates diet quality during pregnancy and postpartum using a scored framework. Adapted from general population dietary quality indices, the MDQI emphasizes nutrients critical for fetal development and maternal health: folate, iron, calcium, protein, and micronutrient-rich foods. Use in research and clinical nutrition assessment to characterize maternal diet quality and its associations with pregnancy outcomes and lactation.

24-hour recall or food frequency questionnaire

Bodnar, L. M., Matus, D. S., & Simhan, H. N. (2010). Maternal nutritional status and maternal-fetal transmission of lipophilic micronutrients. Clinical Obstetrics and Gynecology, 53(3), 621–630.

Coad, J., Al-Rasheid, K., Dunstall, M., & Dunstall, J. (2012). Anatomy and physiology for midwives (4th ed.). Elsevier Health Sciences.


Mathematics Anxiety Rating Scale

The Mathematics Anxiety Rating Scale (MARS) is a self-report questionnaire assessing anxiety and worry related to mathematics learning and performance. Originally developed by Plake and Parker in 1982 with 98 items and refined to a 30-item version (MARS-30) in 1995, the MARS measures multiple facets of math anxiety: anxiety in test/evaluation contexts, mathematics learning contexts, and everyday numerical situations. It is widely used in educational psychology, mathematics education research, and clinical assessment to identify students with math anxiety and to evaluate interventions.

Plake, B. S., & Parker, C. S. (1982). The development and validation of a revised version of the Mathematics Anxiety Rating Scale. Educational and Psychological Measurement, 45(3), 503–518.

Plake, B. S., & Parker, C. S. (2004). The Mathematics Anxiety Rating Scale: A brief version. Measurement and Evaluation in Counseling and Development, 36(4), 224–232.


Subject-specific anxiety and emotional response

The Mathematics Anxiety Rating Scale (MARS) is a self-report instrument measuring the degree of anxiety students experience in mathematical situations. Developed by Richardson and Suinn (1972) and revised by Plake and Parker (1995), it assesses emotional and physiological responses to math learning and performance. Mathematics anxiety—fear or dread anticipating math tasks—significantly undermines achievement, particularly in STEM fields, and is a target for intervention in educational and clinical settings.

Richardson, F. C., & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551-554.

Plake, B. S., & Parker, C. S. (1995). Development and validation of a revised version of the Mathematics Anxiety Rating Scale. Journal of Educational Psychology, 87(2), 331-337.

academic-self-efficacy-scale academic-motivation-scale student-engagement-scale critical-thinking-dispositions-scale


Matheuristics

Matheuristics (Math Programming + Heuristics)

Hybrid Metaheuristics
MIP-based Heuristics
Math-Programming Hybrids
Matematiksel Sezgisel Yöntemler

Matheuristics is a class of hybrid optimization methods that tightly couple exact mathematical programming components—such as mixed-integer programming (MIP) solvers—with metaheuristic search procedures. Formally introduced and named by Maniezzo, Stützle, and Voß in 2009, the framework leverages the global-search capability of metaheuristics and the structural exploitation of mathematical programming to tackle large-scale combinatorial optimization problems that neither approach can solve effectively alone.

Problem-dependent (NP-hard instances typical)

Maniezzo, V., Stützle, T., & Voß, S. (Eds.). (2009). Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Springer.


Matrix Completion

Collaborative Filtering via Low-Rank Recovery

Matrix Completion is a technique for recovering a low-rank matrix from a small, possibly random subset of its entries. Introduced by Emmanuel Candès and Benjamin Recht in 2009, it reformulates the problem as nuclear norm minimization — a convex surrogate for rank minimization — and provides theoretical guarantees that exact recovery is achievable when entries are observed uniformly at random and the matrix satisfies an incoherence condition.

Input: Partially observed matrix

Output: Completed low-rank matrix

Candès, E. J., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9(6), 717–772.


Matrix Element Method

Matrix Element Method for Physics Analysis

MEM
matrix element calculation
amplitude evaluation

The Matrix Element Method (MEM) is a powerful analysis technique that leverages quantum field theory amplitudes to extract maximum physics information from individual events. By comparing observed detector signatures to predictions from matrix elements, MEM provides unbiased, model-independent measurements with excellent theoretical precision and sensitivity to new physics.

Kondo, K. (1988). Dynamical likelihood method for reconstruction of events produced by the top-quark pair in the lepton + jets channel at hadron colliders. Journal of the Physical Society of Japan, 57(12), 4126–4140.

Campbell, J. M., Huston, J., & Krauss, F. (2011). The black book of the LHC: A physics guide. arXiv preprint arXiv:1005.3457. Journal of Physics: Conference Series, 1525(1), 012034.

Martini, T., et al. (2015). Precision electroweak measurements and constraints on the Standard Model. Journal of High Energy Physics, 2015(12), 39.


Matthews Correlation Coefficient

Phi Coefficient
Binary Classification Correlation

The Matthews Correlation Coefficient (MCC) is a correlation measure between predicted and actual binary classifications. It ranges from -1 to 1 and is considered one of the most reliable single-score metrics for evaluating binary classifiers, especially on imbalanced datasets.

Matthews, B. W. (1975). Comparison of predicted and observed secondary structure of T4 phage lysozyme. Biochimica et Biophysica Acta (BBA)-Protein Structure, 405(2), 442-451.

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

f1-score balanced-accuracy youdens-j-statistic precision recall


MAUT

MAUT (Multi-Attribute Utility Theory) is a ranking multi-criteria decision-making (MCDM) method introduced by Keeney, R. L., Raiffa, H. in 1976. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Additive multi-attribute utility function

Keeney, R. L., Raiffa, H. (1976). Decisions with Multiple Objectives: Preferences and Value Trade-offs. Wiley

ahp anp bwm bwm-bayesian ccsd cilos cimas critic


Maximum Covariance Analysis

MCA
Singular value decomposition
SVD analysis
Covariance analysis

Maximum covariance analysis (MCA) is a statistical technique that identifies coupled patterns of variability between two spatially distributed fields (e.g., sea surface temperature and precipitation). Unlike EOF analysis which focuses on variance in a single field, MCA identifies spatial patterns that are maximally correlated between two different fields.

Bretherton, C. S., Widmann, M., Dymnikov, V. P., Wallace, J. M., & Blade, I. (1992). The effective number of spatial degrees of freedom of a time-varying field. Journal of the Atmospheric Sciences, 49(11), 1063-1083.

Newman, M., Sardeshmukh, P. D., & Penland, C. (2016). Relative Contributions to Subseasonal Predictability: Bridging Medium-Range and Climate Time Scales. Journal of Climate, 29(15), 5629-5647.


Maximum Likelihood Estimation

MLE
maximum-likelihood estimator
ML estimation
Fisher's method of maximum likelihood

Maximum Likelihood Estimation (MLE) is a general-purpose parametric method for estimating the unknown parameters of a statistical model by finding the parameter values that make the observed data most probable. Formalized by R. A. Fisher in his landmark 1922 paper in the Philosophical Transactions of the Royal Society, MLE has become the dominant parameter-estimation paradigm in modern statistics and is the foundational engine behind logistic regression, generalized linear models, structural equation modeling, and virtually all parametric inference procedures.

Asymptotically unbiased, consistent, efficient (achieves Cramér–Rao lower bound asymptotically)

Maximize the likelihood L(θ | x) = f(x | θ) over θ

Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, Series A, 222, 309–368.

Casella, G., & Berger, R. L. (2002). Statistical Inference (2nd ed.). Duxbury Press / Cengage Learning.

logistic-regression linear-regression generalized-linear-models structural-equation-modeling em-algorithm bayesian-estimation method-of-moments


Maximum Power Point Tracking

Maximum Power Point Tracking for Photovoltaic Systems

Maximum Power Point Tracking (MPPT) is a control algorithm for photovoltaic and wind energy systems that continuously adjusts the electrical load to extract maximum power regardless of changing irradiance and temperature. Without MPPT, a solar panel or wind turbine operates below its power potential due to impedance mismatch with the load. MPPT boosts the annual energy yield by 15-25% depending on system and climate.

Villalva, M. G., Gazoli, J. R., & Ruppert Filho, E. (2009). Comprehensive approach to modeling and simulation of photovoltaic arrays. IEEE Transactions on Power Electronics, 24(5), 1198-1208.

Esram, T., & Chapman, P. L. (2007). Comparison of photovoltaic array maximum power point tracking techniques. IEEE Transactions on Energy Conversion, 22(2), 439-449.


Maximum Variation Sampling

maximum variation sampling
maximum diversity sampling
MVS
heterogeneous sampling

1985 (Lincoln & Guba); elaborated 1990–2002 (Patton)

Lincoln & Guba; systematised by Michael Quinn Patton

Maximum variation sampling is a purposive qualitative sampling strategy in which the researcher deliberately selects cases that span the widest possible range of variation on dimensions central to the study. The goal is not statistical representation but the identification of common patterns that cut across diverse cases as well as the documentation of the unique ways each context shapes the phenomenon under investigation.

Qualitative data — interviews, observations, documents

Patton, M. Q. (2002). Qualitative Research and Evaluation Methods (3rd ed.). Sage. Chapter 5: Purposeful Sampling.

Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry. Sage.

purposive-sampling theoretical-sampling snowball-sampling deviant-case-sampling typical-case-sampling stratified-sampling


Mayo Score

Mayo Score for Ulcerative Colitis Activity

Schroeder, K. W., Tremaine, W. J., and Ilstrup, D. M.

The Mayo Score is a validated tool for assessing disease activity in ulcerative colitis, integrating clinical symptoms and endoscopic findings. Introduced by Schroeder and colleagues in 1987, it has become the reference standard for UC activity assessment in clinical trials and practice. The score combines stool frequency, rectal bleeding, overall physician global assessment, and endoscopic subscore into a single 0–12 scale.

Schroeder, K. W., Tremaine, W. J., & Ilstrup, D. M. (1987). Coated oral 5-aminosalicylic acid therapy for mildly to moderately active ulcerative colitis. New England Journal of Medicine, 317(26), 1625–1629.

sccai harvey-bradshaw-index ibdq-short cdai-crohns


McCabe-Thiele Method

McCabe-Thiele Graphical Method for Distillation Design

McCabe-Thiele Diagram
Graphical Distillation Method

The McCabe-Thiele Method, introduced by Warren L. McCabe and Ernest W. Thiele in 1925, is a graphical technique for designing and analyzing distillation columns. It predicts the number of theoretical plates (stages) needed to achieve a desired separation between light and heavy components. While primarily a chemical engineering tool, it applies to liquid-vapor separation problems in mining operations such as mercury recovery and rare earth element refining.

Graphical design method for distillation columns

McCabe, W. L., & Thiele, E. W. (1925). Graphical design of fractionating columns. Transactions of the American Institute of Chemical Engineers, 21, 30-60.

Seader, J. D., Henley, E. J., & Roper, D. K. (2011). Separation process principles (3rd ed.). John Wiley & Sons.


McDonald-Kreitman Test

McDonald-Kreitman Test for Detecting Adaptive Evolution

The McDonald-Kreitman (MK) test is a statistical method for detecting adaptive evolution by comparing ratios of synonymous and nonsynonymous substitutions within and between species. Developed by James McDonald and Martin Kreitman in 1991, this test exploits the key insight that neutral mutations accumulate at similar rates within and between species, while adaptive (nonsynonymous) substitutions should be enriched between species if they have been fixed by positive selection. The MK test has become a standard tool in molecular evolutionary biology for identifying genes under natural selection.

McDonald, J. H., & Kreitman, M. (1991). Adaptive protein evolution at the Adh locus in Drosophila. Nature, 351(6328), 652–654.

Smith, N. G., & Eyre-Walker, A. (2002). Estimating the proportion of sites subject to positive selection across a large dataset. Genetics, 160(3), 1079–1086.

Charlesworth, B. (2010). The rate of adaptive evolution. Trends in Ecology & Evolution, 11(1), 22–26.

selection-sweep hka-test f-statistics coalescent-theory


McDonald's Omega

McDonald's Omega Hiyerarşik (ωh) — Kompozit Puan Geçerliliği

McDonald's hierarchical omega (ωh) is a coefficient derived from a bifactor confirmatory factor model that quantifies what proportion of total-score variance is attributable to a single general factor rather than to group-specific factors or item-level error. Introduced by Roderick P. McDonald (1999) and elaborated for bifactor applications by Reise and colleagues (2013) and Rodriguez and colleagues (2016), it is the primary index used in psychometrics to evaluate whether a composite total score is a defensible summary of a multidimensional scale.

Reliability / composite score validity coefficient

Bifactor (hierarchical) confirmatory factor model

Output: ωh coefficient (0–1); ECV (Explained Common Variance)

≥ 0.50 indicates composite adequately reflects the general factor

Reise, S. P., Scheines, R., Widaman, K. F. & Haviland, M. G. (2013). Multidimensionality and structural coefficient bias in structural equation modeling: A bifactor perspective. Educational and Psychological Measurement, 73(1), 5–26.

Rodriguez, A., Reise, S. P. & Haviland, M. G. (2016). Evaluating bifactor models: Calculating and interpreting statistical indices. Psychological Methods, 21(2), 137–150.

confirmatory-factor-analysis exploratory-factor-analysis cronbach-alpha bifactor-model sem


McGill Pain Questionnaire

The McGill Pain Questionnaire (MPQ) is a multidimensional pain assessment instrument developed by Ronald Melzack in 1975. It measures pain across sensory, affective, and evaluative dimensions, allowing clinicians and researchers to capture the qualitative experience of pain beyond simple intensity ratings. The MPQ remains one of the most widely used pain assessment tools in clinical and research settings.

Self-report questionnaire measuring multiple pain dimensions

Melzack, R. (1975). The McGill Pain Questionnaire: Major properties and scoring methods. Pain, 1(3), 277-299.

Melzack, R. (1987). The short-form McGill Pain Questionnaire. Pain, 30(2), 191-197.

Boureau, F., Doubrère, J.F., & Luu, M. (1990). Comparative study of validity and reliability of four French McGill Pain Questionnaire versions. Pain, 42(2), 169-184.

pain-catastrophizing-scale dallas-pain-questionnaire neuropathic-pain-scale pain-self-efficacy-questionnaire pain-anxiety-symptoms-scale


McGill Quality of Life Questionnaire

The McGill Quality of Life Questionnaire (MQOL) is a 17-item, multidimensional self-report measure specifically developed for people with advanced cancer and other life-limiting illnesses. Created by Cohen, Mount, and colleagues at McGill University in 1995, the MQOL captures physical, functional, emotional, spiritual, and social dimensions of quality of life in a concise, patient-centered format. It has become a standard outcome measure in palliative care research, hospice quality improvement, and cancer centers internationally.

Cohen, S. R., Mount, B. M., Strobel, M. G., & Bui, F. (1995). The McGill Quality of Life Questionnaire: a measure of quality of life appropriate for people facing advanced cancer. Journal of Palliative Care, 11(3), 6–15.

Mount, B. M., Kearney, M., Cohen, S. R., Bui, F., & Strobel, M. G. (2007). The McGill Quality of Life Questionnaire: revised format. Journal of Palliative Medicine, 10(1), 167–172.

spiritual-wellbeing-scale facit-palliative patient-dignity-inventory palliative-performance-scale good-death-inventory


MCMC for Model Comparison

Markov Chain Monte Carlo for Bayesian Model Comparison

reversible-jump MCMC
RJMCMC
marginal likelihood estimation via MCMC
Bayesian model selection via MCMC

Peter J. Green (reversible-jump MCMC); Meng & Wong (bridge sampling)

MCMC for model comparison uses Markov chain Monte Carlo algorithms to estimate the marginal likelihoods and Bayes factors needed to formally compare competing statistical models. Techniques such as reversible-jump MCMC and bridge sampling allow exploration across model spaces of different dimensionality, enabling fully Bayesian model selection and averaging.

Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82(4), 711–732.

Meng, X.-L., & Wong, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica, 6(4), 831–860.

bayesian-model-averaging mcmc hamiltonian-monte-carlo gibbs-sampling bayesian-inference-for-model-comparison approximate-bayesian-computation


MCMC with Measurement Error

Markov Chain Monte Carlo with Measurement Error Models

MCMC errors-in-variables
Bayesian measurement error MCMC
MCMC misclassification model
Bayesian errors-in-variables

Richardson & Gilks; Carroll, Ruppert & Stefanski

MCMC with measurement error applies Markov chain Monte Carlo sampling to Bayesian models that explicitly account for the fact that covariates or outcomes are observed with error. By treating the true, unobserved values as latent variables and sampling their joint posterior alongside all other parameters, the method corrects for attenuation bias and produces valid inference even when some variables cannot be measured exactly.

Continuous or categorical data with fallibly measured covariates or outcomes

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

Richardson, S. & Gilks, W. R. (1993). A Bayesian approach to measurement error problems in epidemiology using conditional independence models. American Journal of Epidemiology, 138(6), 430-442.


MCMC with missing data

Markov Chain Monte Carlo with Missing Data

MCMC missing data
data augmentation MCMC
Bayesian multiple imputation
MCMC imputation

Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin

MCMC with missing data is a Bayesian computational strategy that treats unobserved values as additional unknown parameters. By alternating between sampling the missing values from their predictive distribution and sampling the model parameters from their posterior, the algorithm produces a valid joint posterior that fully accounts for uncertainty introduced by the missingness.

any data with MAR or MCAR missingness patterns

Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley.

Tanner, M. A. & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528-540.

gibbs-sampling bayesian-inference-with-missing-data multiple-imputation hamiltonian-monte-carlo metropolis-hastings-algorithm bayesian-hierarchical-model


MCMC

markov chain monte carlo
MCMC sampling
MCMC (Markov Zinciri Monte Carlo)

Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.

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

Brooks, S., Gelman, A., Jones, G. & Meng, X.-L. (Eds.). (2011). Handbook of Markov Chain Monte Carlo. CRC Press.

bayesian-regression hierarchical-bayes bayesian-model-averaging variational-inference


McNemar's test

McNemar chi-square test
test for correlated proportions
paired binary test
McNemar Testi

McNemar's test is a nonparametric hypothesis test that compares two paired (correlated) binary proportions, such as a yes/no measurement taken on the same subjects before and after an intervention. It was introduced by Quinn McNemar in 1947 and works on the 2×2 table of matched outcomes.

Nonparametric test for paired binary data

McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153–157.

chi-square-test cochran-q-test binomial-test paired-t-test wilcoxon-signed-rank


MCP Penalized Regression

Minimax Concave Penalty Penalized Regression

MCP (Minimax Concave Penalty) is a variable selection method developed by Zhang (2010) that uses a concave penalty function for automated feature selection. Like SCAD, MCP addresses bias in lasso by avoiding shrinkage of large coefficients, but uses a different penalty shape that is computationally simpler than SCAD.

Penalized regression with minimax concave penalty

Zhang, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. Annals of Statistics, 38(2), 894-942.

Breheny, P., & Huang, J. (2011). Coordinate descent algorithms for nonconvex penalized regression. Annals of Applied Statistics, 5(1), 232-253.

Zhang, C. H., & Zhang, T. (2012). A general theory of concave regularized M-estimators. Statistical Science, 27(4), 506-537.


MCUSUM Chart

Multivariate Cumulative Sum Chart
MCUSUM Control Chart
Crosier MCUSUM Scheme
Çok Değişkenli CUSUM Kontrol Grafiği

The Multivariate CUSUM (MCUSUM) Chart is a sequential monitoring scheme designed to detect small, persistent mean shifts in a process characterized by multiple correlated quality variables simultaneously. Introduced by Robert Crosier in 1988, it extends the classical univariate CUSUM principle to the multivariate setting by accumulating a vector-valued sum of deviations from the in-control mean, scaled by the process covariance structure, and comparing a scalar norm of that cumulative sum against a control limit.

Multivariate sequential monitoring chart

Cumulative sum of standardized multivariate deviations

Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291–303.


Mood Disorder Questionnaire

The Mood Disorder Questionnaire (MDQ) is a 13-item self-report screening instrument designed to identify individuals at risk for bipolar spectrum disorders. Developed by Hirschfeld and colleagues in 2000, the MDQ assesses symptoms of mania and hypomania as well as the clustering of symptoms into distinct episodes. It is widely used in primary care, psychiatric practice, and research to improve detection of bipolar disorder.

Manic episode and bipolar disorder screening

Hirschfeld, R. M., Williams, J. B., Spitzer, R. L., Calabrese, J. R., Flynn, L., Keck, P. E., ... & Zajecka, J. (2000). Development and validation of a screening instrument for bipolar spectrum disorder: The Mood Disorder Questionnaire. American Journal of Psychiatry, 157(11), 1873-1875.

Zimmerman, M., Galione, J. N., Chelminski, I., Young, D., Dalrymple, K., & Francione, C. (2008). Performance of the Mood Disorder Questionnaire screener for bipolar disorder in psychiatric outpatients. Bipolar Disorders, 10(1), 107-114.

hamilton-anxiety-rating-scale hads ces-d k10-kessler swls


Mean Absolute Error

Mean Absolute Error is a robust metric that measures the average absolute magnitude of prediction errors in regression models. Dating back to Pierre-Simon Laplace's work on observational errors (1799), MAE quantifies typical prediction deviation by averaging the absolute differences between observed and predicted values.

Laplace, P. S. (1799). Traité de Mécanique Céleste. Paris: J.B.M. Duprat.

Brossier, C. L. (1999). Consistency of trimmed and Winsorized L-estimators of location and scale. Journal of the American Statistical Association, 74(368), 813-821.

Huber, P. J. (2009). Robust Statistics (2nd ed.). Hoboken, NJ: John Wiley & Sons.

root-mean-squared-error mean-squared-error mean-absolute-percentage-error median-absolute-deviation


Mean Absolute Percentage Error

Mean Absolute Percentage Error measures prediction accuracy as a percentage relative to actual values, expressing errors in units that are scale-independent and interpretable across datasets. Formalized by J. Scott Armstrong in 1985, MAPE is widely used in forecasting, supply chain, and business analytics where results must be communicated as percentage accuracy.

Armstrong, J. S. (1985). Long-range forecasting: from crystal ball to computer (2nd ed.). New York: John Wiley & Sons.

Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688.

Kim, S., & Kim, H. (2016). A new metric of absolute percentage error for intermittent demand forecasts. International Journal of Forecasting, 32(3), 669-679.

mean-absolute-error root-mean-squared-error symmetric-mape mean-absolute-scaled-error


Mean Absolute Scaled Error

Mean Absolute Scaled Error is a scale-independent metric that measures prediction accuracy relative to a simple baseline (naive forecast). Introduced by Hyndman and Koehler (2006), MASE directly compares model performance to a reference method, overcoming limitations of MAPE and other percentage-based metrics.

Scale-independent baseline comparison metric

Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). Melbourne, Australia: OTexts.

Wang, X., & Petropoulos, F. (2016). To select or to combine? Forecasting from a thousand models. International Journal of Forecasting, 32(3), 594-606.

mean-absolute-error mean-absolute-percentage-error root-mean-squared-error symmetric-mape


Mean Shift

Mean Shift Clustering and Mode-Seeking Algorithm

mean-shift clustering
mean shift mode seeking
kernel mean shift
nonparametric mode detection

Fukunaga, K. & Hostetler, L. D.; extended by Comaniciu, D. & Meer, P.

Mean Shift is a non-parametric, iterative mode-seeking algorithm that identifies clusters as the peaks of an underlying probability density function. Originally introduced by Fukunaga and Hostetler (1975) for gradient estimation in pattern recognition, it was substantially extended and popularized by Comaniciu and Meer (2002) for robust feature-space analysis and image segmentation. Unlike k-means, Mean Shift requires no prior specification of the number of clusters, deriving cluster structure entirely from the data density.

Non-parametric mode-seeking / density-based clustering

Clustering, image segmentation, feature-space analysis

Fukunaga, K. & Hostetler, L. D. (1975). The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Transactions on Information Theory, 21(1), 32–40.

Comaniciu, D. & Meer, P. (2002). Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(5), 603–619.

Hastie, T., Tibshirani, R. & Friedman, J. (2009). The Elements of Statistical Learning (2nd ed., Ch. 14). Springer.

k-means dbscan gaussian-mixture-model spectral-clustering hierarchical-clustering


Mean Squared Error

Mean Squared Error is the foundational loss function for regression models, measuring the average squared deviation between predictions and observations. Originating from Gauss and Legendre's method of least squares (1805-1809), MSE is the basis for ordinary least squares regression and remains central to modern machine learning optimization.

Gauss, C. F. (1809). Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium. Hamburg: Perthes and Besser.

Legendre, A. M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Paris: F. Didot.

Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55(292), 708-713.

root-mean-squared-error mean-absolute-error r-squared akaike-information-criterion


Meaning in Life Questionnaire

The Meaning in Life Questionnaire (MLQ) is a 10-item self-report measure developed by Steger and colleagues in 2006 to assess both the presence of meaning and the active search for meaning in life. It addresses a core existential dimension of well-being: the degree to which individuals experience their life as purposeful and meaningful. The MLQ distinguishes presence of meaning from search for meaning, revealing that growth and psychological adjustment can involve active meaning-seeking even when current meaning-presence is lower.

Steger, M. F., Frazier, P., Kaler, M., & Oishi, S. (2006). The Meaning in Life Questionnaire: Assessing the presence of and search for meaning in life. Journal of Counseling Psychology, 53(1), 80–92.

flourishing-scale who-5-wellbeing-index perma-scale hope-scale


Measurement Invariance

Factorial Invariance
Measurement Equivalence
Configural-Metric-Scalar Testing
Ölçüm Değişmezliği

Measurement invariance testing is a sequence of nested confirmatory factor analysis (CFA) models that examines whether a psychological scale measures the same latent construct in the same way across distinct groups or time points. Systematized and popularized by Vandenberg and Lance (2000), the procedure tests a hierarchy of constraints — from identical factor patterns to identical item intercepts — so that researchers can justify meaningful group comparisons on latent means.

Multi-group confirmatory factor analysis procedure

Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature. Organizational Research Methods, 3(1), 4–70.


Meat Quality Assessment

Comprehensive Meat Quality Assessment and Grading

carcass evaluation
meat grading
objective meat quality measurement

Meat quality assessment is a systematic evaluation of carcass and meat characteristics that determine suitability for consumption and market value. Formalized by the USDA and meat scientists in the early 20th century, the practice integrates objective measurements—color, marbling, tenderness, water-holding capacity—with sensory evaluation to assign quality grades. Assessment guides pricing, processing decisions, and genetic selection to improve consumer satisfaction.

American Meat Board. (1988). Nutritional information on meat. Journal of Food Science, 53(2), 398-407.

Huff-Lonergan, E., & Lonergan, S. M. (2005). Mechanisms of water-holding capacity of meat: The role of postmortem biochemical and structural changes. Meat Science, 71(1), 194-204.

Whipple, G., Koohmaraie, M., Dikeman, M. E., Crouse, J. D., Hunt, M. C., & Klemm, R. D. (1990). Evaluation of attributes that affect longissimus muscle tenderness in Bos taurus and Bos indicus cattle. Journal of Animal Science, 68(9), 2716-2728.


Media Framing Analysis

Media Frames and Framing Effects Analysis

frame analysis
news framing
discourse framing

Media Framing Analysis is a systematic method for examining how news coverage and media messages organize and present information in ways that promote particular interpretations while obscuring others. Originating in Erving Goffman's sociological work (1974) and developed extensively by communication scholars like Robert Entman, the method decodes the frames—organizing principles and narrative structures—embedded in news reports, films, advertising, and public discourse. It reveals how media selections of what to emphasize, what to omit, and what narrative context to provide shape audience understanding of events and issues.

Analytical method for identifying how media structures and presents information

Goffman, E. (1974). Frame Analysis: An Essay on the Organization of Experience. Harvard University Press.

Entman, R. M. (1993). Framing: Toward clarification of a fractured paradigm. Journal of Communication, 43(4), 51-58.

Lakoff, G. (2004). Don't Think of an Elephant!: Know Your Values and Frame Your Arguments. Chelsea Green Publishing.

Scheufele, D. A. (2000). Agenda-setting, priming, and framing revisited: Another look at cognitive effects of political communication. Mass Communication & Society, 3(2-3), 297-316.

discourse-analysis-media agenda-setting-analysis film-narrative-analysis reception-analysis visual-content-analysis


Media Literacy Questionnaire

Rachel Wilson, Susan Luo, Yoong Wan Cheong, and Stella Tan

The Media Literacy Questionnaire is a self-report instrument that assesses individuals' critical abilities regarding digital media: evaluating source credibility, identifying misinformation, recognizing advertising and algorithmic influence, and understanding media ownership and bias. Developed by Wilson and colleagues in 2018, it measures the cognitive and critical skills essential for navigating contemporary media environments effectively.

Wilson, R., Luo, S., Cheong, Y. W., & Tan, S. H. (2018). The development of a media literacy questionnaire in the social media context. Asian Journal of Communication, 28(4), 426–444.

social-media-disorder-scale social-comparison-scale-online online-disinhibition-scale digital-wellbeing-scale


Media Trust Scale

MTS
Press Credibility Scale
News Media Confidence

The Media Trust Scale measures audience confidence in news media credibility, including perceptions of accuracy, fairness, completeness, and journalists' motivations. Developed by West (1994) and extended by Kiousis (2001), the scale captures both medium-specific trust (trust in TV news vs. newspapers vs. online news) and outlet-specific trust (CNN vs. Fox News vs. BBC vs. local news). Media trust is central to understanding political polarization, misinformation vulnerability, and the functioning of the democratic public sphere, as low-trust populations reject news sources entirely, opening space for alternative information ecosystems.

West, M. D. (1994). Validating a scale for the measurement of credibility: A covariance structure modeling approach. Journalism Quarterly, 71(1), 159-168.

Kiousis, S. (2001). Public trust or mistrust? Perceptions of media credibility in the information age. Mass Communication & Society, 4(4), 381-403.

Pew Research Center. (2021). News consumption and media trust in an era of political polarization. Washington, DC: Pew Research Center.


MEDIAN-RANKING

MEDIAN-RANKING (Median ranking — per-alternative median rank) is a aggregationoperator multi-criteria decision-making (MCDM) method introduced by Orakçı, E. in 2024. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Orakçı, E. (2024). Çok Kriterli Karar Verme Problemleri için Toplulaştırma Teknikleri. Özgür Yayınları

borda condorcet copeland dodgson topsis vikor ahp


Mediation Analysis

Mediation Analysis (Baron-Kenny / Bootstrap)

indirect effects analysis
path-based mediation
PROCESS macro mediation
Aracılık Analizi (Mediation / PROCESS)

Mediation analysis is a statistical procedure that tests whether the effect of an independent variable X on an outcome Y operates wholly or partly through a third variable M, called the mediator. Formalised by Baron and Kenny in 1986, it decomposes the total effect of X on Y into a direct path (c′) and an indirect path (a × b), quantifying how much of the relationship is carried by the mediating mechanism.

a (X→M), b (M→Y), c (total X→Y), c′ (direct X→Y)

Bootstrap confidence interval (5000 resamples recommended)

continuous (primary); binary or ordinal outcomes supported with extensions

Baron, R. M. & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research. Journal of Personality and Social Psychology, 51(6), 1173–1182.

Hayes, A. F. (2022). Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach (3rd ed.). The Guilford Press.

Preacher, K. J. & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879–891.

path-analysis structural-equation-modeling moderation-analysis confirmatory-factor-analysis multiple-regression moderated-mediation


Medication Adherence Rating Scale

Kathryn Thompson, Jayashri Kulkarni, and Anthony A. Sergejew

The Medication Adherence Rating Scale (MARS) is a 10-item self-report measure developed by Thompson, Kulkarni, and Sergejew in 2000 to assess medication adherence behaviors and attitudes in psychiatric populations, particularly antipsychotic medication use. Although originally validated in schizophrenia, it has been successfully applied across diverse medical conditions including hypertension, diabetes, and chronic disease management, providing a quick, sensitive assessment of actual adherence frequency and admission of problematic medication-taking behaviors.

Thompson, K., Kulkarni, J., & Sergejew, A. A. (2000). Reliability and validity of a new Medication Adherence Rating Scale (MARS) for the psychoses. Schizophrenia Research, 42(3), 241-247.


Medication Reconciliation

Medication Reconciliation Process for Patient Safety

Med Reconciliation
Medication List Verification
Drug-Drug Interaction Screening

Institute of Medicine, The Joint Commission, and healthcare safety organizations

Medication Reconciliation is a systematic process of identifying and resolving discrepancies between the medications a patient should be taking and what they are actually taking. Endorsed by The Joint Commission as a National Patient Safety Goal, medication reconciliation occurs at critical transition points such as hospital admission, transfer between units, and discharge. The process reduces medication errors and adverse drug events that can result from omissions, duplications, or interactions.

Institute of Medicine. (2006). Preventing Medication Errors. National Academies Press, Washington, DC.

The Joint Commission. (2005). National Patient Safety Goals. Medication Reconciliation Standard NPSG.03.04.01.

cam-delirium-screening nursing-sensitive-indicators early-warning-score patient-fall-risk-assessment


Medication Regimen Complexity Index

The Medication Regimen Complexity Index (MRCI) is a clinician-administered quantitative measure that objectively assesses the complexity of a patient's medication regimen based on the number of medications, frequency of dosing, and form of administration. Developed by Morgado, Rolo, and Castelo-Branco in 2012, the MRCI quantifies an important adherence barrier—the complexity of taking multiple medications with different schedules and administration routes. The MRCI is unique among adherence tools in that it measures an objective regimen characteristic (not patient behavior or belief), making it useful for deprescribing decisions, medication reconciliation, and identifying high-risk patients for non-adherence due to complexity.

Morgado, M., Rolo, S., & Castelo-Branco, M. (2012). Pharmacotherapy, 32(7), 652-660. (Original MRCI); Semla, T., & Beizer, J. (2018). American Geriatrics Society Beers Criteria for Potentially Inappropriate Medication Use in Older Adults. Journal of the American Geriatrics Society.


Sunil Kripalani, Jill Risser, Monica E. Gatti, and Thomas A. Jacobson

The Medication Understanding and Use Self-Efficacy Scale (MUSE-S) is a brief, patient-centered self-report measure assessing both knowledge and confidence regarding medication use. Developed by Kripalani and colleagues at Emory University in 2009, the MUSE-S evaluates whether patients understand their medications (what they are for, how to take them, important side effects) and feel confident managing them in daily life. This dual focus on knowledge and self-efficacy makes the MUSE-S particularly valuable for identifying education gaps, assessing health literacy barriers to medication adherence, and evaluating outcomes of medication counseling or education interventions.

Kripalani, S., Risser, J., Gatti, M. E., & Jacobson, T. A. (2009). Development and validation of a simple questionnaire to measure medication understanding. Medical Care, 47(3), 340-348.


MEDAS

Helmut Schröder, Montserrat Fitó, Ramón Estruch

The Mediterranean Diet Adherence Screener is a 14-item food frequency questionnaire designed to rapidly assess adherence to the Mediterranean dietary pattern. Developed by Schröder and colleagues in 2011 and validated in the PREDIMED randomized controlled trial, it is one of the most widely used tools for measuring Mediterranean diet compliance in research and clinical practice. The MEDAS is particularly valuable for epidemiological studies, intervention trials, and cardiovascular disease prevention programs.

Schröder, H., Fitó, M., Estruch, R., et al. (2011). A short screener is valid for assessing Mediterranean diet adherence. The Journal of Nutrition, 141(6), 1140-1145.

Estruch, R., Ros, E., Salas-Salvadó, J., et al. (2018). Primary prevention of cardiovascular disease with a Mediterranean diet supplemented with extra-virgin olive oil or nuts. The New England Journal of Medicine, 378(25), e34. [Republished after retraction of the 2013 article, doi:10.1056/NEJMoa1200303.]

dietary-quality-index food-frequency-questionnaire nutrition-self-efficacy-scale mini-nutritional-assessment intuitive-eating-scale


MEG Source Localization

MEG localization
magnetic source imaging
MSI

Magnetoencephalography (MEG) source localization is the inverse problem of estimating where in the brain neural currents originate from magnetic field measurements at the scalp. Introduced by David Cohen in 1972, MEG offers superior temporal resolution (milliseconds) and spatial specificity compared to EEG, as magnetic fields are less distorted by tissue conductivity, enabling researchers to pinpoint neural activity with high precision.

Hauk, O., Friston, K. J., & Leff, A. (2019). Functional neuroimaging of language: understanding the complex relationships between localization and function. Journal of Neurolinguistics, 50, 236–250.

Halgren, E., Marinkovic, K., & Chauvel, P. (2006). Generators of the late cognitive potentials in auditory and visual oddball tasks. Electroencephalography and Clinical Neurophysiology, 106(2), 156–164.


MelasQoL

MelasQoL is a disease-specific, patient-administered quality-of-life measure designed to assess the psychosocial burden of melasma, a common chronic disorder of symmetric facial hyperpigmentation. Developed by Cestari and colleagues in 2006, it captures the unique emotional and social impacts of a predominantly cosmetic condition that disproportionately affects women of color. MelasQoL is essential in clinical trials and observational studies of melasma treatments to ensure that efficacy encompasses meaningful quality-of-life outcomes.

Cestari TF, Hexsel D, Brandt FS, et al. Validation of a melasma quality of life questionnaire for Brazilian Portuguese language: the MelasQoL. Br J Dermatol. 2006;156(Suppl 3):13-20.

Pandya AG, Hynan LS, Bhore R, et al. Reliability and validity of the Melasma Area and Severity Index (MASI) and a new modified MASI scoring method. J Am Acad Dermatol. 2011;64(1):78-83.


Melody Extraction

pitch contour extraction
melodic line extraction
f0 tracking

Melody extraction is the task of automatically isolating the main melodic contour from polyphonic music recordings. It originated from music transcription research in the 2000s and addresses the core challenge of human pitch perception: identifying the perceptually dominant pitch when many instruments play simultaneously. Modern approaches use deep learning and are essential for music analysis, cover song detection, and music-to-lyrics alignment.

Salamon, J., & Gómez, E. (2014). Melody extraction from polyphonic music signals using pitch contour characteristics. IEEE Transactions on Audio, Speech, and Language Processing, 20(6), 1759-1770.

Klapuri, A. (2008). Automatic music transcription as we know it today. Journal of New Music Research, 33(3), 323-337.

Bittner, R. M., McVicar, M., Salamon, J., & Ellis, D. P. (2017). An analysis of lead and accompaniment separation in polyphonic music. In Proceedings of the International Society for Music Information Retrieval Conference.

pitch-detection-algorithm automatic-music-transcription harmonic-analysis-music vocal-separation music-segmentation


Member Checking and Respondent Validation

Participant Verification of Qualitative Findings

member validation
respondent validation
participant feedback
credibility check

Member checking is a quality assurance procedure in qualitative research in which the researcher shares preliminary findings, interpretations, or analytical themes with research participants and asks whether the findings accurately reflect their perspectives and experiences. Developed by Lincoln and Guba (1985) as a trustworthiness criterion, member checking is considered a key method for ensuring credibility and reducing researcher misinterpretation. The goal is to verify that the researcher has understood participants correctly and that interpretations are grounded in participants' actual meaning-making, not the researcher's assumptions. Member checking can occur at different points in research (after individual interviews, after initial analysis, or after draft findings are written) and take different forms (individual feedback, group validation, interactive discussion).

Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry. SAGE Publications.

Birt, L., Scott, S., Cavers, D., Campbell, C., & Walter, F. (2016). Member checking: A tool to enhance trustworthiness or merely a nod to validation? Qualitative Health Research, 26(13), 1802-1811.

Carlson, J. A. (2010). Avoiding traps in member checking. The Qualitative Report, 15(5), 1102-1113.

Tong, A., Sainsbury, P., & Craig, J. (2007). Consolidated criteria for reporting qualitative research (COREQ): A 32-item checklist for interviews and focus groups. International Journal for Quality in Health Care, 19(6), 349-357.

in-depth-interview-method reflexivity-in-research qualitative-rigor-criteria participant-observation


Memetic Algorithm

Memetic Algorithms (Hybrid Evolutionary + Local Search)

Cultural Algorithm (local-search variant)

A Memetic Algorithm (MA) is a population-based metaheuristic that combines the global exploration of an evolutionary algorithm with the local exploitation of individual learning procedures. Introduced by Pablo Moscato in 1989 at Caltech, MAs draw on Richard Dawkins' concept of the meme — a unit of cultural transmission — to model the idea that solutions can improve not only through crossover and mutation but also through individual refinement within each generation.

Darwinian evolution + Dawkins meme concept

Faster than pure GAs on many combinatorial problems

Moscato, P. (1989). On evolution, search, optimization, genetic algorithms and martial arts: Towards memetic algorithms. Caltech Concurrent Computation Program Report 826.

Neri, F., & Cotta, C. (2012). Memetic algorithms and memetic computing optimization: A literature review. Swarm and Evolutionary Computation, 2, 1–14.


MSAS

The Memorial Symptom Assessment Scale is a comprehensive multisymptom instrument that captures both prevalence and distress of 32 cancer-related symptoms (full version) or 10 core symptoms (short form). Developed by Portenoy and colleagues at Memorial Sloan Kettering Cancer Center in 1994, the MSAS is designed for detailed symptom profiling in oncology research and clinical practice, enabling identification of symptom clusters and assessment of physical and psychological symptom burden separately.

Patient self-report multisymptom prevalence and distress scale

Portenoy, R. K., Thaler, H. T., Kornblith, A. B., et al. (1994). The Memorial Symptom Assessment Scale: an instrument for the evaluation of symptom prevalence, characteristics and distress. Eur J Cancer, 30A(9), 1326–1336.

Cook, K. F., Broemling, L. D., Johnson, R. L., et al. (2007). Development and preliminary psychometric evaluation of the MSAS-GI: a brief symptom assessment for patients with gastrointestinal cancer. J Pain Symptom Manage, 34(3), 280–289.

edmonton-symptom-assessment distress-thermometer brief-fatigue-inventory fact-g functional-living-index-cancer


Mendelian Randomization

Mendelian randomization is a method for estimating causal effects of exposures on outcomes using genetic variants as instrumental variables. Introduced by George Davey Smith in the 1990s, it exploits Mendel's law of segregation to remove confounding bias. It has become a cornerstone technique in epidemiological causal inference.

Davey Smith, G., & Hemani, G. (2014). Mendelian randomization: genetic anchors for causal inference in epidemiological studies. Human Molecular Genetics, 23(R1), R89-R98.

Hemani, G., Bowden, J., & Davey Smith, G. (2018). Evaluating the potential role of pleiotropy in Mendelian randomization studies. European Journal of Epidemiology, 33(9), 867-876.

Morrison, J., Knoblauch, N., Marcus, J. H., Stephens, M., & He, X. (2020). Mendelian randomization accounting for sample overlap. Nature Communications, 11(1), 574.


Menopause Rating Scale

The MRS is an 11-item self-report symptom scale designed to assess the frequency and severity of menopausal symptoms including vasomotor complaints, psychologic symptoms, and urogenital manifestations. Developed by Heinemann and colleagues in Germany and first published in 2000, it has become the most widely used symptom measure in menopause research and clinical practice across 60+ countries and languages.

Heinemann, K., Assmann, A., Möhner, S., & Schneider, H. P. (2004). The Menopause Rating Scale (MRS) as outcome measure for hormone replacement therapy. Menopause, 11(5), 571–578.

Schneider, H. P., Heinemann, L. A., Rosemeier, H. P., Potthoff, P., & Behre, H. M. (2000). The Menopause Rating Scale (MRS): reliability, validity and cross-cultural comparability. Menopause International, 6(3), 145–161.


The Menopause-Specific Quality of Life Questionnaire (MENQOL) is a 29-item self-report instrument designed to assess quality of life in women experiencing menopausal symptoms. Developed by Hilditch and colleagues in 1996, the MENQOL captures four interrelated symptom domains: vasomotor symptoms (hot flushes, night sweats), psychosocial symptoms (mood, stress, anxiety), physical symptoms (fatigue, aches, sleep), and sexual symptoms. It is the primary menopause-specific outcome measure used in hormone replacement therapy trials and menopause research.

Hilditch, J. R., Lewis, J., Peter, A., van Maris, B., Ross, A., Franssen, E., Guyatt, G. H., Lethargy, S., & Improvement, T. (1996). A menopause-specific quality of life questionnaire: development and psychometric properties. Maturitas, 24(3), 161-175.


Mental Health Continuum Short Form

The Mental Health Continuum Short Form (MHC-SF) is a 14-item measure assessing positive mental health and wellbeing across emotional, social, and psychological domains. Developed by Corey L. M. Keyes in 2002, the MHC-SF operationalizes the conceptualization of mental health as a continuum from languishing to flourishing, distinct from absence of mental illness. The scale captures life satisfaction, positive emotions, autonomy, personal growth, purpose, and social integration. The MHC-SF is widely used in population health research, clinical practice, and recovery-oriented mental health services.

Keyes, C. L. M. (2009). Atlanta: Brief description of the Mental Health Continuum Short Form (MHC-SF). Journal of Mental Health, 18(2), 113-123.

Keyes, C. L. M. (2002). The mental health continuum: From languishing to flourishing in life. Journal of Health and Social Behavior, 43(2), 207-222.

recovery-assessment-scale mental-health-recovery-measure empowerment-scale-rogers social-inclusion-scale


Mental Toughness Questionnaire

The MTQ48 is a 48-item instrument measuring mental toughness—the capacity to perform well under pressure, persist through adversity, maintain emotional control, and sustain commitment toward goals. Developed by Clough, Earle, and Sewell in 2002, the MTQ48 operationalizes mental toughness across four dimensions (the '4Cs': Control, Commitment, Challenge, and Confidence) and has become widely adopted in sport psychology, talent development, and organizational psychology for identifying and developing psychological resilience.

Self-report mental toughness and resilience questionnaire

Clough, P. J., Earle, K., & Sewell, D. (2002). Mental toughness: A definition and measured construct. Journal of Applied Sport Psychology, 14(3), 169–187.

Clough, P. J., Earle, K., Sewell, D., & Strycharczyk, D. (2012). Mental Toughness: The Mindset Behind Sporting Success. Bloomsbury Sport.

sport-confidence-inventory competitive-state-anxiety-inventory task-ego-orientation-sport profile-of-mood-states


MEREC-G

Method Based on the Removal Effects of Criteria - Generalized (MEREC-G)

Keshavarz Ghorabaee, Hosseinzadeh Lotfi et al.

MEREC-G (Method Based on Removal Effects of Criteria - Generalized) is an objective weight derivation method that assigns weights based on the impact of removing each criterion from the decision analysis. The core idea is that important criteria, when removed, cause large changes in the final ranking. Generalized variants extend the original MEREC to various aggregation logic and decision contexts.

Objective weight derivation via removal impact assessment

Keshavarz Ghorabaee, M., Hosseinzadeh Lotfi, F., Behzadi, M., & Sałabun, W. (2021). MEREC: A new multi-criteria model to evaluate wind farm locations. Sustainability, 12(15), 6136.

Pamučar, D., Ćirović, G., & Božanović-Kečan, S. (2021). A new model for determining weight coefficients of criteria in MCDM models: Full consistency method (FUCOM). Symmetry, 12(9), 1549.

merec critic-m entropy-method variance-based-weighting fucom


MEREC

MEREC (MEthod based on the Removal Effects of Criteria) is a weight objective multi-criteria decision-making (MCDM) method introduced by Keshavarz Ghorabaee, M., Amiri, M., Zavadskas, E. K., Antucheviciene, J., Turskis, Z. in 2021. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Removal-effect objective weighting (logarithmic utility)

Keshavarz Ghorabaee, M., Amiri, M., Zavadskas, E. K., Antucheviciene, J., Turskis, Z. (2021). Determination of objective weights using a new method based on the removal effects of criteria (MEREC). Informatica

ahpsort aploco aras aroman artasi cobra cocoso codas


Merton Default Model

Structural Credit Model
Asset-to-Equity Model

The Merton model (1974) is a structural approach to credit risk in which a firm defaults when its asset value falls below liabilities at maturity. Equity is viewed as a call option on firm value, and debt is an implicit short put position. The model links company fundamentals (asset volatility) to default probability and is foundational for modern credit risk measurement.

Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29(2), 449-470.

Vasicek, O. (2002). The distribution of losses on loan portfolios. Journal of Risk, 5(2), 15-25.


Meta-Analysis

Meta-Analysis (Statistical Synthesis and Pooling of Study Results)

quantitative synthesis
meta-synthesis
pooled analysis
statistical integration

Glass (1976, term coining); Fisher and Pearson (statistical foundations)

Meta-analysis is the statistical pooling of quantitative findings from multiple independent studies to produce a combined effect estimate. By aggregating data across studies, meta-analysis increases statistical power, reduces random error, and provides a precise summary of an intervention's effectiveness or an association's magnitude. Gene V. Glass coined the term in 1976, formalizing a technique that has become indispensable for evidence synthesis in medicine, psychology, education, and other evidence-based disciplines.

Page, M. J., et al. (2021). The PRISMA 2020 statement: an updated guideline for reporting systematic reviews. BMJ, 372, n71.

Higgins, J. P., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21(11), 1539–1558.

Deeks, J. J., Higgins, J. P., & Altman, D. G. (2019). Analysing data and undertaking meta-analyses. In J. P. Higgins & J. Thomas (Eds.), Cochrane Handbook for Systematic Reviews of Interventions (Version 6.0). Cochrane.

systematic-review-article forest-plot-interpretation effect-size-statistics heterogeneity-assessment publication-bias


Meta-analytic case-control study

pooled case-control analysis
case-control meta-analysis
meta-analytic case-control design
systematic pooled case-control

1980s–2000 (formalized with MOOSE reporting guidelines in 2000)

Systematic development attributed to multiple epidemiologists; MOOSE guidelines formalized by Stroup et al.

A meta-analytic case-control study systematically identifies, critically appraises, and quantitatively synthesizes data from multiple independent case-control studies examining the same exposure-disease relationship. By pooling odds ratios across studies, it yields a more precise and generalizable estimate of association than any single study can provide, while formally quantifying heterogeneity across populations, settings, and study periods.

Published or individual-level case-control study data (odds ratios, 2×2 tables)

Shapiro, S. (1994). Meta-analysis/Shmeta-analysis. American Journal of Epidemiology, 140(9), 771-778.

Stroup, D. F., Berlin, J. A., Morton, S. C., Olkin, I., Williamson, G. D., Rennie, D., ... & Thacker, S. B. (2000). Meta-analysis of observational studies in epidemiology: a proposal for reporting. JAMA, 283(15), 2008-2012.

case-control-study systematic-review meta-analysis nested-case-control prospective-case-control-study matched-case-control-study


Meta-analytic case-crossover design

systematic pooling of case-crossover studies

1991 (base design); meta-analytic applications from late 1990s onward

Maclure (case-crossover basis, 1991); meta-analytic extension through environmental epidemiology consortia (1990s–2000s)

The meta-analytic case-crossover design combines the within-person control structure of the case-crossover study with formal meta-analytic pooling across multiple studies. Each contributing study uses cases as their own controls by comparing exposure windows immediately preceding an acute event to matched reference windows in the same individual. The pooled approach synthesizes conditional odds ratios across studies, maximizing statistical power and generalizability — commonly applied to short-term environmental exposures such as air pollution, temperature extremes, and drug triggers of acute events.

Observational epidemiological design with meta-analytic synthesis

Individual-level or aggregate case-crossover effect estimates (conditional odds ratios) from multiple studies

Maclure, M. (1991). The case-crossover design: a method for studying transient effects on the risk of acute events. American Journal of Epidemiology, 133(2), 144–153.

Bateson, T. F., & Schwartz, J. (2001). Selection bias and confounding in case-crossover analyses of environmental time-series data. Epidemiology, 12(6), 654–661.

case-crossover-design meta-analysis systematic-review time-series-analysis nested-case-control matched-case-control-study