Statistics — Page 26
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Maximum Likelihood Estimation
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...
McNemar's test
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...
Mean-Variance Portfolio Optimization
Mean-variance portfolio optimization is the foundational model of modern portfolio theory, introduced by Harry Markowitz in 1952. It describes portfolios in an expected-return versus risk (variance) plane and traces the efficient frontier o...
Mediation Analysis
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 de...
Merton Default 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....
Method of Moments Quantile Regression
Method of Moments Quantile Regression combines moment-based estimation (GMM) with quantile regression to estimate distribution parameters while handling endogeneity, panel structure, and dynamic relationships. Introduced by Koenker (2004) a...
Metropolis-Hastings Algorithm
The Metropolis-Hastings (MH) algorithm is a general-purpose Markov chain Monte Carlo (MCMC) method for drawing samples from any probability distribution whose density can be evaluated up to a normalising constant. Introduced by Metropolis,...
Metropolis-Hastings for model comparison
Metropolis-Hastings for model comparison uses the Metropolis-Hastings MCMC algorithm to explore both parameter and model space simultaneously, producing posterior probabilities for competing models and enabling Bayes factor estimation witho...
Metropolis-Hastings with Missing Data
Metropolis-Hastings with missing data treats unobserved values as latent variables and samples them jointly with model parameters inside a single MCMC chain. By augmenting the target distribution to include both parameters and missing value...
Metropolis-Hastings with measurement error
Metropolis-Hastings with measurement error is a Bayesian MCMC approach that jointly estimates model parameters and the true (unobserved) covariate values when predictors or outcomes are recorded with noise. By treating the latent true value...
Migration Models
Migration models are quantitative frameworks for explaining and forecasting population movement between geographic units. Lee's (1966) push-pull theory classifies factors at origin and destination into positive and negative forces, modulate...
Mixed ANOVA
Mixed ANOVA is a parametric factorial analysis of variance that simultaneously examines at least one between-subjects factor and at least one within-subjects (repeated-measures) factor. Rooted in R. A. Fisher's ANOVA framework formalised in...
Mixed Effects Model
A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variabil...
Mixed Logit
The Mixed Logit model, introduced formally by McFadden and Train (2000) and elaborated in Train (2009), is a flexible discrete choice framework that allows preference parameters to vary randomly across decision-makers. By integrating standa...
Mixture Cure Model
The mixture cure model, first proposed by Boag in 1949 for cancer survival data, is a parametric survival model that explicitly accounts for a fraction of subjects who will never experience the event of interest — the so-called cured or imm...
Mixture Modeling
Mixture modeling assumes that a population is composed of K unobserved subpopulations, each described by its own probability distribution. The observed data are treated as draws from a weighted combination of these component distributions....
Model Confidence Set
The Model Confidence Set (MCS) is a sequential hypothesis-testing procedure introduced by Hansen, Lunde, and Nason (2011) that identifies the smallest collection of forecasting or predictive models statistically indistinguishable from the b...
Moderated Mediation
Moderated mediation tests whether the indirect effect of an independent variable on an outcome — transmitted through a mediator — differs in strength depending on the level of a moderator variable. It answers the question: for whom, or unde...
Monte Carlo Simulation with Missing Data
Monte Carlo simulation with missing data combines stochastic simulation — drawing random values from probability distributions — with principled missing-data strategies such as multiple imputation. Instead of discarding incomplete records o...
Mood's Median Test
Mood's median test is a nonparametric procedure that compares the medians of k independent groups by counting how many observations in each group fall above and below the pooled (grand) median, then applying a chi-square test to the resulti...
Moran's I
Moran's I is the standard global statistic for detecting spatial autocorrelation: whether nearby locations tend to share similar values. The index ranges from approximately −1 (perfect dispersion) through 0 (spatial randomness) to +1 (perfe...
Moran's I
Moran's I is a global statistic, introduced by Patrick Moran in 1950, that measures whether and how a continuous variable is spatially autocorrelated across mapped units. A positive value signals clustering of similar values, a negative val...
Moving Average Model
The Moving Average model of order q — written MA(q) — expresses the current value of a time series as a linear combination of the current and past random shocks (innovations). Unlike the AR model which uses lagged values of the series itsel...
Multi-State Model
The multi-state model is a generalised survival framework, formalised in the work of Andersen and Keiding and brought to wide biostatistical practice by Putter, Fiocco and Geskus (2007), that models individuals moving through multiple disti...