Statistics — Page 6
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian Kriging
Bayesian Kriging embeds classical geostatistical interpolation inside a full probabilistic framework. Instead of treating variogram parameters as fixed point estimates, it places prior distributions on them and updates these priors with obs...
Bayesian LASSO Regression
Bayesian LASSO regression places double-exponential (Laplace) priors on regression coefficients, which is the Bayesian analogue of the classical LASSO penalty. It simultaneously shrinks small coefficients toward zero and performs soft varia...
Bayesian Latent Class Analysis
Bayesian latent class analysis extends classical LCA by placing prior distributions on all model parameters and using posterior inference — typically via MCMC — to classify individuals into unobserved categorical groups, quantify uncertaint...
Bayesian Linear Regression
Bayesian linear regression is a probabilistic extension of the ordinary linear model, introduced through Bayes' rule and formalised in its modern computational workflow by Gelman et al. (2013). Rather than returning a single point estimate...
Bayesian Local Indicators of Spatial Association
Bayesian Local Indicators of Spatial Association extend the classical LISA framework by embedding local spatial association statistics within a Bayesian hierarchical model. Rather than relying on asymptotic permutation-based significance te...
Bayesian Logistic Regression
Bayesian logistic regression is a classification model that applies Bayesian inference to a logistic (sigmoid) likelihood for binary or multinomial outcomes. Developed within the weakly-informative prior framework formalised by Gelman, Jaku...
Bayesian MA model
The Bayesian MA model estimates a moving average time series model within a fully Bayesian framework, placing prior distributions on the MA parameters and error variance and updating them via Bayes' theorem. This approach yields full poster...
Bayesian MANOVA
Bayesian Multivariate Analysis of Variance (Bayesian MANOVA) extends the classical MANOVA framework by replacing null-hypothesis significance testing with Bayesian inference. It uses prior distributions on multivariate group means and covar...
Bayesian Mann-Whitney U test
The Bayesian Mann-Whitney U test is a nonparametric Bayesian procedure for comparing two independent groups when data are ordinal or non-normal continuous. Instead of a binary reject/fail-to-reject decision, it quantifies the relative evide...
Bayesian Marginal Structural Model
Bayesian Marginal Structural Model (Bayesian MSM) combines the causal identification power of inverse-probability-weighted marginal structural models with Bayesian posterior inference. Rather than relying on point estimates and asymptotic s...
Bayesian Matching Estimator
The Bayesian Matching Estimator estimates average treatment effects in observational studies by combining classical nearest-neighbour or kernel matching with a Bayesian posterior over the treatment effect. It inherits matching's covariate-b...
Bayesian McDonald's omega
Bayesian McDonald's omega applies Bayesian statistical estimation to the omega reliability coefficient, yielding a full posterior distribution over omega rather than a single point estimate. This provides credible intervals and probabilisti...
Bayesian Measurement Invariance
Bayesian measurement invariance testing evaluates whether a scale's factor loadings and item intercepts are equivalent across groups, using a Bayesian framework that allows parameters to deviate from strict equality by a small, probabilisti...
Bayesian Mixed Effects Model
The Bayesian mixed effects model extends the classical mixed effects framework by placing prior distributions on all parameters — fixed effects, random effect variances, and residual variance — and updating them with data to produce full po...
Bayesian Mixture Modeling
Bayesian mixture modeling represents the population as a weighted sum of K component distributions and estimates all unknowns — mixing weights, component parameters, and even the number of components — through posterior inference. It extend...
Bayesian Model Averaging
Bayesian Model Averaging (BMA), formalised as a tutorial by Hoeting, Madigan, Raftery and Volinsky in 1999, addresses model uncertainty by averaging over all plausible model specifications rather than selecting a single best model. Each can...
Bayesian Model Averaging with Measurement Error
Bayesian model averaging with measurement error (BMA-ME) combines two probabilistic ideas: it averages predictions across competing regression models weighted by each model's posterior probability, while simultaneously accounting for the fa...
Bayesian Moderated Mediation
Bayesian moderated mediation estimates how a mediator transmits the effect of a predictor onto an outcome, and whether that indirect effect varies in size depending on a moderator variable — all within a Bayesian framework that quantifies u...
Bayesian Moderation Analysis
Bayesian moderation analysis tests whether the relationship between a predictor and an outcome changes depending on the value of a third variable (the moderator). By placing prior distributions on all model parameters and updating them with...
Bayesian Moran's I
Bayesian Moran's I embeds the classical Moran's I spatial autocorrelation test within a Bayesian probabilistic framework. Rather than producing a single p-value, it yields a posterior distribution over the spatial autocorrelation parameter,...
Bayesian Multidimensional Scaling
Bayesian Multidimensional Scaling places objects in a low-dimensional latent space so that inter-object distances reproduce observed dissimilarities, while a full Bayesian treatment quantifies uncertainty in the coordinates, handles missing...
Bayesian Multinomial Logistic Regression
Bayesian Multinomial Logistic Regression models a nominal outcome with three or more unordered categories by placing prior distributions over the regression coefficients and updating them with data via Bayes' theorem. The result is a full p...
Bayesian Multiple Correspondence Analysis
Bayesian Multiple Correspondence Analysis extends classical MCA by embedding the geometric decomposition of categorical data tables within a Bayesian probabilistic framework, enabling principled uncertainty quantification around category co...
Bayesian Multiple linear regression
Bayesian Multiple Linear Regression models a continuous outcome as a linear combination of several predictors, but instead of producing a single point estimate it yields a full posterior distribution over all regression coefficients and the...