Statistics — Page 4
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian Differential Item Functioning
Bayesian differential item functioning analysis detects whether a test item behaves differently across demographic or cultural groups — such as males vs. females — after accounting for the underlying ability or trait being measured. It appl...
Bayesian Discriminant Analysis
Bayesian discriminant analysis assigns observations to predefined groups by combining a multivariate Gaussian likelihood for each class with prior distributions over the class means and covariance matrices. Posterior predictive probabilitie...
Bayesian Discriminant Validity
Bayesian discriminant validity assessment evaluates whether two theoretically distinct latent constructs are empirically separable, using posterior distributions and credible intervals rather than single-point null-hypothesis tests. It is a...
Bayesian Doubly Robust Estimation
Bayesian Doubly Robust Estimation combines the classical doubly robust (DR) augmented inverse probability weighting framework with Bayesian inference. It simultaneously models the propensity score and the outcome regression, placing prior d...
Bayesian Dynamic Panel Data Model
The Bayesian dynamic panel data model extends standard dynamic panel models — which include a lagged dependent variable to capture state dependence — by estimating all parameters within a Bayesian framework. Prior distributions are combined...
Bayesian EFA
Bayesian exploratory factor analysis applies a full probabilistic framework to the common factor model. By placing prior distributions over factor loadings and unique variances, it yields posterior distributions rather than point estimates,...
Bayesian EGARCH
The Bayesian EGARCH model combines Nelson's (1991) Exponential GARCH specification — which models the log of conditional variance and captures the leverage effect — with Bayesian posterior inference via Markov Chain Monte Carlo (MCMC). This...
Bayesian Entropy Balancing
Bayesian Entropy Balancing extends the classical entropy balancing approach — which reweights control units so that their covariate moments match the treated group exactly — by embedding this reweighting within a Bayesian framework. This al...
Bayesian Event Study Design
Bayesian Event Study Design extends the classical event study framework by replacing frequentist significance testing with a full Bayesian inferential framework. It estimates how an event (policy change, announcement, shock) alters an outco...
Bayesian Factor Analysis
Bayesian Factor Analysis is a probabilistic latent-variable method that places prior distributions on the factor loading matrix and the residual variances, then infers a full posterior over these parameters from the observed data. Developed...
Bayesian Fisher's exact test
The Bayesian Fisher's exact test evaluates independence between two categorical variables in a 2x2 table by computing a Bayes factor rather than a p-value. Using conjugate priors on cell probabilities — most commonly the Gunel-Dickey framew...
Bayesian Fixed Effects Model
The Bayesian fixed effects model applies Bayesian inference to the classical within-group panel estimator. Unit-specific intercepts capture time-invariant unobserved heterogeneity, while prior distributions on all parameters allow probabili...
Bayesian Fuzzy Regression Discontinuity
Bayesian Fuzzy Regression Discontinuity (Bayesian Fuzzy RD) combines the quasi-experimental logic of fuzzy regression discontinuity design with full Bayesian inference. It estimates a local average treatment effect at a policy threshold whe...
Bayesian GARCH model
The Bayesian GARCH model combines the GARCH framework for time-varying volatility with Bayesian posterior inference. Instead of maximising a likelihood, it specifies prior distributions for the GARCH parameters and draws from the resulting...
Bayesian Geary's C
Bayesian Geary's C embeds the classical Geary contiguity ratio within a Bayesian hierarchical framework. Instead of a single point estimate and asymptotic p-value, it produces a posterior distribution over the statistic (or over spatially s...
Bayesian Generalized Linear Model
A Bayesian Generalized Linear Model (Bayesian GLM) extends the classical GLM framework by placing prior distributions on the regression coefficients and updating them with data via Bayes' theorem. This yields a full posterior distribution o...
Bayesian Generalized additive model
Bayesian Generalized Additive Models extend the frequentist GAM framework by placing prior distributions over the smooth functions and any additional model parameters. This yields full posterior distributions over each smooth effect, enabli...
Bayesian Geographically Weighted Regression
Bayesian Geographically Weighted Regression combines the spatially varying coefficient framework of GWR with Bayesian inference, placing Gaussian process priors on the locally varying regression coefficients. This yields full posterior dist...
Bayesian Granger Causality
Bayesian Granger causality tests whether past values of one time series carry predictive information about another, framing the hypothesis through Bayesian inference rather than frequentist p-values. It combines a vector autoregressive (VAR...
Bayesian Hausman Test
The Bayesian Hausman test is a Bayesian reformulation of Hausman's (1978) classical specification test, used to assess endogeneity or to choose between fixed effects and random effects panel models. Instead of a chi-squared test statistic,...
Bayesian Hierarchical Clustering
Bayesian hierarchical clustering is a probabilistic agglomerative algorithm that builds a tree of nested cluster merges using Bayesian model comparison at each step. Rather than minimising a geometric linkage criterion, it evaluates at ever...
Bayesian Hierarchical Linear Model
The Bayesian Hierarchical Linear Model (Bayesian HLM) estimates linear relationships in nested or clustered data by placing prior distributions on all model parameters and updating them with observed data. It simultaneously models variation...
Bayesian Hierarchical Model
Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing th...
Bayesian Hierarchical Model with Missing Data
A Bayesian hierarchical model with missing data treats unobserved values as additional unknowns and samples them jointly with all model parameters from the posterior. The nested structure of the hierarchy borrows strength across groups, whi...