Statistics — Page 5
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
Bayesian Hot Spot Analysis
Bayesian Hot Spot Analysis identifies spatial clusters of elevated risk or intensity by combining observed data with prior beliefs about spatial structure. It uses Bayesian smoothing — pooling information across neighboring areas — to stabi...
Bayesian Independent Samples t-test
The Bayesian independent samples t-test quantifies evidence for or against a mean difference between two independent groups using a Bayes factor rather than a p-value. Rooted in Jeffreys's probability framework and popularized by Rouder et...
Bayesian Inference
Bayesian inference is a statistical paradigm in which probability represents degrees of belief rather than long-run frequencies. It encodes prior knowledge about parameters in a prior distribution, combines that prior with the likelihood of...
Bayesian Inference with Measurement Error
Bayesian inference with measurement error extends the standard Bayesian framework to situations where one or more covariates or outcomes are observed with noise or misclassification. By treating the true unobserved values as latent variable...
Bayesian Inference with Missing Data
Bayesian inference with missing data treats unobserved values as unknown parameters and integrates them out of the posterior distribution. Rather than deleting or ad hoc imputing incomplete records, the method jointly models observed and mi...
Bayesian Instrumental Variables
Bayesian Instrumental Variables combines the instrumental variable strategy for addressing endogeneity with Bayesian posterior inference. Instead of relying on asymptotic sampling distributions, it places prior distributions over all struct...
Bayesian Inverse Probability Weighting
Bayesian Inverse Probability Weighting (Bayesian IPW) extends the classical IPW estimator by placing prior distributions over the propensity-score model parameters and propagating that uncertainty into the causal-effect estimate. The result...
Bayesian Item Analysis
Bayesian item analysis applies Bayesian inference to estimate item-level statistics — difficulty, discrimination, and distractor effectiveness — by combining observed response data with prior knowledge. It produces full posterior distributi...
Bayesian Item Response Theory in Politics
Bayesian item response theory (IRT) in political science measures latent traits — such as ideology, level of democracy, or political knowledge — from observed binary or ordinal items, treating each item's response probability as a function...
Bayesian K-means clustering
Bayesian K-means clustering extends the classical K-means algorithm by placing prior distributions over cluster centroids and mixing proportions. This probabilistic framework provides uncertainty estimates for cluster assignments, allows pr...
Bayesian Kernel Density Estimation
Bayesian Kernel Density Estimation (BKDE) is a nonparametric method for estimating the probability density function of a spatial or attribute variable by combining a kernel smoother with a Bayesian prior over the bandwidth parameter. The po...