Statistics — Page 3
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian ANCOVA
Bayesian Analysis of Covariance (Bayesian ANCOVA) extends classical ANCOVA by placing prior distributions on group effects and covariate slopes, then updating them with observed data to obtain posterior distributions and Bayes factors. It q...
Bayesian ANOVA
Bayesian ANOVA, formalised by Rouder, Morey, Speckman and Province (2012), tests whether group means differ by quantifying the evidence for the alternative hypothesis relative to the null using the Bayes Factor (BF₁₀). Unlike classical ANOV...
Bayesian AR model
The Bayesian AR model estimates an autoregressive time-series process by combining a likelihood derived from the AR structure with prior distributions over the lag coefficients and error variance. Rather than producing single point estimate...
Bayesian ARCH model
The Bayesian ARCH model estimates Engle's Autoregressive Conditional Heteroskedasticity specification within a Bayesian framework. Instead of maximising a likelihood, it combines a prior distribution over the volatility parameters with the...
Bayesian ARDL Bounds Test
The Bayesian ARDL Bounds Test extends the classical Pesaran-Shin-Smith (2001) bounds testing approach to cointegration by embedding it within a Bayesian inferential framework. Instead of relying on frequentist F- and t-statistics with tabul...
Bayesian ARIMA model
The Bayesian ARIMA model combines the classical Box-Jenkins ARIMA framework with Bayesian inference. Instead of obtaining single point estimates for autoregressive and moving average parameters, it places prior distributions over them and u...
Bayesian ARMA model
The Bayesian ARMA model applies Bayesian inference to the classical autoregressive moving average framework for stationary univariate time series. Rather than producing single point estimates for the AR and MA parameters, it yields full pos...
Bayesian Bootstrap
The Bayesian Bootstrap, introduced by Donald B. Rubin in 1981, is a resampling method that produces a Bayesian counterpart to the frequentist bootstrap by assigning each observation a random weight drawn from a Dirichlet distribution. It yi...
Bayesian Canonical Correlation Analysis
Bayesian canonical correlation analysis is a probabilistic generative model that identifies shared latent structure between two or more sets of observed variables. It extends classical CCA by placing priors on model parameters, enabling pri...
Bayesian Causal Impact Analysis
Bayesian Causal Impact Analysis uses a Bayesian structural time series (BSTS) model to estimate the causal effect of an intervention on a time series outcome. Developed by Brodersen and colleagues at Google in 2015, it builds a probabilisti...
Bayesian Chronological Modeling
Bayesian chronological modeling refines archaeological chronologies by combining the calibrated probability distributions of individual radiocarbon dates with prior archaeological knowledge — most importantly the stratigraphic order of samp...
Bayesian Cluster Analysis
Bayesian cluster analysis assigns observations to latent groups by combining a probabilistic model of within-cluster data with prior beliefs about cluster parameters and the number of clusters. It yields posterior probabilities of cluster m...
Bayesian Co-Kriging
Bayesian Co-Kriging is a multivariate geostatistical method that uses auxiliary spatially correlated variables to improve predictions of a primary variable of interest. By placing Bayesian priors on cross-covariance parameters, it propagate...
Bayesian Coarsened Exact Matching
Bayesian Coarsened Exact Matching (Bayesian CEM) combines the coarsening-and-exact-matching framework of Iacus, King, and Porro with Bayesian posterior inference. Covariates are discretised into coarser bins so that treated and control unit...
Bayesian Confirmatory Factor Analysis
Bayesian confirmatory factor analysis tests a pre-specified factor structure using Bayesian inference. Instead of point estimates with p-values, it produces full posterior distributions for loadings, factor correlations, and residual varian...
Bayesian Conjoint Analysis
Bayesian conjoint analysis estimates individual-level consumer preference weights for product attributes by combining conjoint choice tasks with a hierarchical Bayesian model. It yields part-worth utilities for each respondent rather than o...
Bayesian Construct Validity
Bayesian construct validity assessment uses Bayesian confirmatory factor analysis and related Bayesian structural equation models to evaluate whether a scale or test measures the intended latent construct. It yields full posterior distribut...
Bayesian Convergent Validity
Bayesian convergent validity applies Bayesian statistical inference to assess whether different measures of the same construct converge as theory predicts. Rather than a single-point correlation estimate, it yields a full posterior distribu...
Bayesian Counterfactual Impact Evaluation
Bayesian Counterfactual Impact Evaluation estimates the causal effect of an intervention by constructing a Bayesian posterior distribution over the counterfactual outcome — what would have happened without treatment. The method, popularized...
Bayesian Cox Regression
Bayesian Cox regression combines the Cox proportional hazards model for time-to-event data with Bayesian inference. Instead of point estimates, it produces full posterior distributions over the hazard ratios, naturally incorporating prior k...
Bayesian Cronbach's alpha
Bayesian Cronbach's alpha applies Bayesian inference to estimate the classical internal-consistency coefficient, yielding a full posterior distribution over alpha rather than a single point estimate. This allows researchers to quantify unce...
Bayesian DCC-GARCH
Bayesian DCC-GARCH estimates time-varying correlations across multiple financial or economic series by combining Engle's DCC-GARCH structure with Bayesian inference. Rather than maximising a likelihood, it places prior distributions over al...
Bayesian Difference GMM
Bayesian Difference GMM combines the Arellano-Bond first-differencing strategy for dynamic panel data with a Bayesian inference framework. By treating the GMM moment conditions as a quasi-likelihood and placing priors on parameters, the app...
Bayesian Difference-in-Differences
Bayesian Difference-in-Differences applies Bayesian statistical inference to the classic DiD design, replacing frequentist point estimates with full posterior distributions over the treatment effect. This yields not only an estimate of the...