Statistics — Page 8
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian Spatial Panel Model
The Bayesian Spatial Panel Model estimates spatial interaction effects (spatial lag, spatial error, or Durbin) in panel data using Bayesian inference via Markov Chain Monte Carlo (MCMC). It combines the ability to control for unobserved uni...
Bayesian Spatial Regression
Bayesian Spatial Regression embeds a spatially structured random effect into a regression framework and estimates all parameters — including spatial range and variance — through posterior inference rather than point estimation. It handles s...
Bayesian Structural Time Series
Bayesian Structural Time Series (BSTS) is a state-space modelling framework, introduced by Scott and Varian (2014), that decomposes a time series into additive components — trend, seasonality, and regression — and estimates them jointly thr...
Bayesian Survival Analysis
Bayesian survival analysis applies Bayesian inference to time-to-event models — Cox proportional hazards, parametric (Weibull, exponential), and cure models. Formalised comprehensively by Ibrahim, Chen and Sinha (2001), the approach encodes...
Bayesian Survival regression
Bayesian Survival Regression combines parametric or semiparametric survival models — such as Weibull, log-normal, or Cox proportional hazards — with Bayesian inference. Instead of point estimates, it produces full posterior distributions fo...
Bayesian Synthetic Control Method
The Bayesian Synthetic Control Method estimates the causal effect of an intervention on a single treated unit by constructing a probabilistic counterfactual from a weighted combination of untreated donor units. Unlike the classical SCM, it...
Bayesian System GMM
Bayesian System GMM combines the Blundell-Bond System Generalized Method of Moments estimator for dynamic panel data with Bayesian prior distributions and posterior inference via MCMC. It handles endogeneity, individual fixed effects, and w...
Bayesian TGARCH
Bayesian TGARCH combines the Threshold GARCH volatility model — which captures the asymmetric response of volatility to positive versus negative shocks — with full Bayesian inference via Markov Chain Monte Carlo sampling. The result is a pr...
Bayesian Tobit Model
The Bayesian Tobit model extends Tobin's censored regression framework by replacing maximum-likelihood point estimates with a full posterior distribution over regression coefficients and error variance. By embedding Gibbs sampling with data...
Bayesian Toda-Yamamoto Causality
The Bayesian Toda-Yamamoto causality procedure combines the Toda-Yamamoto VAR augmentation strategy — which sidesteps the need for pre-testing integration and cointegration — with Bayesian prior-posterior updating. It tests Granger non-caus...
Bayesian Universal Kriging
Bayesian Universal Kriging (BUK) extends classical universal kriging by placing prior distributions on trend coefficients and spatial covariance parameters, then propagating full posterior uncertainty into predictions. It interpolates spati...
Bayesian VAR
Bayesian VAR adds Minnesota or other prior distributions to a vector autoregressive model to control over-parameterisation. Introduced by Litterman (1986) and extended to high dimensions by Bańbura, Giannone and Reichlin (2010), it outperfo...
Bayesian VAR model
The Bayesian Vector Autoregression (BVAR) model extends the classical VAR framework by incorporating prior beliefs about the model coefficients. Priors — most commonly the Minnesota prior — shrink VAR coefficients toward economically sensib...
Bayesian VECM
The Bayesian VECM combines the classical Vector Error Correction Model — which captures both short-run dynamics and long-run cointegrating relationships among non-stationary multivariate time series — with Bayesian prior distributions over...
Bayesian WLS
Bayesian Weighted Least Squares combines the classical WLS weighting scheme — which downweights observations with high error variance — with Bayesian prior distributions over the regression coefficients and error variance. The result is a p...
Bayesian Wilcoxon signed-rank test
The Bayesian Wilcoxon signed-rank test is a Bayesian nonparametric method for comparing two paired or related samples. Rather than returning a single p-value, it produces posterior probabilities that one condition is better, practically equ...
Bayesian Zero-inflated model
The Bayesian zero-inflated model handles count data with excess zeros by combining a binary component — identifying structural zeros — with a count component (Poisson or negative binomial) for the remaining counts. Bayesian inference via MC...
Bayesian chi-square test
The Bayesian chi-square test evaluates independence or goodness-of-fit in frequency tables using Bayes factors rather than classical p-values. It quantifies evidence for or against an association between categorical variables, updating prio...
Bayesian cross-tabulation analysis
Bayesian cross-tabulation analysis tests whether two categorical variables are associated by computing a Bayes factor that quantifies the evidence for an association model against an independence model. Unlike classical chi-square testing,...
Bayesian descriptive statistics
Bayesian descriptive statistics summarizes data by combining observed information with prior knowledge through Bayes' theorem, yielding posterior distributions over parameters such as the mean and variance. Instead of point estimates and p-...
Bayesian model averaging with missing data
Bayesian Model Averaging with missing data (BMA-MD) simultaneously addresses two sources of uncertainty: which model best describes the data, and what the unobserved values are. Rather than selecting a single imputed dataset and a single mo...
Bayesian one-sample t-test
The Bayesian one-sample t-test compares a single group's mean against a fixed reference value using a Bayes factor rather than a p-value. It quantifies the evidence the data provide for the null hypothesis (mean equals the reference) versus...
Bayesian one-way ANOVA
Bayesian one-way ANOVA tests whether the means of three or more independent groups differ by computing a Bayes factor — a ratio that quantifies how much more likely the data are under a model that allows group differences than under the nul...
Bayesian t-Test
The Bayesian t-test, formalised by Rouder and colleagues in 2009, is a two-group comparison method that works within a Bayesian framework. Instead of a p-value, it produces a Bayes Factor (BF₁₀) that quantifies the evidence the data provide...