Statistics — Page 7
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian Multiscale Geographically Weighted Regression
Bayesian Multiscale Geographically Weighted Regression (Bayesian MGWR) extends the MGWR framework by placing Bayesian priors on each spatially varying coefficient. Each predictor is allowed its own bandwidth — its own geographic scale of in...
Bayesian NARDL
Bayesian NARDL combines the Nonlinear Autoregressive Distributed Lag framework of Shin, Yu, and Greenwood-Nimmo (2014) with Bayesian posterior inference. It models asymmetric long-run cointegration — allowing positive and negative shocks to...
Bayesian Negative Binomial Regression
Bayesian Negative Binomial Regression models non-negative integer count outcomes that exhibit overdispersion — where the variance exceeds the mean — by placing a negative binomial likelihood on the data and specifying prior distributions ov...
Bayesian Network
A Bayesian network is a probabilistic graphical model, introduced by Judea Pearl in 1988, that encodes a set of variables and their conditional dependencies as a directed acyclic graph (DAG). Each node represents a variable; each directed e...
Bayesian Network with Measurement Error
A Bayesian network with measurement error is a probabilistic directed acyclic graphical model in which one or more node variables are observed with error rather than exactly. Latent true-value nodes are introduced for mismeasured variables,...
Bayesian Nonparametric Methods
Bayesian nonparametric methods are a family of flexible Bayesian models in which model complexity is not fixed in advance but grows automatically with the data. The two most widely used members are the Dirichlet Process Mixture (DPM), which...
Bayesian OLS
Bayesian OLS combines the classical linear regression likelihood with prior distributions over the coefficients and error variance. Rather than reporting point estimates, it produces full posterior distributions that quantify both estimated...
Bayesian Ordinal Logistic Regression
Bayesian ordinal logistic regression extends the classical proportional odds model by placing prior distributions on the regression coefficients and threshold parameters and updating them with observed data via Bayes' theorem. The result is...
Bayesian Ordinary Kriging
Bayesian Ordinary Kriging is a geostatistical interpolation method that combines classical ordinary kriging with a Bayesian framework to jointly estimate the spatial covariance parameters and produce predictions at unsampled locations. Unli...
Bayesian PP unit root test
The Bayesian Phillips-Perron unit root test combines the nonparametric long-run variance correction of the classical Phillips-Perron test with a Bayesian inferential framework. Instead of a p-value, it yields a posterior probability or Baye...
Bayesian Panel Data Analysis
Bayesian panel data analysis applies Bayesian inference to models with repeated observations on multiple units. By placing prior distributions on coefficients and variance components, it merges prior knowledge with the observed panel likeli...
Bayesian Panel Event Study
Bayesian Panel Event Study is a causal inference design that estimates dynamic treatment effects around a datable event using panel data, replacing classical frequentist estimation with Bayesian posterior inference. It produces period-by-pe...
Bayesian Placebo Test
The Bayesian Placebo Test is a falsification strategy for causal inference that applies Bayesian inference to placebo scenarios — either fake treatments in the pre-intervention period, on unaffected units, or at fictitious cut-offs — to ver...
Bayesian Poisson Regression
Bayesian Poisson regression models non-negative integer count outcomes using a Poisson likelihood with a log link, placing prior distributions on the regression coefficients. Posterior inference — combining prior beliefs with the data likel...
Bayesian Power Analysis
Bayesian power analysis — also called assurance — is a sample size determination method that replaces the frequentist notion of power with a probability-weighted average over a prior distribution on the effect size. First formalised by Spie...
Bayesian Principal Component Analysis
Bayesian principal component analysis embeds probabilistic PCA within a Bayesian framework, placing priors over the loading matrix so that irrelevant components are automatically pruned. It handles missing data naturally and provides princi...
Bayesian Probit model
The Bayesian Probit model is a binary regression method that models the probability of a binary outcome using the normal CDF (probit link) within a Bayesian framework. It assigns prior distributions to regression coefficients and updates th...
Bayesian Propensity Score Matching
Bayesian Propensity Score Matching (Bayesian PSM) extends classical propensity score matching by placing a prior distribution over the propensity model parameters and propagating posterior uncertainty through the matching and outcome stages...
Bayesian Propensity Score Weighting
Bayesian Propensity Score Weighting estimates causal treatment effects in observational data by combining a Bayesian model for the propensity score with inverse probability weighting. By placing a prior over propensity-score parameters and...
Bayesian Quantile Regression
Bayesian Quantile Regression estimates the full posterior distribution of regression coefficients at any chosen quantile of the outcome. By combining the asymmetric Laplace likelihood with prior distributions over the coefficients, it deliv...
Bayesian Quantile-on-Quantile Regression
Bayesian Quantile-on-Quantile (BQQ) Regression extends the Sim-Zhou quantile-on-quantile framework by replacing frequentist local linear estimation with Bayesian posterior inference. For each pair of quantiles (theta of the outcome, tau of...
Bayesian Random Effects Model
The Bayesian random effects model combines panel-data random effects with a Bayesian prior framework, allowing unit-specific effects to be treated as draws from a population distribution whose hyperparameters are estimated from the data. Th...
Bayesian Regression
Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a f...
Bayesian Regression Discontinuity Design
Bayesian Regression Discontinuity Design (Bayesian RDD) embeds the classical RD framework — which estimates a local causal effect at a known assignment cutoff — within a Bayesian inferential engine. Prior distributions are placed on the reg...