Statistics — Page 7
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
Bayesian Reliability Analysis
Bayesian reliability analysis estimates how long components or systems survive — their reliability, failure rate, and lifetime distribution — by combining observed (often censored) failure data with prior knowledge through Bayes' rule. As d...
Bayesian Ridge Regression
Bayesian Ridge Regression is a probabilistic formulation of ridge regression, introduced by David J. C. MacKay in 1992, in which the regularisation strength and noise precision are not fixed by the analyst but are instead estimated automati...
Bayesian Robust Regression
Bayesian Robust Regression replaces the Gaussian error assumption of ordinary linear regression with a heavy-tailed distribution — most commonly the Student-t — and estimates all parameters in a Bayesian framework. The heavier tails give ou...
Bayesian SARIMA Model
The Bayesian SARIMA model combines the classical Box-Jenkins Seasonal ARIMA framework with Bayesian inference to handle seasonal time-series data. Rather than producing a single point estimate, it yields a full posterior distribution over m...
Bayesian SEM
Bayesian SEM, introduced by Muthén and Asparouhov in 2012, extends classical structural equation modeling by placing prior distributions on factor loadings, path coefficients, and covariances. Instead of returning a single maximum-likelihoo...
Bayesian SVAR model
The Bayesian Structural Vector Autoregression model combines the structural identification of SVAR with Bayesian prior distributions over parameters. It estimates causal impulse responses between multiple time series while incorporating pri...
Bayesian Scale Development
Bayesian scale development applies Bayesian statistical inference to the construction and evaluation of psychometric scales. Rather than relying on single point estimates of item and person parameters, it produces full posterior distributio...
Bayesian Sensitivity Analysis for Causality
Bayesian sensitivity analysis for causality quantifies how much an unmeasured confounder would need to influence both treatment assignment and outcome to overturn a causal conclusion. Rather than testing a single worst-case scenario, it pla...
Bayesian Simple linear regression
Bayesian Simple Linear Regression models the relationship between a continuous outcome and a single predictor by combining a Gaussian likelihood with prior distributions over the intercept, slope, and error variance. The result is a full po...
Bayesian Spatial Autocorrelation
Bayesian Spatial Autocorrelation embeds spatial dependence directly into a Bayesian hierarchical model. A Conditional Autoregressive (CAR) prior encodes the expectation that neighboring areas are more similar than distant ones, and posterio...
Bayesian Spatial Durbin Model
The Bayesian Spatial Durbin Model (BSDM) estimates a spatial regression that simultaneously includes a spatially lagged outcome variable and spatially lagged covariates, using Bayesian inference with Markov Chain Monte Carlo sampling. It ca...
Bayesian Spatial Error Model
The Bayesian Spatial Error Model (Bayesian SEM) estimates a regression in which spatially correlated disturbances are explicitly modelled through a spatial weights matrix, while all parameters — regression coefficients, spatial error autoco...
Bayesian Spatial Lag Model
The Bayesian Spatial Lag Model (BSLM) extends the classical spatial autoregressive (SAR) regression by placing prior distributions over all parameters and recovering full posterior distributions via MCMC sampling. It explicitly accounts for...