Statistics — Page 8
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
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...