Statistics — Page 6
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Bayesian Mixed Effects Model
The Bayesian mixed effects model extends the classical mixed effects framework by placing prior distributions on all parameters — fixed effects, random effect variances, and residual variance — and updating them with data to produce full po...
Bayesian Mixture Modeling
Bayesian mixture modeling represents the population as a weighted sum of K component distributions and estimates all unknowns — mixing weights, component parameters, and even the number of components — through posterior inference. It extend...
Bayesian Model Averaging
Bayesian Model Averaging (BMA), formalised as a tutorial by Hoeting, Madigan, Raftery and Volinsky in 1999, addresses model uncertainty by averaging over all plausible model specifications rather than selecting a single best model. Each can...
Bayesian Model Averaging with Measurement Error
Bayesian model averaging with measurement error (BMA-ME) combines two probabilistic ideas: it averages predictions across competing regression models weighted by each model's posterior probability, while simultaneously accounting for the fa...
Bayesian Moderated Mediation
Bayesian moderated mediation estimates how a mediator transmits the effect of a predictor onto an outcome, and whether that indirect effect varies in size depending on a moderator variable — all within a Bayesian framework that quantifies u...
Bayesian Moderation Analysis
Bayesian moderation analysis tests whether the relationship between a predictor and an outcome changes depending on the value of a third variable (the moderator). By placing prior distributions on all model parameters and updating them with...
Bayesian Moran's I
Bayesian Moran's I embeds the classical Moran's I spatial autocorrelation test within a Bayesian probabilistic framework. Rather than producing a single p-value, it yields a posterior distribution over the spatial autocorrelation parameter,...
Bayesian Multidimensional Scaling
Bayesian Multidimensional Scaling places objects in a low-dimensional latent space so that inter-object distances reproduce observed dissimilarities, while a full Bayesian treatment quantifies uncertainty in the coordinates, handles missing...
Bayesian Multinomial Logistic Regression
Bayesian Multinomial Logistic Regression models a nominal outcome with three or more unordered categories by placing prior distributions over the regression coefficients and updating them with data via Bayes' theorem. The result is a full p...
Bayesian Multiple Correspondence Analysis
Bayesian Multiple Correspondence Analysis extends classical MCA by embedding the geometric decomposition of categorical data tables within a Bayesian probabilistic framework, enabling principled uncertainty quantification around category co...
Bayesian Multiple linear regression
Bayesian Multiple Linear Regression models a continuous outcome as a linear combination of several predictors, but instead of producing a single point estimate it yields a full posterior distribution over all regression coefficients and the...
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...