Sequential Variable Selection as Bayesian Pragmatism in Linear Factor Models

Sequential Variable Selection as Bayesian Pragmatism in Linear Factor Models

We examine a popular practitioner methodology used in the construction of linear factor models whereby particular factors are increased or decreased in relative importance within the model. This allows model builders to customise models and, as such, reflect those factors that the client and modeller may think important. We call this process Pragmatic Bayesianism (or prag-Bayes for short) and w...

Bayesian variable selection in additive partial linear models

Many studies in recent time include a large number of predictor variables, but typically only a few of the predictors have significant roles. Variable selection techniques have been developed using both non-Bayesian and Bayesian approaches. Additive partial linear models (APLM) provide a flexible yet manageable extension of linear models, where some variables can have non-linear effects. We dev...

Bayesian projection approaches to variable selection in generalized linear models

A Bayesian approach to variable selection which is based on the expected Kullback–Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. For generalized linear models an extension of this idea is proposed by considering projections onto subspaces defined via some form of L1 constraint on the parameter in the full model. This l...

Adaptive Bayesian Criteria in Variable Selection for Generalized Linear Models

For the problem of variable selection in generalized linear models, we develop various adaptive Bayesian criteria. Using a hierarchical mixture setup for model uncertainty, combined with an integrated Laplace approximation, we derive Empirical Bayes and Fully Bayes criteria that can be computed easily and quickly. The performance of these criteria is assessed via simulation and compared to othe...

Bayesian variable selection in linear mixed effects models