Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models
This work addresses model selection and prediction challenges in linear models for statisticians and data scientists, offering an incremental improvement by bridging model selection and continuous shrinkage priors.
The paper tackles model selection and prediction in linear models by introducing Dirichlet process mixtures of block g priors, which allow differential shrinkage for parameter blocks and account for predictor correlations, showing consistency and avoiding the conditional Lindley paradox. In empirical tests, these priors lead to higher power for detecting smaller significant effects with minimal increase in false discoveries in datasets with a few large effects.
This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various (data-selected) blocks of parameters while fully accounting for the predictors' correlation structure, providing a bridge between the literatures on model selection and continuous shrinkage priors. We show that Dirichlet process mixtures of block $g$ priors are consistent in various senses and, in particular, that they avoid the conditional Lindley ``paradox'' highlighted by Som et al.(2016). Further, we develop a Markov chain Monte Carlo algorithm for posterior inference that requires only minimal ad-hoc tuning. Finally, we investigate the empirical performance of the prior in various real and simulated datasets. In the presence of a small number of very large effects, Dirichlet process mixtures of block $g$ priors lead to higher power for detecting smaller but significant effects without only a minimal increase in the number of false discoveries.