# Dirichlet process mixtures of block g priors for model selection and prediction in linear models

arXiv: https://arxiv.org/abs/2411.00471 · HTML: https://mlsanity.com/paper/2411.00471/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2024.

## Abstract (arXiv)

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.