Bayesian block-diagonal variable selection and model averaging
成果类型：
Article
署名作者：
Papaspiliopoulos, O.; Rossell, D.
署名单位：
ICREA; Pompeu Fabra University
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asx019
发表日期：
2017
页码：
343359
关键词：
摘要：
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf.
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