文章基本信息

标题：Fast Exact Bayesian Inference for Sparse Signals in the Normal Sequence Model
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作者：Tim van Erven ; Botond Szabó
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2021
卷号：16
期号：3
页码：933-960
DOI：10.1214/20-BA1227
语种：English
出版社：International Society for Bayesian Analysis
摘要：We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes over n=500, there has been much attention for alternative approaches like approximate algorithms (Gibbs sampling, variational Bayes, etc.), shrinkage priors (e.g. the Horseshoe prior and the Spike-and-Slab LASSO) or empirical Bayesian methods. However, by introducing algorithmic ideas from online sequential prediction, we show that exact calculations are feasible for much larger sample sizes: for general model selection priors we reach n=25000, and for certain spike-and-slab priors we can easily reach n=100000. We further prove a de Finetti-like result for finite sample sizes that characterizes exactly which model selection priors can be expressed as spike-and-slab priors. The computational speed and numerical accuracy of the proposed methods are demonstrated in experiments on simulated data, on a differential gene expression data set, and to compare the effect of multiple hyper-parameter settings in the beta-binomial prior. In our experimental evaluation we compute guaranteed bounds on the numerical accuracy of all new algorithms, which shows that the proposed methods are numerically reliable whereas an alternative based on long division is not.
关键词：62F15; 62G05; High-dimensional statistics; Model selection; spike-and-slab prior