Adjusted Bayesian inference for selected parameters

Daniel Yekutieli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that providing Bayesian inference for selected parameters is a truncated data problem. We show that if the prior for the parameter is non-informative, or if the parameter is a 'fixed' unknown constant, then it is necessary to adjust the Bayesian inference for selection. Our second contribution is the introduction of Bayesian false discovery rate controlling methodology, which generalizes existing Bayesian false discovery rate methods that are only defined in the two-group mixture model. We illustrate our results by applying them to simulated data and data from a microarray experiment.

Original languageEnglish
Pages (from-to)515-541
Number of pages27
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume74
Issue number3
DOIs
StatePublished - Jun 2012

Keywords

  • Bayesian false discovery rate
  • Directional decisions
  • False discovery rate
  • Selection bias
  • Selective inference

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