Model checking after Bayesian inference

Matteo Pozzi, Daniele Zonta

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Bayesian analysis provides a consistent logical framework for processing data, inferring parameters and estimating relevant quantities in engineering prob- lems. However, its outcomes are valid conditional to the specific model assump- tions. Whether these assumptions are questioned, possibly because of some factors knowingly left out, they can be checked by further analysis of the available empirical data. Again, this can be done inside the Bayesian framework, by prob- abilistically comparing expanded models with the original one; however, this may be computational impractical in many applications. Test statistics and p-value analysis, historically developed under the frequentist approach but adapted to the Bayesian setting, provide an alternative for model checking coupled with proba- bilistic inference. In this chapter, we illustrate the relation between p-value analysis and Bayesian model comparison: after presenting it in a general context, we focus on Gaussian linear models under known perturbation, for which this relation can be stated in close formulas, and explore an example outside that domain.

Original languageEnglish
Title of host publicationRisk and Reliability Analysis
Subtitle of host publicationTheory and Applications
Place of PublicationCham, Switzerland
PublisherSpringer
Pages317-339
Number of pages23
ISBN (Print)978-3-319-52424-5
DOIs
Publication statusPublished - 25 Feb 2017

Publication series

NameSpringer Series in Reliability Engineering
ISSN (Print)16147839
ISSN (Electronic)2196999X

Keywords

  • Bayesian analysis
  • model checking
  • quality

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  • Cite this

    Pozzi, M., & Zonta, D. (2017). Model checking after Bayesian inference. In Risk and Reliability Analysis: Theory and Applications (pp. 317-339). (Springer Series in Reliability Engineering). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-52425-2_14