Bayesian Checking of the Second Levels of Hierarchical Models

Abstract

Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many (nuisance) parameters in these complicated models; in this paper we investigate Bayesian methods for model checking. Since we contemplate model checking as a preliminary, exploratory analysis, we concentrate on objective Bayesian methods in which careful specification of an informative prior distribution is avoided. Numerous examples are given and different proposals are investigated and critically compared.

This paper commented in: [arXiv:0802.0746], [arXiv:0802.0747], [arXiv:0802.0749], [arXiv:0802.0752]. Rejoinder in [arXiv:0802.0754]. Published in at http://dx.doi.org/10.1214/07-STS235 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (14)

• X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue
• Philosophy and the practice of Bayesian statistics
• New Important Developments in Small Area Estimation
• Investigating hot-Jupiter inflated radii with hierarchical Bayesian modelling
• Conflict Diagnostics in Directed Acyclic Graphs, with Applications in Bayesian Evidence Synthesis
• Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal
• Gravitational waves carry information beyond effective spin parameters but it is hard to extract
• Invariant $P$-values for model checking
• Bayesian astrostatistics: a backward look to the future
• Using prior expansions for prior-data conflict checking
• Fast and accurate Bayesian model criticism and conflict diagnostics using R-INLA
• The Posterior Predictive Null
• Comment: Bayesian Checking of the Second Level of Hierarchical Models: Cross-Validated Posterior Predictive Checks Using Discrepancy Measures
• Discussion of "Calibrated Bayes, for Statistics in General, and Missing Data in Particular" by R. J. A. Little