What is it about?
The literature is full of methods of checking a Bayesian model, including the prior distribution. Less is said about how to proceed with inference after a Bayesian model is found to be inadequate. This paper addresses that issue.
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Why is it important?
Inference has to proceed in some way even after a Bayesian model is found to be inadequate. Should the researcher infer that no conclusions can be drawn? If not, what conclusion may be drawn and with what posterior probability does the conclusion hold? This paper provides answers to those questions.
Perspectives
This paper provides a broad framework, inviting many details to be filled in for specific applications. An application to the estimation of local false discovery rates is given as an example.
David R. Bickel
University of North Carolina at Greensboro
Read the Original
This page is a summary of: Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priors, International Journal of Approximate Reasoning, November 2015, Elsevier,
DOI: 10.1016/j.ijar.2015.07.012.
You can read the full text:
Resources
Slides
“Inference under the entropy-maximizing Bayesian model of sufficient evidence” The Third International Conference on Mathematical and Computational Medicine Columbus, Ohio David R. Bickel 18 May 2016
Summary and preprint
The proposed procedure combines Bayesian model checking with robust Bayes acts to guide inference whether or not the model is found to be inadequate: The first stage of the procedure checks each model within a large class of models to determine which models are in conflict with the data and which are adequate for purposes of data analysis. The second stage of the procedure applies distribution combination or decision rules developed for imprecise probability. This proposed procedure is illustrated by the application of a class of hierarchical models to a simple data set.
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