Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Other literature type . 2023
License: CC BY NC ND
Data sources: ZENODO
The American Statistician
Article . 2025 . Peer-reviewed
Data sources: Crossref
ZENODO
Research . 2023
License: CC BY NC ND
Data sources: Datacite
ZENODO
Research . 2023
License: CC BY NC ND
Data sources: Datacite
versions View all 3 versions
addClaim

Bayesian Model Checking by Betting: A Game-Theoretic Alternative to Bayesian p -values and Classical Bayes Factors

Authors: Bickel, David R.;

Bayesian Model Checking by Betting: A Game-Theoretic Alternative to Bayesian p -values and Classical Bayes Factors

Abstract

A strictly Bayesian model consists of a set of possible data distributions and a prior distribution over that set. If there are other models available, how well they predicted the data may be compared using Bayes factors. If not, a model may be checked using a Bayesian p-value such as a prior predictive p-value or a posterior predictive p-value. However, recent criticisms of ordinary p-values apply with equal force against Bayesian p-values. Many of those criticisms are overcome by e-values, martingales interpreted as the amount of evidence discrediting a null hypothesis, measured as a payoff for betting against it. This paper proposes the use of e-values to check Bayesian models by testing their prior predictive distributions as null hypotheses. Two generally applicable methods for checking strictly Bayesian models are provided. The first method calibrates Bayesian p-values by transforming them into Bayesian e-values. The second method uses Bayes factors or their approximations as Bayesian e-values. A robust Bayesian model, a set of strictly Bayesian models, may be checked using various functions that use the e-values of those strictly Bayesian models. Other functions measure how much the data support a Bayesian model. Relations to possibility theory are discussed.

Related Organizations
  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    1
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green