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Cited by 785

The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.

Posterior Predictive $p$-Values

Open access
Meng, Xiao-Li·1994·The Annals of Statistics
DOI 10.1214/aos/1176325622
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Abstract

Extending work of Rubin, this paper explores a Bayesian counterpart of the classical $p$-value, namely, a tail-area probability of a "test statistic" under a null hypothesis. The Bayesian formulation, using posterior predictive replications of the data, allows a "test statistic" to depend on both data and unknown (nuisance) parameters and thus permits a direct measure of the discrepancy between sample and population quantities. The tail-area probability for a "test statistic" is then found under the joint posterior distribution of replicate data and the (nuisance) parameters, both conditional on the null hypothesis. This posterior predictive $p$-value can also be viewed as the posterior mean of a classical $p$-value, averaging over the posterior distribution of (nuisance) parameters under the null hypothesis, and thus it provides one general method for dealing with nuisance parameters. Two classical examples, including the Behrens-Fisher problem, are used to illustrate the posterior predictive $p$-value and some of its interesting properties, which also reveal a new (Bayesian) interpretation for some classical $p$-values. An application to multiple-imputation inference is also presented. A frequency evaluation shows that, in general, if the replication is defined by new (nuisance) parameters and new data, then the Type I frequentist error of an $\alpha$-level posterior predictive test is often close to but less than $\alpha$ and will never exceed $2\alpha$.

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Metadata

Authors
Meng, X.-L.
Venue
The Annals of Statistics
Publisher
Institute of Mathematical Statistics
Published
1994-09-01
Volume
22
Issue
3
ISSN
0090-5364 (ISSN-L)
DOI
10.1214/aos/1176325622
OpenAlex
W2005587766
Cited by
785
References
11
FWCI
7.48
Type
journal article
Language
en
Open access
bronze

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CoChat. (2026). Citation check: Posterior Predictive $p$-Values. https://app.cochat.ai/papers/10.1214/aos/1176325622
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Meng, X.-L. (1994). Posterior Predictive $p$-Values. The Annals of Statistics. https://doi.org/10.1214/aos/1176325622

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