The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion
Abstract
To compute a Bayes factor for testing H 0: ψ = ψ0 in the presence of a nuisance parameter β, priors under the null and alternative hypotheses must be chosen. As in Bayesian estimation, an important problem has been to define automatic, or “reference,” methods for determining priors based only on the structure of the model. In this article we apply the heuristic device of taking the amount of information in the prior on ψ equal to the amount of information in a single observation. Then, after transforming β to be “null orthogonal” to ψ, we take the marginal priors on β to be equal under the null and alternative hypotheses. Doing so, and taking the prior on ψ to be Normal, we find that the log of the Bayes factor may be approximated by the Schwarz criterion with an error of order O p (n −½), rather than the usual error of order O p (1). This result suggests the Schwarz criterion should provide sensible approximate solutions to Bayesian testing problems, at least when the hypotheses are nested. When instead the prior on ψ is elliptically Cauchy, a constant correction term must be added to the Schwarz criterion; the result then becomes a multidimensional generalization of Jeffreys's method.
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Cites
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Metadata
- Authors
- Kass, R. E., & Wasserman, L.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1995-09
- Volume
- 90
- Issue
- 431
- Pages
- 928-934
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1985593448
- Cited by
- 1,253
- References
- 15
- FWCI
- 10.41
- Type
- journal article
- Language
- en
- Open access
- closed
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