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On the use of non-local prior densities in Bayesian hypothesis tests
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Johnson, Valen E. and Rossell, David (2010) On the use of non-local prior densities in Bayesian hypothesis tests. Journal of the Royal Statistical Society Series B: Statistical Methodology, Vol.72 (No.2). pp. 143-170. doi:10.1111/j.1467-9868.2009.00730.x
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Official URL: http://dx.doi.org/10.1111/j.1467-9868.2009.00730.x
Abstract
We examine philosophical problems and sampling deficiencies that are associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities that are used to define alternative hypotheses in many Bayesian tests assign non-negligible probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses, but only sublinear accumulation of evidence in favour of true null hypotheses. Thus, it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis, even when moderately large sample sizes have been obtained. We review asymptotic convergence rates of Bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most Bayesian tests. Using members of these classes, we obtain analytic expressions for Bayes factors in linear models and derive approximations to Bayes factors in large sample settings.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Statistics | ||||
| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Statistical hypothesis testing, Density functionals | ||||
| Journal or Publication Title: | Journal of the Royal Statistical Society Series B: Statistical Methodology | ||||
| Publisher: | Wiley-Blackwell Publishing, Inc | ||||
| ISSN: | 1369-7412 | ||||
| Official Date: | March 2010 | ||||
| Dates: |
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| Volume: | Vol.72 | ||||
| Number: | No.2 | ||||
| Page Range: | pp. 143-170 | ||||
| DOI: | 10.1111/j.1467-9868.2009.00730.x | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access |
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