Abstract
Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart, uniformly most powerful Bayesian tests are most easily defined in one-parameter exponential family models, although extensions outside of this class are possible. The connection between uniformly most powerful tests and uniformly most powerful Bayesian tests can be used to provide an approximate calibration between <i>p</i>-values and Bayes factors. Finally, issues regarding the strong dependence of resulting Bayes factors and <i>p</i>-values on sample size are discussed.
Keywords
Bayes factorHiggs bosonJeffreys–Lindley paradoxNeyman–Pearson lemmanonlocal prior densityobjective Bayesone-parameter exponential family modeluniformly most powerful test
Related Publications
Bayes Factors
Abstract In a 1935 paper and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece wa...
Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models)
Abstract We consider two-stage models of the kind used in parametric empirical Bayes (PEB) methodology, calling them conditionally independent hierarchical models. We suppose th...
Modified Randomization Tests for Nonparametric Hypotheses
Suppose $X_1, \\cdots, X_m, Y_1, \\cdots, Y_n$ are $m + n = N$ independent random variables, the $X$'s identically distributed and the $Y$'s identically distributed, each with a...
Testing the Random Walk Hypothesis: Power versus Frequency of Observation
Power functions of tests of the random walk hypothesis versus stationary first order autoregressive alternatives are tabulated for samples of fixed span but various frequencies ...
Inference in Models with Nearly Integrated Regressors
This paper examines regression tests of whether x forecasts y when the largest autoregressive root of the regressor is unknown. It is shown that previously proposed two-step pro...
Publication Info
- Year
- 2013
- Type
- article
- Volume
- 41
- Issue
- 4
- Pages
- 1716-1741
- Citations
- 86
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
86
OpenAlex
17
Influential
56
CrossRef
Cite This
Valen E. Johnson
(2013).
Uniformly most powerful Bayesian tests.
The Annals of Statistics
, 41
(4)
, 1716-1741.
https://doi.org/10.1214/13-aos1123
Identifiers
- DOI
- 10.1214/13-aos1123
- PMID
- 24659829
- PMCID
- PMC3960084
- arXiv
- 1309.4656