Bayes factors for peri-null hypotheses

Alexander Ly () and Eric-Jan Wagenmakers ()
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Alexander Ly: University of Amsterdam
Eric-Jan Wagenmakers: University of Amsterdam

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 31, issue 4, No 11, 1142 pages

Abstract: Abstract A perennial objection against Bayes factor point-null hypothesis tests is that the point-null hypothesis is known to be false from the outset. We examine the consequences of approximating the sharp point-null hypothesis by a hazy ‘peri-null’ hypothesis instantiated as a narrow prior distribution centered on the point of interest. The peri-null Bayes factor then equals the point-null Bayes factor multiplied by a correction term which is itself a Bayes factor. For moderate sample sizes, the correction term is relatively inconsequential; however, for large sample sizes, the correction term becomes influential and causes the peri-null Bayes factor to be inconsistent and approach a limit that depends on the ratio of prior ordinates evaluated at the maximum likelihood estimate. We characterize the asymptotic behavior of the peri-null Bayes factor and briefly discuss suggestions on how to construct peri-null Bayes factor hypothesis tests that are also consistent.

Keywords: Consistency; Peri-null correction factor; Asymptotic sampling distribution; 62F03; 62F15; 62F05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11749-022-00819-w

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