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Bayes factors for peri-null hypotheses

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  • Alexander Ly

    (University of Amsterdam
    Machine Learning Group, Centrum Wiskunde & Informatica)

  • Eric-Jan Wagenmakers

    (University of Amsterdam)

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.

Suggested Citation

  • Alexander Ly & Eric-Jan Wagenmakers, 2022. "Bayes factors for peri-null hypotheses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1121-1142, December.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:4:d:10.1007_s11749-022-00819-w
    DOI: 10.1007/s11749-022-00819-w
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    References listed on IDEAS

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    1. Valen E. Johnson & David Rossell, 2010. "On the use of non‐local prior densities in Bayesian hypothesis tests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 143-170, March.
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