A Bayesian perspective on the bonferroni adjustment
Abstract
Bayes/frequentist correspondences between the p-value and the posterior probability of the null hypothesis have been studied in univariate hypothesis testing situations. This paper extends these comparisons to multiple testing and in particular to the Bonferroni multiple testing method, in which p-values are adjusted by multiplying by k, the number of tests considered. In the Bayesian setting, prior assessments may need to be adjusted to account for multiple hypotheses, resulting in corresponding adjustments to the posterior probabilities. Conditions are given for which the adjusted posterior probabilities roughly correspond to Bonferroni adjusted p-values.
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Bayes Factors were computed using a Bayesian ANOVA based on extracted activation from significant clusters in the pooled sample for each parameter and corrected for multiple comparisons.
“Furthermore, we computed Bayes Factors using a Bayesian ANOVA based on the extracted activation from the significant clusters in the pooled sample for each of the parameters and corrected for multiple comparisons following Westfall et al. (1997) as described in de Jong (2019).”
From Are prediction error modifications domain specific in autism but domain general in ADHD? (2025) · cites this paper as Westfall et al. (1997)
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“Furthermore, we computed Bayes Factors using a Bayesian ANOVA based on the extracted activation from the significant clusters in the pooled sample for each of the parameters and corrected for multiple comparisons following Westfall et al. (1997) as described in de Jong (2019).”
- Authors
- Westfall, P.
- Affiliations
- Texas Tech University (US)
- Corresponding author
- Westfall, P.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1997-06-01
- Volume
- 84
- Issue
- 2
- Pages
- 419-427
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2078409704
- Cited by
- 316
- References
- 21
- Citations by year
- 2026: 14 · 2025: 31 · 2024: 26 · 2023: 27 · 2022: 31 · 2021: 36 · 2020: 24 · 2019: 17 · 2018: 6 · 2017: 3 · 2016: 4 · 2015: 7 · 2014: 7 · 2013: 1 · 2012: 24
- FWCI
- 1.47
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrika (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- Bonferroni correction, multiple comparisons, p-values, prior specification, false discovery rate
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