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Normalized power priors always discount historical data


Pawel, Samuel; Aust, Frederik; Held, Leonhard; Wagenmakers, Eric‐Jan (2023). Normalized power priors always discount historical data. Stat, 12(1):e591.

Abstract

Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power as the prior distribution for the model parameters. The power parameter is typically unknown and assigned a prior distribution, most commonly a beta distribution. Here, we give a novel theoretical result on the resulting marginal posterior distribution of in case of the normal and binomial model. Counterintuitively, when the current data perfectly mirror the historical data and the sample sizes from both data sets become arbitrarily large, the marginal posterior of does not converge to a point mass at but approaches a distribution that hardly differs from the prior. The result implies that a complete pooling of historical and current data is impossible if a power prior with beta prior for is used.

Abstract

Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power as the prior distribution for the model parameters. The power parameter is typically unknown and assigned a prior distribution, most commonly a beta distribution. Here, we give a novel theoretical result on the resulting marginal posterior distribution of in case of the normal and binomial model. Counterintuitively, when the current data perfectly mirror the historical data and the sample sizes from both data sets become arbitrarily large, the marginal posterior of does not converge to a point mass at but approaches a distribution that hardly differs from the prior. The result implies that a complete pooling of historical and current data is impossible if a power prior with beta prior for is used.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Statistics and Probability
Language:English
Date:1 January 2023
Deposited On:16 Jan 2024 12:15
Last Modified:30 Jun 2024 01:37
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:2049-1573
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1002/sta4.591
Project Information:
  • : FunderSNSF
  • : Grant ID189295
  • : Project TitleReverse-Bayes Design and Analysis of Replication Studies
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)