Power priors for replication studies

Samuel Pawel (), Frederik Aust, Leonhard Held and Eric-Jan Wagenmakers
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Samuel Pawel: University of Zurich
Frederik Aust: University of Amsterdam
Leonhard Held: University of Zurich
Eric-Jan Wagenmakers: University of Amsterdam

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 1, No 10, 127-154

Abstract: Abstract The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study’s data is raised to the power of $$\alpha $$ α , and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter $$\alpha $$ α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter $$\alpha $$ α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance $$I^2$$ I 2 . The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.

Keywords: Bayes factor; Bayesian hypothesis testing; Bayesian parameter estimation; Hierarchical models; Historical data; 62Fxx Parametric inference; 62Kxx Design of statistical experiments; 62Jxx Linear inference; regression; 62Lxx Sequential statistical methods; 62Pxx Applications of statistics (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-023-00888-5

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