Fully Bayesian Inference for Meta-Analytic Deconvolution Using Efron’s Log-Spline Prior

JoonHo Lee () and Daihe Sui
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JoonHo Lee: Department of Educational Studies in Psychology, Research Methodology, and Counseling, The University of Alabama, Tuscaloosa, AL 35487, USA
Daihe Sui: Department of Statistics and Data Science, Northwestern University, Evanston, IL 60201, USA

Mathematics, 2025, vol. 13, issue 16, 1-49

Abstract: Meta-analytic deconvolution seeks to recover the distribution of true effects from noisy site-specific estimates. While Efron’s log-spline prior provides an elegant empirical Bayes solution with excellent point estimation properties, its plug-in nature yields severely anti-conservative uncertainty quantification for individual site effects—a critical limitation for what Efron terms “finite-Bayes inference.” We develop a fully Bayesian extension that preserves the computational advantages of the log-spline framework while properly propagating hyperparameter uncertainty into site-level posteriors. Our approach embeds the log-spline prior within a hierarchical model with adaptive regularization, enabling exact finite-sample inference without asymptotic approximations. Through simulation studies calibrated to realistic meta-analytic scenarios, we demonstrate that our method achieves near-nominal coverage (88-91%) for 90% credible intervals while matching empirical Bayes point estimation accuracy. We provide a complete Stan implementation handling heteroscedastic observations—a critical feature absent from existing software. The method enables principled uncertainty quantification for individual effects at modest computational cost, making it particularly valuable for applications requiring accurate site-specific inference, such as multisite trials and institutional performance assessment.

Keywords: meta-analytic deconvolution; empirical Bayes; fully Bayesian inference; log-spline prior; finite-Bayes inference; uncertainty quantification; hierarchical models; heteroscedastic observations; Stan (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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