Fully Bayesian Inference for Meta-Analytic Deconvolution Using Efron’s Log-Spline Prior
Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13162639
Authors: JoonHo Lee, Daihe Sui
Institutions: University of Alabama, Northwestern University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: Institute of Education Sciences
OpenAlex ID: W4413286378