Status : Verified
| Personal Name | Siete-Galeos, Jhoanne Rose T. |
|---|---|
| Resource Title | Hybrid Prior Configurations for Bayesian Hierarchical Meta-Analysis of Standardized Mean Differences Under Sparse-Data Conditions |
| Date Issued | July 2026 |
| Abstract | Meta-analysis is a widely used method for synthesizing evidence across studies, but its performance is severely degraded when the number of studies is small. This thesis focuses on the standardized mean difference (SMD)—one of the most common effect size measures in clinical and behavioral research—because its variance formula depends on the observed effect size itself, creating a feedback loop that makes between-study heterogeneity estimation especially unstable under sparse-data conditions. To address this instability, this thesis proposes and evaluates a family of Hybrid Bayesian meta-analysis (Hybrid BMA) configurations, each assigning a flat (non-informative) prior on the overall effect µ while varying the prior on the heterogeneity parameter τ. Four Hybrid specifications are examined: (1) Hybrid HC(0.3): flat µ, τ ∼ Half-Cauchy(0, 0.3) (primary); (2) Hybrid HC(1.0): flat µ, τ ∼ Half-Cauchy(0, 1.0) (for high-heterogeneity settings); (3) Hybrid IG(0.3): flat µ, τ2 ∼ IG(2, 0.5025) (median- parity substitute for HC(0.3)); and (4) Hybrid IG(1.0): flat µ, τ2 ∼ IG(2, 1.675) (median- parity substitute for HC(1.0)). The IG specifications serve as software-compatible al-ternatives for implementations lacking native Half-Cauchy distributions. Formal proofs establish that all four Hybrid posteriors are proper—with the IG specifications yielding the stronger guarantee of propriety for k ≥ 1 (versus k ≥ 2 for the HC specifications). The four Hybrid configurations are compared against a fully non-informative Bayesian configuration (flat µ, Jeffreys π(τ) ∝ 1/τ), a fully weakly informative configuration (µ ∼ N(0, 1), τ ∼ Half-Cauchy(0, 0.3)), and the Modified Knapp–Hartung (mKH) fre-quentist estimator. A simulation study with R = 1,000 replications across k ∈ {3, 5, 10, 30} studies and heterogeneity levels τ ∈ {0.10, 0.30, 0.50, 0.80} demonstrates that all four Hybrid con- figurations substantially outperform the Weakly I |
| Degree Course | Master of Science in Statistics |
| Language | English |
| Keyword | Bayesian meta-analysis, hybrid prior, standardized mean difference, small-sample inference, hierarchical model, numerical grid integration, Half-Cauchy prior, inverse-gamma prior, median-parity specification |
| Material Type | Thesis/Dissertation |
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Category : F - Regular work, i.e., it has no patentable invention or creation, the author does not wish for personal publication, there is no confidential information.
Access Permission : Open Access