2021/09/24 by Sona Hunanyan, Håvard Rue, Hunanyan, Sona +5
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Bayesian hierarchical modeling #Bayesian inference #Bayesian probability #Computation (stat.CO) #Computer science #Determinacy #Econometrics #Economic and Environmental Valuation #FOS: Computer and information sciences #Marginal likelihood #Mathematics #Methodology (stat.ME) #Posterior probability #Prior probability #Statistical Methods and Bayesian Inference #Statistics #Weighting #stat.CO #stat.ME
paper · pdf · doi:10.48550/arxiv.2109.11870
published in arXiv (Cornell University) (Cornell University) · 22 pages, 1 figure
arxiv created 2021/09/24 · openalex publication_date 2021/09/24 · arxiv updated 2021/09/27 · openalex created_date 2022/10/09 · openalex updated_date 2026/08/06
The popular Bayesian meta-analysis expressed by Bayesian normal-normal\nhierarchical model (NNHM) synthesizes knowledge from several studies and is\nhighly relevant in practice. Moreover, NNHM is the simplest Bayesian\nhierarchical model (BHM), which illustrates problems typical in more complex\nBHMs. Until now, it has been unclear to what extent the data determines the\nmarginal posterior distributions of the parameters in NNHM. To address this\nissue we computed the second derivative of the Bhattacharyya coefficient with\nrespect to the weighted likelihood, defined the total empirical determinacy\n(TED), the proportion of the empirical determinacy of location to TED (pEDL),\nand the proportion of the empirical determinacy of spread to TED (pEDS). We\nimplemented this method in the R package \ed4bhm and considered two\ncase studies and one simulation study. We quantified TED, pEDL and pEDS under\ndifferent modeling conditions such as model parametrization, the primary\noutcome, and the prior. This clarified to what extent the location and spread\nof the marginal posterior distributions of the parameters are determined by the\ndata. Although these investigations focused on Bayesian NNHM, the method\nproposed is applicable more generally to complex BHMs.\n