2014/06/23 by Matthew Reimherr, Xiao-Li Meng, Reimherr, Matthew +3
Economics, Econometrics and Finance · Mathematics · #62F15 #Advanced Causal Inference Techniques #FOS: Computer and information sciences #Health Systems, Economic Evaluations, Quality of Life #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1406.5958
openalex publication_date 2014/06/23 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28
This paper outlines a framework for quantifying the prior's contribution to\nposterior inference in the presence of prior-likelihood discordance, a broader\nconcept than the usual notion of prior-likelihood conflict. We achieve this\ndual purpose by extending the classic notion of \prior sample size,\nM, in three directions: (I) estimating M beyond conjugate families; (II)\nformulating M as a relative notion, i.e., as a function of the likelihood\nsample size k, M(k), which also leads naturally to a graphical diagnosis; and\n(III) permitting negative M, as a measure of prior-likelihood conflict, i.e.,\nharmful discordance. Our asymptotic regime permits the prior sample size to\ngrow with the likelihood data size, hence making asymptotic arguments\nmeaningful for investigating the impact of the prior relative to that of\nlikelihood. It leads to a simple asymptotic formula for quantifying the impact\nof a proper prior that only involves computing a centrality and a spread\nmeasure of the prior and the posterior. We use simulated and real data to\nillustrate the potential of the proposed framework, including quantifying how\nweak is a "weakly informative" prior adopted in a study of lupus nephritis.\nWhereas we take a pragmatic perspective in assessing the impact of a prior on a\ngiven inference problem under a specific evaluative metric, we also touch upon\nconceptual and theoretical issues such as using improper priors and permitting\npriors with asymptotically non-vanishing influence.\n