文章基本信息

标题：Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models
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作者：Ioannis Ntzoufras ; Claudia Tarantola ; Monia Lupparelli 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2019
卷号：14
期号：3
页码：777-803
DOI：10.1214/18-BA1128
语种：English
出版社：International Society for Bayesian Analysis
摘要：We introduce a novel Bayesian approach for quantitative learning for graphical log-linear marginal models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. The likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and Markov Chain Monte Carlo (MCMC) methods are needed. Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities. Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for such models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. We exploit a conditional conjugate setup to build an efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset.
关键词：graphical models; marginal log-linear parameterisation; Markov Chain Monte Carlo computation.