Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is particularly cumbersome in linear mixed models (LMMs) because marginal likelihood functions involve integrals of large dimensions determined by the number of parameters and the number of random effects, which in turn increase with the number of individuals in the sample. The power posterior is an attractive proposal in the context of the Markov chain Monte Carlo algorithms that allows expressing marginal likelihoods as one-dimensional integrals over the unit range. This paper explores the use of power posteriors in LMMs and discusses their behaviour through two simulation studies and a real data set on European sardine landings in the Mediterranean Sea.
翻译:Bayes系数被界定为两个相互竞争的模型的边际可能性功能之比,是贝叶斯自然的模型选择程序。边际可能性通常在计算上要求很高而且复杂。在线性混合模型中,这种假设特别麻烦,因为边际可能性功能涉及由参数数量和随机效应数量决定的较大维度的内涵,而随机效应又随着样本中个人数量的增加而增加。在Markov连锁的Monte Carlo算法中,权力后继器是一个有吸引力的提议,该算法允许将边际可能性作为单位范围的一维组成部分来表达。本文探讨了LMMMs中电源后继器的使用情况,并通过两次模拟研究和关于欧洲沙丁鱼在地中海登陆的真实数据集来讨论其行为。