Generalized Linear Models for Small-Area Estimation
针对离散或分类调查数据，提出分层贝叶斯广义线性模型，统一分析离散和连续数据，并给出后验分布合理的定理，通过MCMC实现，附有空间相关性的实例。
Abstract Bayesian methods have been used quite extensively in recent years for solving small-area estimation problems. Particularly effective in this regard has been the hierarchical or empirical Bayes approach, which is especially suitable for a systematic connection of local areas through models. However, the development to date has mainly concentrated on continuous-valued variates. Often the survey data are discrete or categorical, so that hierarchical or empirical Bayes techniques designed for continuous variates are inappropriate. This article considers hierarchical Bayes generalized linear models for a unified analysis of both discrete and continuous data. A general theorem is provided that ensures the propriety of posteriors under diffuse priors. This result is then extended to the case of spatial generalized linear models. The hierarchical Bayes procedure is implemented via Markov chain Monte Carlo integration techniques. Two examples (one featuring spatial correlation structure) are given to illustrate the general method.