Bayesian Estimation of Finite Population Parameters in Categorical Data Models Incorporating Order Restrictions
J. Sedransk, John F. Monahan, H. Y. Chiu · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1985
SUMMARY This note describes a Bayesian method for estimation of finite population parameters in general population surveys where acceptable regression-type models are typically unavailable. A categorical data model is adopted as in Ericson (1969, Section 4). However, specifications of smoothness are incorporated into the prior distribution. These smoothness conditions are expressed as unimodal or, possibly, multi-modal order relations among the category probabilities. Emphasis is placed on posterior inference about the finite population mean. Of independent interest is the methodology for evaluating the posterior moments and probabilities using Monte Carlo integration with importance sampling.