Bayesian Methods for Small Area Estimation and Latent Structure Models

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The primary focus on this research is on applications of Bayesian methods to small area estimation with discrete outcomes. Small area estimation is becoming increasingly popular in survey sampling owing to the demand for small area estimates from both public and private sectors. In typical instances of small area estimation, only a few samples are available from individual areas. The direct survey estimates, therefore, tend to have large standard errors and coefficients of variation. Incorporating information from similar neighboring areas typically improves an estimate of a certain area mean, or the simultaneous estimation of several area means. Empirical and hierarchical Bayes methods are particularly well-suited to meet this need of `borrowing strength` from related small areas. The new methods of estimation will provide much more reliable estimates with reduced standard errors. The investigator will apply the new methods to the analysis of various social, medical, and environmental data; e.g., the investigator will estimate the percentage of people satisfied with their job in several local areas cross-classified by age, sex, and race. Other possible applications include exposure to health hazards in jobs, estimation of cancer mortality rates, analysis of mortality rates in the presence of hazardous waste sites, and analysis of spatial data. Another aspect of the investigator's research will concentrate on hierarchical and empirical Bayes analysis of latent structure models. The celebrated Rasch model will be included as a special case. This analysis will provide unified method for the analysis of social and psychological data.