Bayesian Nonparametric Models for Pooled Data

This work examines two applications of pooling: group testing and pooled biomonitoring. Group testing, introduced by Dorfman in the early 1940s, was initially developed to screen for syphilis among U.S. inductees during World War II. Since then, the approach has demonstrated cost-saving benefits in diverse fields, including drug discovery, genetics, and infectious disease testing. While various regression methods—parametric, nonparametric, and semiparametric—have been proposed to analyze group testing data, they fall short in addressing age-related disparities in disease presence if such variations exist. In Chapter 2, we address this gap by expanding varying coefficient regression within a Bayesian framework to accommodate all types of group testing data. Pooled biomonitoring, which combines individual biological samples for collective analysis, offers a cost-effective approach to assessing human exposure to environmental contaminants. However, challenges arise in estimating the association between pooled measurements of the contaminants and individual-level covariates. In Chapter 3, we introduce soft Bayesian additive regression trees for pooled biomonitoring data, allowing for flexible modeling of complex dependencies and interactions between covariates without requiring a predefined structure.