Recent Advances in Bayesian Analysis for Complex Datasets

In this work, our main objective is to identify the risk factors associated with adolescent marijuana use in Washington State, utilizing data from the 2021 Healthy Youth Survey (HYS). While the survey guarantees anonymity, the possibility of over- or under-reporting exists due to various reasons, such as fear of being exposed, social stigma, peer pressure, and so on. We are interested in identifying factors that are associated with the true marijuana use as well as the occurrence of misreport. We develop a full Bayesian framework with a two-level latent linear regression model. The top level is for the true Marijuana use response and the second level is for the occurrence of misreporting. A partially collapsed Gibbs Sampling algorithm is proposed to sample the regression coefficients. Intensive Monte Carlo simulation is used to demonstrate the performance of the proposed methods. Our analysis of HYS data discovers multiple factors for identifying at-risk adolescents and informing future prevention efforts.  

We provide a novel latent variable representation of independent component analysis, that enables both point estimates via expectation-maximization (EM) and full posterior sampling via Markov Chain Monte Carlo (MCMC) algorithms for fast implementation. Our method also applies to flow-based methods for nonlinear feature extraction. We discuss how to implement conditional posteriors and envelope-based methods for optimization. Through this representation hierarchy, we unify a number of hitherto disjoint estimation procedures. We illustrate our methodology and algorithms on a numerical example. Finally, we conclude with directions for future research.