Bayesian Modeling and Analysis of Multivariate Time Series, with Applications in Finance and Health Policy
This dissertation develops Bayesian theory and computation to address important issues in two main socio-economic areas: financial modeling and institutional assessment. The first part focusses on computational developments for model fitting and forecasting of multiple series of crude oil futures prices. The methodology is motivated by the central role that the stochastic behavior of commodity prices plays in the evaluation of commodity-related securities. A class of Bayesian multivariate dynamic linear models for oil future prices is developed based on a theoretical financial model that assumes two latent factor processes: a notional equilibrium price level and a process representing short-term deviations from equilibrium levels. A customized Markov Chain Monte Carlo (MCMC) sampling scheme is developed for inference and analysis of such model. In addition, several structures on the observational variance are explored including the challenging case of a singular variance matrix. Relevant and supporting theory of singular densities and DLMs under singular observational variance is reviewed and developed. The second part involves the development of large-scale longitudinal models for institutional comparisons. Complex non-Gaussian hierarchical models are developed to profile providers in health-care delivery systems. The key motivating concern is to estimate health-care return-time distributions for individuals, and to evaluate differences due to year of care and hospital, in the context of a range of possible individual-level explanatory variables. Results indicate significant system-wide improvement in the health-care areas of study, in addition to large amounts of variation in this improvement across medical centers. Covariates such as age of patient, treatment priority, and diagnoses help to illustrate important potential new health policy interventions and the outcomes of previous interventions. The study involves innovation in hierarchical/longitudinal models for the very large and complex data set, a range of exploratory data analytic developments, customized MCMC for Bayesian model fitting and some creativity in exploring the very high-dimensional posterior distributions and summarizing MCMC outputs.