Some applications of hierarchical Bayesian approaches to longitudinal and time series data

This thesis focuses on the application of the hierarchical Bayesian (HB) methodology to real data. The HB method is employed because of its many advantages in modeling, interpretation and in computation. It improves model fitting by pooling the data and borrowing strength from each other, and simplifies a complicated problem by breaking down a one-level structure into a multi-level hierarchical structure. The powerful Markov chain Monte Carlo technique allows us to apply the HB method to many complicated statistical problems that cannot be solved or would not be justified by the classical method. ^ We apply the HB method on three different examples, all of which are related to the longitudinal or time series data. ^ In the first example, we discuss a change point model that applies to a dementia longitudinal problem. Two of the memory and cognitive measures are modeled in different time scales. We are interested in uncovering and comparing several different change points models.^ Our second example is on predicting the stock price from the book value and the projected future earnings. The objective is to consider a hierarchical structure for the regression coefficients to allow companies share information and borrow strength from each other. Moreover, an AR(1) structure of stock prices within each company is incorporated in the model. Different models are compared in terms of their forecasting powers. ^ In the last example, we consider an asset allocation problem. The traditional finance model is extended by incorporating a stochastic volatility structure with skewness and leptokurtosis in the distribution of asset returns. Different models are then compared in terms of their cumulative portfolio returns with an optimal allocation scheme.