Bayesian dynamic modeling and its applications in marketing and neuroscience

This thesis considers models in which the response is a binary (univariate or multivariate) outcome. The common theme is that the responses are observed over time. In addition, values for covariates that might or might not be time varying are also observed. The length of the time series, correlation structure, sparsity of the data and heterogeneity govern the choice of model. Specifically, two applications are presented, one in the area of marketing and the other in neuroscience. In the marketing application, we model brand equity as a dynamic latent process that governs the intrinsic preference of a customer for a brand over time, and allow it to be correlated with other observed covariates (or their coefficients) to capture the notion of perceived value created by brands. We model the correlated binary purchase data using a multivariate probit model. The latent brand equity process and the parameters in the model are estimated using an MCMC sampling method coupled with the Kalman filter. In addition, the new model of brand equity provides insights into pricing and marketing strategy that could otherwise be misleading under a misspecified model. In the neuroscience application, we consider the task of extracting a feature that can reflect the underlying physiological process of the brain during mental tasks. We propose a parametric multivariate stochastic volatility (MSV) model to extract the time-varying volatility of intracranial electroencephalographic (iEEG) signals as a biomarker for the behavior of the brain. We utilize a particle learning method to analyze the long iEEG time series. In addition, we investigate the relationship between volatility and spectral power. We then study the volatility process and its associated parameters across brain regions during a free-recall task. The results indicate that volatility is correlated with neural activity during mental tasks and can be used as a tool for understanding how activity in the brain relates to learning. Both applications involve Bayesian dynamic modeling of a latent process. A rich data set is analyzed for each of the applications. These data sets serve to illustrate the models and estimation techniques that are developed in the thesis