Dynamic hierarchical models with applications

This thesis presents the new methodological approach for carrying out Bayesian inference of the Dynamic hierarchical models for different application areas. The first application is carried out in time series of compositional data. This kind of data comprises of multivariate observations which at each time point are essentially proportion of a whole quantity. This kind of data occurs frequently in many disciplines such as economics, geology and ecology. Usual multivariate statistical procedures available in the literature are not applicable for the analysis of such data since they ignore the inherent constrained nature of these observations as parts of a whole. A new technique for modeling compositional time series data is studied in a hierarchical Bayesian framework. The distribution of the underlying errors is assumed to be a scale mixture of normals of which the multivariate normal, multivariate t, multivariate logistic etc. are special cases. In particular, multivariate normal and Student-t error structures are considered and compared using DIC. The approach is illustrated on two data sets. ^ The second kind of application is focused on the modeling of the time series of correlated binary data. Scale mixture of multivariate normal links are again used to develop a general class of link functions to model such data. This large class of link functions give us the flexibility to consider different kinds of links as a special case. Markov chain Monte Carlo method is used to simulate from posterior distributions. Bayesian inference, model diagnostics and model selections are considered. The proposed methodology is illustrated on a real data set on house price from Dade county, Florida over a period of 21 years, where the objective is to model binary responses of house prices (high versus low) in presence of assessed value, age and square feet. ^ The third application is an immediate extension of the second application. All the link functions used in the second application are symmetric. However in some applications the overall fit can be significantly improved by the use of asymmetric link function. A new skewed link model is introduced to model time series of binary responses through dynamic linear model in this chapter. A new class of distributions which is more versatile than Student\u27s t distribution is used to model the data. Skewness is introduced by using a skewed distribution for the underlying latent variable. The new class of distribution is developed by using scale mixture of normal distribution with suitably chosen mixing density. (Abstract shortened by UMI.)