| This thesis presents a new, comprehensive, integrated mathematical framework for doing Bayesian graphical modeling and data analysis, and discusses its connection with posterior inference, replication distributions, prior and posterior predictive inference, and modeling coarse, incomplete, and missing data.; We introduce an object-oriented programming paradigm based on a random variable object type that is implicitly represented by simulations. This makes it possible to define vector and array objects that may contain both random and deterministic quantities, and syntax rules that allow treating these objects like any numeric vectors or arrays, providing a solution to various problems encountered in Bayesian computing involving posterior simulations.; We introduce a software application Umacs (Universal Markov chain sampler), which is a software package that facilitates the construction of the Gibbs sampler and Metropolis algorithm for Bayesian inference by generating samplers automatically from user-defined Gibbs updating functions and posterior density functions. |
