ABSTRACT
This chapter discusses the hierarchical multimodel Bayesian framework is developed using probabilistic modeling. It provides an efficient updating algorithm is formulated based on the principle of minimum discrimination information to reduce the computational complexity in updating. The standard Markov chain Monte Carlo (MCMC) simulation technique was first introduced in as a method to simulate discrete-time homogeneous Markov chain using the random walk (RW) algorithm. The RW algorithm is based on symmetric proposal distributions. In the transdimensional MCMC algorithm, the chain explores both across and within models in the general state space. Across model moves involves model coordinate transformations. Local moves within models can rely on the usual RW or Metropolis-Hastings (M-H) algorithms because no model coordinate transformation is needed. The standard M-H algorithm is used in usual MCMC simulations for fixed dimensional problems. Since MCMC simulations are employed intensively in the updating process, its capability and performance plays an important role.
