Improving Efficiency in Parameter Estimation Using the Hamiltonian Monte Carlo Algorithm

This thesis investigates three approaches to improve the performance of the Hamiltonian Monte Carlo algorithm. The first approach enhances the Hamiltonian Monte Carlo by suppressing random walk in the Gibbs sampling using ordered over--relaxation. The second approach investigates the simulation of the Hamiltonian dynamics using an adaptive step--size to reduce the error of the simulation. The third proposal is to combine the two versions into one algorithm.