by Tang Hing Sing. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 92-96.

Markov chain Monte Carlo (MCMC) is one of the most popular statistical inference methods in machine learning. Recent work shows that a significant improvement of the statistical efficiency of MCMC on complex distributions can be achieved by exploiting geometric properties of the target distribution. This is known as geometric MCMC. However, many such methods, like Riemannian manifold Hamiltonian Monte Carlo (RMHMC), are computationally challenging to scale up to high dimensional distributions. The primary goal of this thesis is to develop novel geometric MCMC methods applicable to large-scale problems. To overcome the computational bottleneck of computing second order derivatives in geometric MCMC, I propose an adaptive MCMC algorithm using an efficient approximation based on Limited memory BFGS. I also propose a simplified variant of RMHMC that is able to work effectively on larger scale than the previous methods. Finally, I address an important limitation of geometric MCMC, namely that is only available for continuous distributions. I investigate a relaxation of discrete variables to continuous variables that allows us to apply the geometric methods. This is a new direction of MCMC research which is of potential interest to many applications. The effectiveness of the proposed methods is demonstrated on a wide range of popular models, including generalised linear models, conditional random fields (CRFs), hierarchical models and Boltzmann machines.

A turbomolecular pump (TMP) with good performance must have higher compress ratio and higher pumping speed. At the same time, the performance of turbomolecular pump depends on blade geometries and the rotational speed. When design the blade of Turbomolecular Pump, the blade geometries including, the blade angle, the blade spacing, the blade chord, the spacing-chord ratio, the tip diameter, the root diameter, and the number of blades and as well as the rotational speed of the rotor must be considered. In this paper the simulation for gas molecular behavior is obtained by the Monte Carlo method. Therefore, a Maxwellian distribution of particles at the inlet and outlet of the flow region and diffuse reflection for the particles that collide with the walls are assumed. Models of this type have been applied to the two-dimensional case. The most important result is to compare the performance between turbomolecular pumps with curve style and plane style of blades. Furthermore, that direct multi-stage simulation (DMS) by Monte Carlo method is used in this paper. The compression ratio multiplication (CRM) method is the improved due to the considering the change of velocity distribution of molecular at the adjacent stages. From results of the simulation, the effect upon the geometric parameters of the blades and the arrangement in the multi-stage are concluded, that are very useful in designing the turbomolecular.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 92-97). Available also in a digital version from Dissertation Abstracts.

published_or_final_version / Physics / Master / Master of Philosophy

Computing marginal likelihoods to perform Bayesian model selection is a challenging task, particularly when the models considered involve a large number of parameters. In this thesis, we propose the use of an adaptive quadrature algorithm to automate the selection of the grid in path sampling, an integration technique recognized as one of the most powerful Monte Carlo integration statistical methods for marginal likelihood estimation. We begin by examining the impact of two tuning parameters of path sampling, the choice of the importance density and the specification of the grid, which are both shown to be potentially very influential. We then present, in detail, the Grid Selection by Adaptive Quadrature (GSAQ) algorithm for selecting the grid. We perform a comparison between the GSAQ and standard grid implementation of path sampling using two well-studied data sets; the GSAQ approach is found to yield superior results. GSAQ is then successfully applied to a longitudinal hierarchical regression model selection problem in Multiple Sclerosis research. / Using an identity arising in path sampling, we then derive general expressions for the Kullback-Leibler (KL) and Jeffrey (J) divergences between two distributions with common support but from possibly different parametric families. These expressions naturally stem from path sampling when the popular geometric path is used to link the extreme densities. Expressions for the KL and J-divergences are also given for any two intermediate densities lying on the path. Estimates for the KL divergence (up to a constant) and for the J-divergence, between a posterior distribution and a selected importance density, can be obtained directly, prior to path sampling implementation. The J-divergence is shown to be helpful for choosing importance densities that minimize the error of the path sampling estimates. / Finally we present the results of a simulation study devised to investigate whether improvement in performance can be achieved by using the KL and J-divergences to select sequences of distributions in parallel (population-based) simulations, such as in the Sequential Monte Carlo Sampling and the Annealed Importance Sampling algorithms. We compare these choices of sequences to more conventional choices in the context of a mixture example. Unexpected results are obtained, and those for the KL and J-divergences are mixed. More fundamentally, we uncover the need to select the sequence of tempered distributions in accordance with the resampling scheme.

Thesis (M.S. - Hydrology and Water Resources) - University of Arizona. / Includes bibliographical references (leaves 87-93).

Dissertation (Ph.D.)--University of Toledo, 2008. / Typescript. "As partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics." Bibliography: leaves 130-137.

Thesis (M.S.)--State University of New York at Binghamton, Watson School of Engineering and Applied Science (Systems Science), 2007. / Includes bibliographical references.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 85-86). Also available via the Internet.