published_or_final_version / Clinical Oncology / Doctoral / Doctor of Philosophy

Perfect Gibbs sampling is a method to turn Markov Chain Monte Carlo (MCMC) samplers into exact generators for independent random vectors. We show that a perfect Gibbs sampling algorithm suggested in the literature is not always generating from the correct distribution. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

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In this work, the method of streaming rays have been expanded to two spatial dimensions (three phase space dimensions, x, y, and s) and was used as a basis for the development of the electron transport computer code SR2D. The streaming ray algorithm is an Eulerian-Lagrangian hybrid. Electrons are followed as they traverse the medium along specified streaming rays. Fluxes, however, are computed at the centers of the fixed cells. The development of the SR2D code required the specification of a Lagrangian streaming ray network overlaying a three dimensional Eulerian grid. In contrast to its one dimensional predecessor, the SR2D code accommodates non-uniform cell sizes and allows for arbitrary quadrature sets (S₂, S₄, S₆, S₈, S₁₂, or S₁₆). The critical aspect of the streaming ray method is the determination of the pathlengths of each and every streaming ray through all of the Eulerian cells. These values must be precalculated and stored because of the iterative nature of the solution scheme. Although the number of pathlengths may be exceedingly large, computer memory requirements are minimized, however, in the two dimensional algorithm by the symmetry of the geometry in each pathlength increment. The SR2D code was used to calculate the energy deposition profile for two kinds of sources, an isotropic point source and a monodirectional point at the periphery of a two dimensional medium. For each case, we chose aluminum with dimensions 0.01g/cm² thick by 0.02g/cm² wide as the medium and specified a grid of 5 by 10 uniform cells, respectively. The pathlength increment was 0.002g/cm² with 25 pathlength increments chosen. An S₈ quadrature set was selected for the monodirectional point source while an S₁₂ quadrature set was used for the isotropic point source. Both sources were normalized to one incident particle with an energy of 200 keV. SR2D results were compared with those from the electron/photon Monte Carlo code TIGER. The total energy deposited in the medium and peak cell was selected to facilitate the comparison. For the monodirectional point source SR2D results were within 1% for total energy deposited into the medium and peak cell energy. The total energy deposited for the isotropic point source was within 1%, but peak cell energy varied by 4%.

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