Applications of Bayesian Probability Theory in Fusion Data Analysis

Bayesian probability theory is a powerful tool for solving complex problems in experimental data analysis. In this thesis we explore the use of Bayesian methods in magnetic confinement fusion with an emphasis toward developing analysis tools and techniques. The original research content is presented in three chapters. In the first we develop a new approach to efficiently characterising multi-dimensional posterior distributions. This is achieved through an algorithm which, for any number of posterior dimensions, can decide which areas of the probability space contain significant information and evaluate only those areas. This addresses the computational challenges which arise in calculating marginal distributions from many-dimensional posteriors. In the second research chapter Bayesian probability theory is applied to the discrete Fourier-transform of an arbitrary real series containing random noise. The effect of the noise on the Fourier coefficients is used to derive a correction to the Fourier magnitudes, which results in a reduction in the overall noise-level after an inverse-transform. Calculating these corrections requires the solution of a challenging inverse problem which is discussed at length, and several methods for obtaining approximate solutions are developed and tested. The correction itself, plus the methods allowing its calculation together form the basis of a new technique for noise correction which is completely general, as no assumptions are made about the series which is to be corrected. In the final research chapter the inference of physics parameters using the DIII-D CER system is discussed. A Bayesian network approach is used to derive a model for the observed charge-exchange spectrum, which is itself used to construct a posterior distribution for the model parameters. The spectrum model is used to explore the possibility of inferring the time-evolution of physical parameters on sub-integration time-scales.