A problem in particle physics and its Bayesian analysis

An up and coming field in contemporary nuclear and particle physics is "Lattice Quantum Chromodynamics", henceforth Lattice QCD. Indeed the 2004 Nobel Prize in Physics went to the developers of equations that describe QCD. In this dissertation, following a layperson's introduction to the structure of matter, we outline the statistical aspects of a problem in Lattice QCD faced by particle physicists, and point out the difficulties encountered by them in trying to address the problem. The difficulties stem from the fact that one is required to estimate a large -- conceptually infinite -- number of parameters based on a finite number of non-linear equations, each of which is a sum of exponential functions.; We then present a plausible approach for solving the problem. Our approach is Bayesian and is driven by a computationally intensive Markov Chain Monte Carlo based solution. However, in order to invoke our approach we first look at the underlying anatomy of the problem and synthesize its essentials. These essentials reveal a pattern that can be harnessed via some assumptions, and this in turn enables us to outline a pathway towards a solution. We demonstrate the viability of our approach via simulated data, followed by its validation against real data provided to us by our physicist colleagues. Our approach yields results that in the past were not obtainable via alternate approaches.; The contribution of this dissertation is two-fold. The first is a use of computationally intensive statistical technology to produce results in physics that could not be obtained using physics based techniques. Since the statistical architecture of the problem considered here can arise in other contexts as well, the second contribution of this dissertation is to indicate a plausible approach for addressing a generic class of problems wherein the number of parameters to be estimated exceeds the number of constraints, each constraint being a non-linear equation that is the sum of exponential functions.