Abstract:
An important challenge in gravitational microlensing observation is robustly classifying the number of masses that are in a lens system for a given event. The difficulty is that the underlying model depends upon the number of masses in the lens system. This makes classifying the number of lenses a model selection problem. There is also considerable effort that goes into finding accurate methods for statistically estimating the parameters for each of these models, which includes the corresponding uncertainty in the estimates. In this thesis we develop a new method to address all of these problems at once by constructing a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler for single and binary lens models. RJMCMC is a method that explores the posterior of multiple candidate models simultaneously. The appeal of RJMCMC comes from the fact that it provides all of the following: parameter fits for all models, corresponding uncertainties in the fits, the model selection probabilities and, likewise, the corresponding uncertainties in those probabilities. To the best of our knowledge RJMCMC has not been used before in this context. RJMCMC is notoriously difficult to implement and the RJMCMC sampler we have developed forms a promising first pass method. We analyse its performance and highlight areas for future work and extension. The results clearly suggest this method could, with further development, provide the microlensing community with an exciting and robust tool for event analysis.
