UC Irvine

Spectral analysis in high-energy astrophysics typically requires sampling from difficult posterior distributions, e.g., multimodal distributions, in a highly structured model with complex data collection mechanisms. Markov chain Monte Carlo (MCMC) methods have been widely explored in such tasks. However, traditional MCMC methods suffer from slow convergence incurred by the local trap problem. In this thesis, we propose a general population-based MCMC strategy, which is able to speed up convergence significantly. Specifically, we initialize multiple chains from dispersed starting values and perform a two-step jump with our proposed between-chain jump. The novel between-chain jumping proposal tries to move to the neighborhood of the iterate in another chain, which encourages full exploration of the parameter space. As for the numerical illustration, we apply the proposed method to fit thermal models to Capella data. The results indicate that our method is effective in two aspects. First, it can be applied in Bayesian model selection to decide which mixture model is more appropriate; secondly, it can be served as an exploratory step to identify modes. The strength shown from the second aspect can help determine the importance of those temperature components and decide upon the relative proportion among those modes. In addition, we show that our method is also useful in other applications including Bayes factor computation for Bayesian model selection, variance component estimation in mixed effect models, and sensor network localization.