| Abstract: | We consider the estimation of the marginal likelihood in Bayesian statistics, a essential and important task known to be computationally expensive when the dimension of the parameter space is large. We propose a general algorithm with numerous extensions that can be widely applied to a variety of problem settings and excels particularly when dealing with near log-concave posteriors. Our method hinges on a novel idea that uses MCMC samples to partition the parameter space and forms local approximations over these partition sets as a means of estimating the marginal likelihood. In this dissertation, we provide both the motivation and the groundwork for developing what we call the Hybrid estimator. Our numerical experiments show the versatility and accuracy of the proposed estimator, even as the parameter space becomes increasingly high-dimensional and complicated. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969.1/197902 |
|---|