Hessian-based Markov Chain Monte-Carlo Algorithms

In this paper, we propose two efficient Markov chain Monte-Carlo sampling methods, namely, the Hessian-based Metropolis-Hastings (HMH) and adaptive multiple importance-try (AMIT) algorithms. HMH utilizes Newton’s optimization method to generate transition distribution in a Metropolis-Hasting sampling scheme. In the experiment, the AMIT sampler outperforms the other samplers. Though only tested on a probit model, these new sampling methods can be easily applied to any generalized linear model and other models for which we can efficiently compute or approximate Hessian matrices.