Bayesian Hyperparameter Estimation Using Gaussian Process And Bayesian Optimization

To reduce the computational cost of Bayesian inference, we propose a method to estimate the distribution of the Bayesian posterior probability from a small number of samples using a Gaussian process and Bayesian optimization. Our aim was to estimate the hyperparameter distribution of a Markov random field (MRF) model that corresponds to a lattice gas model. We used a small number of samples for the Gaussian process and estimated the distribution. In addition, we applied Bayesian optimization as a sampler for the Gaussian process and estimated the distribution from fewer sampled points than random sampling. Numerical experiments showed that our method can estimate the distribution of the Bayesian posterior probability accurately while reducing the computational cost.