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Markov Chain Monte Carlo (MCMC) methods have a drawback when working with atarget distribution or likelihood function that is computationally expensive toevaluate, specially when working with big data. This paper focuses onMetropolis-Hastings (MH) algorithm for unimodal distributions. Here, anenhanced MH algorithm is proposed that requires less number of expensivefunction evaluations, has shorter burn-in period, and uses a better proposaldistribution. The main innovations include the use of Bayesian optimization toreach the high probability region quickly, emulating the target distributionusing Gaussian processes (GP), and using Laplace approximation of the GP tobuild a proposal distribution that captures the underlying correlation better.The experiments show significant improvement over the regular MH. Statisticalcomparison between the results from two algorithms is presented.

Approximate Sampling using an Accelerated Metropolis-Hastings based on Bayesian Optimization and Gaussian Processes