Fast Bayesian inference for an inverse heat transfer problem using approximations

The Bayesian inversion of measured data forms an attractive approach to gain statistical knowledge like confidential intervals about the unknown variables given measured data and a model. Out of the class of Markov chain Monte Carlo (MCMC) methods, the Metropolis Hastings (MH) algorithm is a commonly used algorithm to generate samples from the posterior distribution for computational inference. Though easy to implement, the MH algorithm offers drawbacks in terms of computation time and greater modeling costs. In this paper we present an acceleration approach to speed up MCMC with the MH algorithm for an inverse heat transfer problem using two different types of approximations. We will demonstrate the possibility to decrease computation times while maintaining the same estimation accuracy.