Approximation of the likelihood function in the Bayesian technique for the solution of inverse problems

Abstract

This work deals with the use of radial basis functions for the interpolation of the likelihood function in parameter estimation problems. The focus is on the use of Bayesian techniques based on Markov Chain Monte Carlo (MCMC) methods. The proposed interpolation of the likelihood function is applied to test cases of inverse problems in heat and mass transfer, solved with the Metropolis–Hastings algorithm. The use of the interpolated likelihood function reduces significantly the computational cost associated with the implementation of such Markov Chain Monte Carlo method without loss of accuracy in the estimated parameters.