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

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.

[1]  George S. Dulikravich,et al.  A COMPARISON OF TWO METHODS FOR FITTING HIGH DIMENSIONAL RESPONSE SURFACES , 2007 .

[2]  V. Leitão.  RBF-based meshless methods for 2D elastostatic problems , 2004 .

[3]  M. N. Özişik,et al.  Effects of the Heating Process and Body Dimensions on the Estimation of the Thermal Conductivity Components of Orthotropic Solids , 2003 .

[4]  Faming Liang,et al.  Statistical and Computational Inverse Problems , 2006, Technometrics.

[5]  Robert L. Winkler,et al.  An Introduction to Bayesian Inference and Decision , 1972 .

[6]  James V. Beck,et al.  Parameter Estimation in Engineering and Science , 1977 .

[7]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[8]  Ken-ichi Yoshihara,et al.  Conditional empirical processes defined by Φ-mixing sequences , 1990 .

[9]  Nicholas Zabaras,et al.  Using Bayesian statistics in the estimation of heat source in radiation , 2005 .

[10]  Vitor M. A. Leitão,et al.  A meshless method for Kirchhoff plate bending problems , 2001 .

[11]  Alain J. Kassab,et al.  An Efficient Localized Radial Basis Function Meshless Method for Fluid Flow and Conjugate Heat Transfer , 2007 .

[12]  Nicholas Zabaras,et al.  A Bayesian inference approach to the inverse heat conduction problem , 2004 .

[13]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[14]  M. Maeda,et al.  [Heat conduction]. , 1972, Kango kyoshitsu. [Nursing classroom].

[15]  Nicholas Zabaras,et al.  Inverse Problems in Heat Transfer , 2009 .

[16]  Dennis V. Lindley,et al.  An Introduction to Bayesian Inference and Decision , 1974 .

[17]  J. Coyle.  Inverse Problems , 2004 .