Statistical inverse problems: discretization, model reduction and inverse crimes
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Inversion of Robin coefficient by a spectral stochastic finite element approach
Journal of Computational Physics
Reconstruction of heat transfer coefficients using the boundary element method
Computers & Mathematics with Applications
Determination of a time-dependent heat transfer coefficient from non-standard boundary measurements
Mathematics and Computers in Simulation
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized beta prior models on fraction defective in reliability test planning
Journal of Computational and Applied Mathematics
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This paper investigates a nonlinear inverse problem associated with the heat conduction problem of identifying a Robin coefficient from boundary temperature measurement. A Bayesian inference approach is presented for the solution of this problem. The prior modeling is achieved via the Markov random field (MRF). The use of a hierarchical Bayesian method for automatic selection of the regularization parameter in the function estimation inverse problem is discussed. The Markov chain Monte Carlo (MCMC) algorithm is used to explore the posterior state space. Numerical results indicate that MRF provides an effective prior regularization, and the Bayesian inference approach can provide accurate estimates as well as uncertainty quantification to the solution of the inverse problem.