Combining discrepancy models with hierarchical Bayesian inference for parameter estimation of very ill posed thermal problems

Parameter estimation assumes that the model is an accurate representation of the system being studied and that any deviations are caused by measurement noise. For real experimental data this is often not the case. Clearly, the model will constructed to the highest fidelity by the analyst but when it is deficient, the remedy is not always obvious. One approach is to include a discrepancy function which one hopes will resolve any differences. The paper describes the use of such a function for a very ill posed problem using Bayesian inference effected by Markov Chain Monte Carlo sampling.