Bayesian calibration for multiple source regression model

In large variety of practical applications, using information from different sources or different kind of data is a reasonable demand. The problem of studying multiple source data can be represented as a multi-task learning problem, and then the information from one source can help to study the information from the other source by extracting a shared common structure. From the other hand, parameter evaluations obtained from various sources can be confused and conflicting. This paper proposes a Bayesian based approach to calibrate data obtained from different sources and to solve nonlinear regression problem in the presence of heteroscedastisity of the multiple-source model. An efficient algorithm is developed for implementation. Using analytical and simulation studies, it is shown that the proposed Bayesian calibration improves the convergence rate of the algorithm and precision of the model. The theoretical results are supported by a synthetic example, and a real-world problem, namely, modeling unsteady pitching moment coefficient of aircraft, for which a recurrent neural network is constructed.