Bayesian Calibration of Computationally Expensive Models Using Optimization and Radial Basis Function Approximation

We present a Bayesian approach to model calibration when evaluation of the model is computationally expensive. Here, calibration is a nonlinear regression problem: given data vector Y corresponding to the regression model f(β), find plausible values of β. As an intermediate step, Y and f are embedded into a statistical model allowing transformation and dependence. Typically, this problem is solved by sampling from the posterior distribution of β given Y using MCMC. To reduce computational cost, we limit evaluation of f to small number of points chosen on a high posterior density region found by optimization. Then, we approximate the log-posterior using radial basis functions and use the resulting cheap-to-evaluate surface in MCMC. We illustrate our approach on simulated data for a pollutant diffusion problem and study frequentist coverage properties of credible intervals. Our experiments indicate that our method can produce results similar to those when the true “expensive ” posterior is sampled b