Bayesian options for computer model calibration with examples in astronomy.

*(English)*Zbl 1284.62165Summary: Computer model calibration involves selecting good model parameter values by comparing model output to field data. Having good model parameter values enables effective evaluation of the relation between model inputs and outputs, which is often a key modeling goal. For example, there is new interest in modeling the relationship between solar wind velocity as one input and electron flux as one output in a model applicable to the earth’s radiation belt. Particularly when a computer model is relatively slow to run and the number of model parameters is large, it is infeasible to evaluate the computer model at a densely sampled collection of parameter values. Therefore, ongoing research is aimed at fitting computer model output with an “emulator”, which enables more extensive evaluation of the relation between model inputs and outputs. Instead of, or perhaps in addition to, fitting a model emulator, approximate Bayesian computation (ABC) is another option for using field data to calibrate a computer model. To obtain samples from the approximate posterior distribution for model parameters, ABC invokes a type of Markov chain Monte Carlo sampling that compares summary statistics such as the first few moments of the observed data to those in the simulated data for a trial set of parameter values.

This review paper describes both model emulation and ABC and their roles in “computer model calibration” in applications for which there is no explicit form for the probability density function (the “likelihood”) for the data for a specified value of each model parameter. In this context of Bayesian inference without an explicit likelihood, this review also describes cross validation to assess emulation error, describes how to assess the quality of the approximation to the posterior using ABC, and gives three examples along with directions for research.

This review paper describes both model emulation and ABC and their roles in “computer model calibration” in applications for which there is no explicit form for the probability density function (the “likelihood”) for the data for a specified value of each model parameter. In this context of Bayesian inference without an explicit likelihood, this review also describes cross validation to assess emulation error, describes how to assess the quality of the approximation to the posterior using ABC, and gives three examples along with directions for research.