On the Bayesian calibration of expensive computer models with input dependent parameters

TL;DR

This paper introduces a Bayesian approach for calibrating complex computer models with input-dependent parameters, allowing for more flexible and accurate modeling by capturing how optimal parameters vary with inputs.

Contribution

It proposes a novel Bayesian methodology that models calibration parameters as input-dependent functions using a binary treed process, enabling sub-model selection based on inputs.

Findings

Method accurately captures input-dependent calibration parameters.

Effective in selecting sub-models that vary with inputs.

Performs well on benchmark examples and real climate data.

Abstract

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model inputs. In several real world applications where models involve complex parametrizations whose optimal values depend on the model inputs, such an assumption can be too restrictive and may lead to misleading results. We propose a fully Bayesian methodology that produces input dependent optimal values for the calibration parameters, as well as it characterizes the associated uncertainties via posterior distributions. Central to methodology is the idea of formulating the calibration parameter as a step function whose uncertain structure is modeled properly via a binary treed process. Our method is particularly suitable to address problems where the computer model requires the selection of a sub-model from a set of competing ones, but the choice of the `best' sub-model may change with the input values. The method produces a selection probability for each sub-model given the input. We propose suitable reversible jump operations to facilitate the challenging computations. We assess the performance of our method against benchmark examples, and use it to analyze a real world application with a large-scale climate model.