A Framework for the Bayesian Calibration of Complex and Data-Scarce Models in Applied Sciences

TL;DR

This paper reviews Bayesian calibration methods for complex, data-scarce models, introduces a unified framework and an open-source Python library, and provides practical guidelines for reliable model calibration in engineering.

Contribution

It presents a comprehensive framework and software tools for Bayesian calibration, integrating various methods and addressing practical implementation challenges.

Findings

Unified Bayesian calibration framework developed.

Open-source Python library ACBICI introduced.

Practical guidelines for model calibration provided.

Abstract

In this work, we review the theory involved in the Bayesian calibration of complex computer models, with particular emphasis on their use for applications involving computationally expensive simulations and scarce experimental data. In the article, we present a unified framework that incorporates various Bayesian calibration methods, including well-established approaches. Furthermore, we describe their implementation and use with a new, open-source Python library, ACBICI (A Configurable BayesIan Calibration and Inference Package). All algorithms are implemented with an object-oriented structure designed to be both easy to use and readily extensible. In particular, single-output and multiple-output calibration are addressed in a consistent manner. The article completes the theory and its implementation with practical recommendations for calibrating the problems of interest. These guidelines -- currently unavailable in a unified form elsewhere -- together with the open-source Python library, are intended to support the reliable calibration of computational codes and models commonly used in engineering and related fields. Overall, this work aims to serve both as a comprehensive review of the statistical foundations and (computational) tools required to perform such calculations, and as a practical guide to Bayesian calibration with modern software tools.