Non-Parametric Model Calibration with Stochastic Control Parameters

2026-07-18

AI Summary

This study addresses the challenge of jointly modeling calibration and control parameters in computer model calibration, where the distribution of calibration parameters is unknown while that of control parameters is known. To tackle this issue, the authors propose a nonparametric Bayesian calibration method based on measure decomposition. The approach preserves the known marginal distribution of the control parameters while employing stochastic process modeling and Bayesian inference to construct a posterior distribution over the input space that aligns with field observations. Notably, this work is the first within a nonparametric calibration framework to explicitly maintain the prior distributional properties of the control parameters, thereby substantially enhancing the physical consistency and scientific credibility of the calibration results.

Abstract

We present a method for calibrating a computer model using non-parametric techniques where the inputs are stochastic but include calibration parameters whose distributions are unknown and control parameters whose distributions are specified. Our solution gives a distributional estimate over the input space that is consistent with observed field data, while also preserving the distribution of the known marginal of the control parameters. This property is desirable since stochastic inputs often include physical processes affecting the experimental conditions, and a scientifically plausible calibration estimate should preserve well-established distributional properties of these inputs. The method builds on recently developed non-parametric computer model calibration techniques based on the disintegration of measure and Bayesian inference.

Problem

• Non-Parametric Calibration
• Stochastic Inputs
• Control Parameters
• Calibration Parameters
• Distribution Preservation

Innovation

• non-parametric calibration
• stochastic control parameters
• disintegration of measure
• Bayesian inference
• distributional consistency