Prediction based on the Kennedy-O'Hagan calibration model: asymptotic consistency and other properties

TL;DR

This paper analyzes the Kennedy-O'Hagan calibration model, demonstrating its asymptotic consistency in prediction despite known identifiability issues and calibration challenges, through theoretical analysis involving radial basis functions.

Contribution

It provides the first theoretical proof of the predictor’s consistency based on the Kennedy-O'Hagan model using radial basis functions.

Findings

Predictor based on Kennedy-O'Hagan model is asymptotically consistent.

The model exhibits robust predictive performance despite calibration issues.

Theoretical analysis confirms the model's reliability in prediction tasks.

Abstract

Kennedy and O'Hagan (2001) propose a model for calibrating some unknown parameters in a computer model and estimating the discrepancy between the computer output and physical response. This model is known to have certain identifiability issues. Tuo and Wu (2016) show that there are examples for which the Kennedy-O'Hagan method renders unreasonable results in calibration. In spite of its unstable performance in calibration, the Kennedy-O'Hagan approach has a more robust behavior in predicting the physical response. In this work, we present some theoretical analysis to show the consistency of predictor based on their calibration model in the context of radial basis functions.