# Nonparametric Bayesian Calibration of Computer Models

arXiv: https://arxiv.org/abs/2509.22597 · HTML: https://mlsanity.com/paper/2509.22597/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2025.

## Built on by (most cited first, 1 of 1)

- [An efficient, accurate, and interpretable machine learning method for computing probability of failure](https://mlsanity.com/paper/2601.21089/) (2026)

## Abstract (arXiv)

Combining field data and computer models is a crucial step for making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for calibrating the distribution of parameters in a computer model using field observations. Our results include establishing; a unique nonparametric Bayesian posterior corresponding to a chosen prior with an explicit formula for the posterior density; a maximum entropy property of the posterior corresponding to the uniform prior; the almost everywhere continuity of the posterior density; and a comprehensive statistical analysis of an estimator based on importance sampling. They also include establishing the well-posedness of the nonparametric Bayesian solution of the calibration problem. We illustrate the results using several examples.