# Validation of the thermal challenge problem using Bayesian Belief Networks.

## Abstract

The thermal challenge problem has been developed at Sandia National Laboratories as a testbed for demonstrating various types of validation approaches and prediction methods. This report discusses one particular methodology to assess the validity of a computational model given experimental data. This methodology is based on Bayesian Belief Networks (BBNs) and can incorporate uncertainty in experimental measurements, in physical quantities, and model uncertainties. The approach uses the prior and posterior distributions of model output to compute a validation metric based on Bayesian hypothesis testing (a Bayes' factor). This report discusses various aspects of the BBN, specifically in the context of the thermal challenge problem. A BBN is developed for a given set of experimental data in a particular experimental configuration. The development of the BBN and the method for ''solving'' the BBN to develop the posterior distribution of model output through Monte Carlo Markov Chain sampling is discussed in detail. The use of the BBN to compute a Bayes' factor is demonstrated.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 875636

- Report Number(s):
- SAND2005-5980

TRN: US200603%%264

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; VALIDATION; FORECASTING; COMPUTER CODES; CALCULATION METHODS; Bayesian statistical decision theory.; Thermal analysis.

### Citation Formats

```
McFarland, John, and Swiler, Laura Painton.
```*Validation of the thermal challenge problem using Bayesian Belief Networks.*. United States: N. p., 2005.
Web. doi:10.2172/875636.

```
McFarland, John, & Swiler, Laura Painton.
```*Validation of the thermal challenge problem using Bayesian Belief Networks.*. United States. doi:10.2172/875636.

```
McFarland, John, and Swiler, Laura Painton. Tue .
"Validation of the thermal challenge problem using Bayesian Belief Networks.". United States.
doi:10.2172/875636. https://www.osti.gov/servlets/purl/875636.
```

```
@article{osti_875636,
```

title = {Validation of the thermal challenge problem using Bayesian Belief Networks.},

author = {McFarland, John and Swiler, Laura Painton},

abstractNote = {The thermal challenge problem has been developed at Sandia National Laboratories as a testbed for demonstrating various types of validation approaches and prediction methods. This report discusses one particular methodology to assess the validity of a computational model given experimental data. This methodology is based on Bayesian Belief Networks (BBNs) and can incorporate uncertainty in experimental measurements, in physical quantities, and model uncertainties. The approach uses the prior and posterior distributions of model output to compute a validation metric based on Bayesian hypothesis testing (a Bayes' factor). This report discusses various aspects of the BBN, specifically in the context of the thermal challenge problem. A BBN is developed for a given set of experimental data in a particular experimental configuration. The development of the BBN and the method for ''solving'' the BBN to develop the posterior distribution of model output through Monte Carlo Markov Chain sampling is discussed in detail. The use of the BBN to compute a Bayes' factor is demonstrated.},

doi = {10.2172/875636},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}