# Optimal Experimental Design Using a Consistent Bayesian Approach

## Abstract

We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent Bayesian approach for solving stochastic inverse problems, which seeks a posterior probability density that is consistent with the model and the data in the sense that the push-forward of the posterior (through the computational model) matches the observed density on the observations almost everywhere. Given a set of potential observations, our optimal experimental design (OED) seeks the observation, or set of observations, that maximizes the expected information gain from the prior probability density on the model parameters. We discuss the characterization of the space of observed densities and a computationally efficient approach for rescaling observed densities to satisfy the fundamental assumptions of the consistent Bayesian approach. Finally, numerical results are presented to compare our approach with existing OED methodologies using the classical/statistical Bayesian approach and to demonstrate our OED on a set of representative partial differential equations (PDE)-based models.

- Authors:

- Univ. of Colorado, Denver, CO (United States). Dept. of Mathematical and Statistical Sciences
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1478379

- Report Number(s):
- SAND-2017-4749J

Journal ID: ISSN 2332-9017; 666529

- Grant/Contract Number:
- AC04-94AL85000; NA0003525

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering

- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2332-9017

- Publisher:
- American Society of Mechanical Engineers

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING

### Citation Formats

```
Walsh, Scott, Wildey, Timothy Michael, and Jakeman, John Davis.
```*Optimal Experimental Design Using a Consistent Bayesian Approach*. United States: N. p., 2017.
Web. doi:10.1115/1.4037457.

```
Walsh, Scott, Wildey, Timothy Michael, & Jakeman, John Davis.
```*Optimal Experimental Design Using a Consistent Bayesian Approach*. United States. doi:10.1115/1.4037457.

```
Walsh, Scott, Wildey, Timothy Michael, and Jakeman, John Davis. Thu .
"Optimal Experimental Design Using a Consistent Bayesian Approach". United States. doi:10.1115/1.4037457. https://www.osti.gov/servlets/purl/1478379.
```

```
@article{osti_1478379,
```

title = {Optimal Experimental Design Using a Consistent Bayesian Approach},

author = {Walsh, Scott and Wildey, Timothy Michael and Jakeman, John Davis},

abstractNote = {We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent Bayesian approach for solving stochastic inverse problems, which seeks a posterior probability density that is consistent with the model and the data in the sense that the push-forward of the posterior (through the computational model) matches the observed density on the observations almost everywhere. Given a set of potential observations, our optimal experimental design (OED) seeks the observation, or set of observations, that maximizes the expected information gain from the prior probability density on the model parameters. We discuss the characterization of the space of observed densities and a computationally efficient approach for rescaling observed densities to satisfy the fundamental assumptions of the consistent Bayesian approach. Finally, numerical results are presented to compare our approach with existing OED methodologies using the classical/statistical Bayesian approach and to demonstrate our OED on a set of representative partial differential equations (PDE)-based models.},

doi = {10.1115/1.4037457},

journal = {ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering},

issn = {2332-9017},

number = 1,

volume = 4,

place = {United States},

year = {2017},

month = {9}

}