# Optimal Experimental Design Using A Consistent Bayesian Approach

## TL;DR

This paper introduces a novel optimal experimental design method based on a consistent Bayesian framework, which ensures the posterior distribution aligns with observed data and model predictions, improving data acquisition strategies.

## Contribution

It develops a new OED approach utilizing the consistent Bayesian method, ensuring posterior-data consistency and computational efficiency in PDE-based models.

## Key findings

- Outperforms classical Bayesian OED methods in numerical tests.
- Ensures posterior consistency with observed data.
- Effective for PDE-based model experiments.

## 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 a 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. 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 PDE-based models.