Efficient Bayesian experimentation using an expected information gain lower bound

TL;DR

This paper introduces a computationally efficient Bayesian experimental design method using a lower bound of expected information gain, demonstrated on a contaminant transport inference problem.

Contribution

It proposes a novel lower bound approach for expected information gain to reduce computational costs and bias in Bayesian experimental design.

Findings

Lower bound reduces computational complexity.

Method effectively accelerates information gain evaluation.

Validated on a large-scale permeability inference problem.

Abstract

Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data the most informative possible. In a Bayesian setting this is translated to updating to the best possible posterior. Information theoretic arguments have led to the formation of the expected information gain as a design criterion. This can be evaluated mainly by Monte Carlo sampling and maximized by using stochastic approximation methods, both known for being computationally expensive tasks. We propose a framework where a lower bound of the expected information gain is used as an alternative design criterion. In addition to alleviating the computational burden, this also addresses issues concerning estimation bias. The problem of permeability inference in a large contaminated area is used to demonstrate the validity of our approach where we employ the massively parallel version of the multiphase multicomponent simulator TOUGH2 to simulate contaminant transport and a Polynomial Chaos approximation of the forward model that further accelerates the objective function evaluations. The proposed methodology is demonstrated to a setting where field measurements are available.