  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.
