  Since the cost of installing and maintaining sensors is usually high, sensor
locations are always strategically selected. For those aiming at inferring
certain quantities of interest (QoI), it is desirable to explore the dependency
between sensor measurements and QoI. One of the most popular metric for the
dependency is mutual information which naturally measures how much information
about one variable can be obtained given the other. However, computing mutual
information is always challenging, and the result is unreliable in high
dimension. In this paper, we propose an approach to find an approximate lower
bound of mutual information and compute it in a lower dimension. Then, sensors
are placed where highest mutual information (lower bound) is achieved and QoI
is inferred via Bayes rule given sensor measurements. In addition, Bayesian
optimization is introduced to provide a continuous mutual information surface
over the domain and thus reduce the number of evaluations. A chemical release
accident is simulated where multiple sensors are placed to locate the source of
the release. The result shows that the proposed approach is both effective and
efficient in inferring QoI.
