  The scientific method relies on the iterated processes of inference and
inquiry. The inference phase consists of selecting the most probable models
based on the available data; whereas the inquiry phase consists of using what
is known about the models to select the most relevant experiment. Optimizing
inquiry involves searching the parameterized space of experiments to select the
experiment that promises, on average, to be maximally informative. In the case
where it is important to learn about each of the model parameters, the
relevance of an experiment is quantified by Shannon entropy of the distribution
of experimental outcomes predicted by a probable set of models. If the set of
potential experiments is described by many parameters, we must search this
high-dimensional entropy space. Brute force search methods will be slow and
computationally expensive. We present an entropy-based search algorithm, called
nested entropy sampling, to select the most informative experiment for
efficient experimental design. This algorithm is inspired by Skilling's nested
sampling algorithm used in inference and borrows the concept of a rising
threshold while a set of experiment samples are maintained. We demonstrate that
this algorithm not only selects highly relevant experiments, but also is more
efficient than brute force search. Such entropic search techniques promise to
greatly benefit autonomous experimental design.
