  Design of experiments is a fundamental topic in applied statistics with a
long history. Yet its application is often limited by the complexity and
costliness of constructing experimental designs, which involve searching a
high-dimensional input space and evaluating computationally expensive criterion
functions. In this work, we introduce a novel approach to the challenging
design problem. We will take a probabilistic view of the problem by
representing the optimal design as being one element (or a subset of elements)
of a probability space. Given a suitable distribution on this space, a
generative point process can be specified from which stochastic design
realizations can be drawn. In particular, we describe a scenario where the
classical entropy-optimal design for Gaussian Process regression coincides with
the mode of a particular point process. We conclude with outlining an algorithm
for drawing such design realizations, its extension to sequential designs, and
applying the techniques developed to constructing designs for Stochastic
Gradient Descent and Gaussian process regression.
