  We view sequential design as a model selection problem to determine which new
observation is expected to be the most informative, given the existing set of
observations. For estimating a probability distribution on a bounded interval,
we use bounds constructed from kernel density estimators along with the
estimated density itself to estimate the information gain expected from each
observation. We choose Bernstein polynomials for the kernel functions because
they provide a complete set of basis functions for polynomials of finite degree
and thus have useful convergence properties. We illustrate the method with
applications to estimating network reliability polynomials, which give the
probability of certain sets of configurations in finite, discrete stochastic
systems.
