Model selection for sequential designs in discrete finite systems using Bernstein kernels

TL;DR

This paper introduces a model selection approach for sequential experimental design in discrete finite systems, utilizing Bernstein kernels to estimate information gain and improve the efficiency of data collection.

Contribution

It proposes a novel method using Bernstein polynomial kernels for model selection in sequential designs, specifically applied to network reliability estimation.

Findings

Effective estimation of information gain using Bernstein kernels.

Improved sequential design for network reliability analysis.

Convergence properties of the Bernstein-based estimators.

Abstract

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.