Bayesian Adaptive Exploration

Abstract

We describe a framework for adaptive astronomical exploration based on iterating an Observation-Inference-Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data; and Bayesian decision theory to identify which new observations would teach us the most. In the design stage, the utility of possible future observations is determined by how much information they are expected to add to current inferences as measured by the (negative) entropies of the probability distributions involved. Such a Bayesian approach to experimental design dates back to the 1970s, but most existing work focuses on linear models. We use a simple nonlinear problem—planning observations to best determine the orbit of an extrasolar planet—to illustrate the approach and demonstrate that it can significantly improve observing efficiency (i.e., reduce uncertainties at a rate faster than the familiar “root-N” rule) in some situations. We highlight open issues requiring further research, including dependence on model specification, generalizing the utility of an observation (e.g., to include observing “costs”), and computational issues.

This paper is followed by a commentary by David A. van Dyk.