Bayesian Adaptive Exploration in a Nutshell
Thomas J. Loredo · 2003
I describe a framework for adaptive scientific 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. When the goal of the experiment is simply to make inferences, the framework identifies a computationally efficient iterative “maximum entropy sampling ” strategy as the optimal strategy in settings where the noise statistics are independent of signal properties. Results of applying the method to two “toy ” problems with simulated data—measuring the orbit of an extrasolar planet, and locating a hidden one-dimensional object—show the approach can significantly improve observational efficiency in settings that have well-defined, reliable models. 1.