In large projects astronomers typically pose a well-defined question, plan a set of observations, take all the data, and then analyze it. When observational resources are scarce and expensive, an adaptive approach to selecting which observations to make, based on the data assembled thus far, should be able to improve the accuracy, precision and efficiency of the work. This research will develop a general framework for flexible, adaptive scientific exploration based on iterating an Observation-Inference-Design cycle, relying on Bayesian methods and called Bayesian Adaptive Exploration (BAE). Developing BAE through a broad range of methodological research, and then applying BAE to several time-variable phenomena, will lead to numerous theoretical and algorithmic innovations in statistics, and to significantly improved answers in the study of extra-solar planets, binary star systems, minor planets in our solar system, and variable stars in nearby galaxies. Since the required calculations are extremely demanding, several approaches will be explored, including extending existing Markov Chain Monte Carlo and sequential Monte Carlo inference algorithms, developing bridge/path importance sampling algorithms and Gaussian process meta-models, and the use of sub-region-adaptive quadrature.
BAE is an adaptive generalization of the scientific method and will therefore be broadly applicable in many disciplines. This project will create and widely disseminate public-domain software implementing the methods, with tutorial and instructional material. At least one graduate student will receive extensive interdisciplinary training.
