Nonparametric Inference for Complex Physical Models

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

The recent years have seen rapid growth in the depth, richness, and scope of scientific data, a trend that is likely to accelerate. At the same time, simulation and analytical models have sharpened to unprecedented detail the understanding of the processes that generate these data. But what has advanced more slowly is the methodology to efficiently combine the information from rich, massive data sets with the detailed, and often nonlinear, constraints of theory and simulations. This project will bridge that gap. The investigators develop, implement, and disseminate new statistical methods that can fully exploit the available data by adhering to the constraints imposed by current theoretical understanding. The central idea in the work is constructing sparse, possibly nonlinear, representations of both the data and the distributions for the data predicted by theory. These representations can then be transformed onto a common space to allow sharp inferences that respect the inherent geometry of the model. The methodology developed in this project will apply to a wide range of scientific problems. The investigators focus, however, on a critical challenge in astronomy: using observations of Type Ia supernovae to improve constraints on cosmological theories explaining the nature of dark energy, a significant, yet little- understood, component of the Universe. Crucial scientific fields have enjoyed huge advances in the ability both to gather high-quality data and to understand the physical systems that generated these data. Nevertheless, the full societal and scientific value of this progress will only be realized with new, advanced statistical methods of analyzing the massive amounts of available data. The investigators develop statistical methods for combining theoretical modelling and observational evidence into improved understanding of these physical processes. The analysis of these data will requirenot only new methods, but also the use of high-performance computing resources. There is a particular need for these tools in cosmology and astronomy, and this project will bring together statisticians and astronomers to combine expertise, but this research is motivated by problems that are present in other fields, such as the climate sciences.