DMS-EPSRC Collaborative Research: Advancing Statistical Foundations and Frontiers for and from Emerging Astronomical Data Challenges

Statistical theory and methods play a fundamental role in scientific discovery and advancement, including in modern astronomy, where data are collected on increasingly massive scales and with more varieties and complexity. New technology and instrumentation are spawning a diverse array of emerging data types and data analytic challenges, which in turn require and inspire ever more innovative statistical methods and theories.

This research is guided by the dual aims of advancing statistical foundations and frontiers, motivated by astronomical problems and providing principled data analytic solutions to challenges in astronomy. The CHASC (California-Harvard Astrostatistics Collaboration) International Center has an extensive track record in accomplishing both tasks. This research leverages CHASC’s track record to make progress in several new projects.

Fitting sophisticated astrophysical models to complex data that were collected with high-tech instruments, for example, often involves a sequence of statistical analyses. Several projects center on developing new statistical methods that properly account for errors and carry uncertainty forward within such sequences of analyses. Additional work will focus on developing theoretical properties of novel statistical estimation procedures to address data-analytic challenges associated with solar flares and X-ray observations.

Other projects involve fast and automatic detection of astronomical objects such as galaxies from 2D or even 4D data. The PIs will develop statistical theory and methods in the context of these projects, building statistical foundations and pushing the frontiers of statistics forward for broad impact that will extend well beyond astrostatistics. The PIs plan to offer effective methods and algorithms for tackling emerging challenges in astronomy, with the aspiration of promoting such principled data-analytic methods among researchers in astronomy.

Its provision of free software via the CHASC GitHub Software Library will enable the distribution and impact of the proposed methods and algorithms.

The projects reflect three broad themes: (1) Exploring fundamental statistical theory with immediate impact in astronomy, including a general approach for obtaining confidence regions by leveraging the pivot-property of maximal product spacing, which is then applied to assess the power law of solar flares, and a statistically principled correction to the use of the popular C-stat in astrophysics; (2) Assessing the misspecification of models and prior distributions in multi-stage statistical analyses, and post processing posterior draws to correct for defects in prior modeling when redoing a Bayesian analysis is impractical; and (3) Identifying breakpoints in complex models, which includes a fast algorithm for identifying astronomical boundaries and identifying breakpoints in joint spatial, spectral, temporal models. Theme 1 is more theory driven, while Themes 2 and 3 are more methods and computation driven.

Together they form a rich suite of case studies for developing statistical methods for astronomical problems, ranging from new theoretical foundations to innovative modeling strategies and to efficient computational techniques. Consequently, the research will impact both the fields of statistics and astronomy: spurring more interest and new problems for statisticians and resolving long standing problems in astronomy.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.