Astrostatistics

Catalog description

Modern astronomical research -- the study of planets, stars, galaxies and the Universe -- and the linking of observational data to astrophysical theory encounter a wide array of challenges falling under the rubric of statistical inference. Cosmology, for example, addresses spatial clustering of galaxies, nonlinear regression of Big Bang astrophysical models, supervised regression of galaxy photometric redshifts, multiple hypothesis tests for faint source detection in images, multivariate classification, and time series analysis of billion-object multi-epoch surveys. Big Data arising from large-scale astronomical surveys and Bayesian modeling of astrophysical models are propelling astrostatistics into greater importance than in the past. Yet the curriculum for young astronomers typically includes no courses in statistical methodology. This course is designed to fill this gap. The course progresses through three stages. First, basic principles in statistical inference are presented and discussed including elements of probability theory, point and interval estimation, and probability distributions. The techniques of least squares, maximum likelihood, and Bayesian inference are outlined here and exercised later in the course. Second, central fields of applied statistics are investigated including nonparametric statistics and density estimation, regression (including nonlinear models from astrophysical theory), and multivariate analysis (including unsupervised clustering and supervised classification). Specific statistical methods are linked to specific astronomical problems at each step. Third, the instructor and students choose topics for study, such as time series analysis, spatial point processes, censoring and truncation, Bayesian computation, and scientific visualization. Common characteristics of astronomical data that are not treated in standard statistical presentations are discussed in detail, including heteroscedastic measurement errors, irregularly-spaced time series, and nonlinear astrophysical models. A crucial element of the course is practical training in the implementation of these statistical methods using sophisticated public-domain software environments. Software tutorials in class and text help educate the student to a level where data and science analysis can proceed at a mature level.