  This review outlines concepts of mathematical statistics, elements of
probability theory, hypothesis tests and point estimation for use in the
analysis of modern astronomical data. Least squares, maximum likelihood, and
Bayesian approaches to statistical inference are treated. Resampling methods,
particularly the bootstrap, provide valuable procedures when distributions
functions of statistics are not known. Several approaches to model selection
and good- ness of fit are considered. Applied statistics relevant to
astronomical research are briefly discussed: nonparametric methods for use when
little is known about the behavior of the astronomical populations or
processes; data smoothing with kernel density estimation and nonparametric
regression; unsupervised clustering and supervised classification procedures
for multivariate problems; survival analysis for astronomical datasets with
nondetections; time- and frequency-domain times series analysis for light
curves; and spatial statistics to interpret the spatial distributions of points
in low dimensions. Two types of resources are presented: about 40 recommended
texts and monographs in various fields of statistics, and the public domain R
software system for statistical analysis. Together with its \sim 3500 (and
growing) add-on CRAN packages, R implements a vast range of statistical
procedures in a coherent high-level language with advanced graphics.
