Variability, Information, and Prediction

Introductory statistics courses often start with summary statistics, then develop a notion of probability, and finally turn to parametric models – mostly the normal – for inference. By the end of the course, the student has seen estimation and hypothesis testing for means, proportions, ANOVA, and maybe linear regression. This is a good approach for a first encounter with statistical thinking. The student who goes on takes a familiar series of courses: survey sampling, regression, Bayesian inference, multivariate analysis, nonparametrics and so forth, up to the crowning glories of decision theory, measure theory, and asymptotics. In aggregate, these courses develop a view of statistics that continues to provide insights and challenges.