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The advanced theory of statistics, including methods of estimation (unbiasedness, equivariance, maximum likelihood, Bayesian, minimax), optimality properties of estimators, hypothesis testing, uniformly most powerful tests, unbiased tests, invariant tests, relationship between confidence regions and tests, large sample properties of tests and estimators. Prerequisites: Statistc 605 and 608.

First semester of two-semester sequence in the theory of linear models. Basic results on the multivariate normal distribution; linear and quadratic forms; noncentral Chi-square and F distributions; inference in linear models, including point and interval estimation, hypothesis testing, etc. Prerequisites: Statistc 607-608 or equivalent; linear algebra.

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This course gives students a rigorous introduction to the theory of Bayesian Statistical Inference and Data Analysis, including prior and posterior distributions, Bayesian estimation and testing, Bayesian computation theories and methods, and implementation of Bayesian computation methods using popular statistical software. The early part of the course focuses on fundamental Bayesian inference and data analysis. The second part covers more advanced topics including various sampling methods and regression models.

Using data to estimate relationships between predictors and responses is an important task in statistics and data science. When datasets are large, modern methods have been developed that allow us to estimate those relationships without making strong assumptions about those relationships- i.e. we can let the data determine how E(y|x) relates to x. In statistics, these methods are generally referred to as ?nonparametric regression.? This applied graduate course will focus on learning to use nonparametric regression to analyze data. We will read a book, ?Semiparametric Regression with R,?

This course provides an introduction to the statistical techniques that are most applicable to data science. Topics include regression, classification, resampling, linear model selection and regularization, tree-based methods, support vector machines and unsupervised learning. The course includes a computing component using statistical software.