Fall Only

Linear Models

Multiple linear regression and model building. Exploratory data analysis techniques, variable transformations and selection, parameter estimation and interpretation, prediction, Bayesian hierarchical models, Bayes factors and intrinsic Bayes factors for linear models, and Bayesian model averaging. The concepts of linear models from Bayesian and classical viewpoints. Topics in Markov chain Monte Carlo simulation introduced as required. Prerequisite: Statistics 213 and 290 or equivalent. Instructor: Clyde

Generalized Linear Models

Likelihood-based and Bayesian inference of binomial, ordinal, and Poisson regression models, and the relation of these models to item response theory and other psychometric models. Focus on latent variable interpretations of categorical variables, computational techniques of estimating posterior distributions on model parameters, and Bayesian and likelihood approaches to case analyses and goodness-of-fit criterion. Theory and practice of modern regression modeling within the unifying context of generalized linear models. A brief review of hierarchical linear models.

Introduction to Mathematical Statistics

Formal introduction to basic theory and methods of probability and statistics: probability and sample spaces, independence, conditional probability and Bayes' theorem; random variables, distributions, moments and transformations. Parametric families of distributions and central limit theorem. Sampling distributions, traditional methods of estimation and hypothesis testing. Elements of likelihood and Bayesian inference. Basic discrete and continuous statistical models.

Probability and Measure Theory

Introduction to probability spaces, the theory of measure and integration, random variables, and limit theorems. Distribution functions, densities, and characteristic functions; convergence of random variables and of their distributions; uniform integrability and the Lebesgue convergence theorems. Weak and strong laws of large numbers, central limit theorem.  Prerequisite: elementary real analysis and elementary probability theory.

Research Seminar in Statistical Science I

Statistical and mathematical underpinnings of methodological research in statistical science. Student presentations of their statistical research in collaboration with, and under the supervision of, an DSS faculty mentor.