Studies analysis of data using generalized linear models, as well as models with generalized variance structure. Parametric models include exponential families such as normal, binomial, Poisson, and gamma. Iterative reweighted least squares and quasi-likelihood methods are used for estimation of parameters. Methods for examining model assumptions are studied. Generalized estimating equations (GEE) and quadratic estimating equations are introduced for problems where no distributional assumptions are made about the errors except for the structure of the first two moments. Illustrations with data from various basic science, medicine, and public health settings. Prerequisite: BIOS 511 and BIOS 707

Axioms of probability, univariate and multivariate distributions, convergence of sequences of random variables, Markov chains, random processes, martingales.

Examines the fundamental role of the likelihood function in statistical inference, ancillary and sufficient statistics, estimating functions, and asymptotic theory. This course presents conditional, profile and other approximate likelihoods; various ancillary concepts; generalizations of Fisher information in the presence of nuisance parameters; optimality results for estimating functions; and consistency/asymptotic normality of maximum likelihood and estimation function-based estimators. It briefly discusses alternative approaches to inference including Bayesian, Likelihood Principle, and decision theory. Prerequisite: BIOS 710.

This course covers the theories and applications of some common statistical computing methods. Topics include Markov chain Monte Carlo (MCMC), hidden Markov model (HMM), Expectation-Maximization (EM) and Minorization-Maximization (MM), and optimization algorithms such as linear and quadratic programming. The class has two main goals for students: (1) learn the general theory and algorithmic procedures of some widely used statistical models; (2) develop fluency in statistical programming skills. The class puts more emphasis on implementation instead of statistical theories. Students will gain computational skills and practical experiences on simulations and statistical modeling. This course requires significant amount of programming. Each set of homework involves the implementation of certain algorithms using high-level programming language (such as Matlab or R).

Examines topics in the theory of estimating functions. This course presents measures of efficiency of estimating functions; methods to produce efficient estimating functions using orthogonal projection theory; modern methods to reduce the sensitivity of an estimating function to nuisance parameters; artificial likelihood functions to accompany estimating functions; and model selection issues. Applications from biomedical studies are used to illustrate the concepts discussed in class. Prerequisites: BIOS 711 or permission of instructor; some knowledge of statistical computing will be needed to complete the final project.

The goal of the course is to introduce the concepts and methods of analysis for missing data. Topics will include methods for distinguishing ignorable and non-ignorable missing data mechanisms, single and multiple imputation, hot-deck imputation. Computer intensive methods will be used. Prerequisites: BIOS 511 and PhD Biostatistics student.

This course will familiarize students with statistical methods and underlying theory for the spatial analysis of georeferenced public health data. Topics covered include kriging and spatial point processes. In addition, review recent computational advances for applying these methods. Prerequisites: BIOS 506, BIOS 507, BIOS 510, BIOS 511.

The first part of the course is dedicated to preparing students to act as consultants through discussions of consulting models, interpersonal communication, ethics, common client types, time and financial management and other issues. This course is also designed to give students some practical experience as a biostatistical consultant. Students will meet with clients, analyze data sets and produce summary reports.

A faculty member offers a new course on a current topic of interest for PhD students.

This course provides a survey of modern topics in causal inference. Fundamental concepts in causal inference will be covered including: counterfactual random variables, assessing identifiability of causal effects, graphical frameworks, Gcomputation, inverse probability of treatment weighting, methods for efficient, doubly (multiply) robust estimation of causal effects, and causal mediation. Where possible, the course emphasizes the use of modern regression (e.g., machine learning) in causal effect estimation and provides an applied introduction to this area is provided as well.