Faculty of Arts & Sciences

Axiomatic foundations of probability, independence, conditional probability, joint distributions, transformations, moment generating functions, characteristic functions, moment inequalities, sampling distributions, modes of convergence and their interrelationships, laws of large numbers, central limit theorem, and stochastic processes.

Exponential families, sufficiency, ancillarity, completeness, method of moments, maximum likelihood, unbiased estimation, Rao-Blackwell and Lehmann-Scheffe theorems, information inequality, Neyman-Pearson theory, likelihood ratio, score and Wald tests, uniformly and locally most powerful tests, asymptotic relative efficiency.

Introductory course in the analysis of Gaussian and categorical data. The general linear regression model, ANOVA, robust alternatives based on permutations, model building, resampling methods (bootstrap and jackknife), contingency tables, exact methods, logistic regression.

Intermediate course in the analysis of Gaussian, categorical, and survival data. The generalized linear model, Poisson regression, random effects and mixed models, comparing survival distributions, proportional hazards regression, splines and smoothing, the generalized additive model.

An advanced course in linear models, including both classical theory and methods for high dimensional data. Topics include theory of estimation and hypothesis testing, multiple testing problems and false discovery rates, cross validation and model selection, regularization and the LASSO, principal components and dimension reduction, and classification methods. Background in matrix algebra and linear regression required.

This course focuses on selected advanced topics in design, analysis, and interpretation of clinical trials, including study design; choice of endpoints (including surrogate endpoints); interim analyses and group sequential methods; subgroup analyses; and meta-analyses.

Discusses the theoretical basis of concepts and methodologies associated with survival data and censoring, nonparametric tests, and competing risk models. Much of the theory is developed using counting processes and martingale methods.

The multivariate normal distribution, Hotelling's T2, MANOVA, repeated measures, the multivariate linear model, random effects and growth curve models, generalized estimating equations, multivariate categorical outcomes, missing data, computational issues for traditional and new methodologies.

General principles of the Bayesian approach, prior distributions, hierarchical models and modeling techniques, approximate inference, Markov chain Monte Carlo methods, model assessment and comparison. Bayesian approaches to GLMMs, multiple testing, nonparametrics, clinical trials, survival analysis.

A foundational course in measure theoretic probability. Topics include measure theory, Lebesgue integration, product measure and Fubini's Theorem, Radon-Nikodym derivatives, conditional probability, conditional expectation, limit theorems on sequences of random variables, stochastic processes, and weak convergence.

Advanced topics in statistical inference. Limit theorems, multivariate delta method, properties of maximum likelihood estimators, saddle point approximations, asymptotic relative efficiency, robust and rank-based procedures, resampling methods, nonparametric curve estimation.

Theory of directed acyclic graph models. Identifiability of causal contrasts. Theory and applications of locally semiparametric efficient doubly-robust estimation in two models for counterfactual variables: marginal structural models and structural nested models.

Introduction to genomic data, computational methods for interpreting these data, and survey of current functional genomics research. Covers biological data processing, programming for large datasets, high-throughput data (sequencing, proteomics, expression, etc.), and related publications.

Basic problems, technology platforms, algorithms and data analysis approaches in computational biology. Algorithms covered include dynamic programming, hidden Markov model, Gibbs sampler, clustering and classification methods.

Students will explore current topics in computational biology in a seminar format with a focus on interpretation of 'omics data. They will develop skills necessary for independent research using computational biology.

For doctoral candidates who have passed their written qualifying examination and who are undertaking advanced work along the lines of fundamental or applied dissertation research in the department.