Programs & Curriculum

Statistics for Data Science I
This course starts with an introduction to R that will be used to study and explore various features of data sets and summarize important features using R graphical tools. It also aims to provide theoretical tools to understand randomness through elementary probability and probability laws governing random variables and their interactions. It integrates analytical and computational tools to investigate statistical distributional properties of complex functions of data. The course lays the foundation for statistical inference and covers important estimation techniques and their properties. It also provides an introduction to more complex statistical inference concepts involving the testing of hypotheses and interval estimation. 

Elementary to Intermediate Statistics and Data Analysis
Students are provided an introduction to probability and statistics. Major topics include elementary probability, special distributions, experimental design, exploratory data analysis, estimation of mean and proportion, hypothesis testing and confidence, regression, and analysis of variance. Emphasis is placed on the development of statistical reasoning, basic analytic skills, and critical thinking in empirical research studies. The use of the statistical software R is integrated into lectures and weekly assignments. 

Biostatistics
A second course in elementary statistics with applications to life sciences and medicine, students will review basic statistics using biological and medical examples. New topics include incidence and prevalence, medical diagnosis, sensitivity and specificity, Bayes' rule, decision-making, maximum likelihood, logistic regression, ROC curves and survival analysis. Each student will be required to perform and write a report on a data analysis project. 

Statistics for Data Science II
This builds on the foundation from the first course (SDS I) and further develops the theory of statistical hypotheses testing. It also covers advanced computer-intensive statistical methods, such as the Bootstrap, that will make extensive use of R. The emphasis of the course is to expose students to modern statistical modeling tools beyond linear models that allow for flexible and tractable interaction among response variables and covariates/feature sets. Statistical modeling and analysis of real datasets is a key course component.

Introduction to Analysis
The course covers the real number system and the least upper bound property; metric spaces (completeness, compactness, and connectedness); continuous functions (in R^n; on compact spaces; on connected spaces); C(X) (pointwise and uniform convergence; Weierstrass approximation theorem); differentiation (mean value theorem; Taylor's theorem); the contraction mapping theorem; and the inverse and implicit function theorems. 

Multivariate Statistical Analysis
This is a modern course in multivariate statistics with elements of classical multivariate analysis as needed, including multivariate normal and Wishart distributions. Instruction covers clustering, principal component analysis, model selection and evaluation, prediction error, variable selection, stepwise regression, regularized regression, cross-validation, classification, linear discriminant analysis, and tree-based methods. Optional topics may include nonparametric density estimation, multivariate regression, support vector machines, and random forests.

Survival Analysis
The course will instruct students in life table analysis and testing, mortality and failure rates, Kaplan-Meier or product-limit estimators, hypothesis testing and estimation in the presence of random arrivals and departures, and the Cox proportional hazards model. Techniques of survival analysis are used in medical research, industrial planning and the insurance industry. 

Stochastic Processes
Content varies with each offering of the course. Past offerings have included such topics as random walks, Markov chains, Gaussian processes, empirical processes, Markov jump processes, and a short introduction to martingales, Brownian motion and stochastic integrals. 

Bayesian Statistics
This course introduces the Bayesian approach to statistical inference for data analysis in a variety of applications. Topics include: comparison of Bayesian and frequentist methods; Bayesian model specification; choice of priors; computational methods such as rejection sampling, and stochastic simulation (Markov chain Monte Carlo); empirical Bayes method; and hands-on Bayesian data analysis using appropriate software.

Probability
Coursework will focus on mathematical theory and application of probability at the advanced undergraduate level: a calculus-based introduction to probability theory. Topics include the computational basics of probability theory; combinatorial methods; conditional probability including Bayes' theorem; random variables and distributions, expectations and moments; the classical distributions; and the central limit theorem.