Course Descriptions

STAT 53600 - Introduction to Survival Analysis

Credits:

3

Description:

Deals with the modern statistical methods for analyzing time-to-event data. Background theory is provided, but the emphasis is on the applications and the interpretations of results. Provides coverage of survivorship functions and censoring patterns; parametric models and likelihood methods, special life-time distributions; nonparametric inference, life-tables, estimation of cumulative hazard functions, the Kaplan-Meier estimator; one and two-sample nonparametric tests for censored data; semiparametric proportional hazards regression (Cox Regression), parameters’ estimation, stratification, model fitting strategies and model interpretations. Heavy use of statistical software such as Splus and SAS.

Prerequisite:

STAT 51700.

STAT-I 598 - Topics in Statistical Methods

Credits:

0-6

Description:

Directed study and reports for students who wish to undertake individual reading and study on approved topics.

Prerequisite:

Consent of instructor.

STAT-S 612 - Reproducible Results and the Workflow of Data Analysis

Credits:

3

Description:

This course presents methods for producing statistical analyses that are reproducible. Topics include creating datasets containing metadata, using script files that allow results to be replicated, methods to organize and preserve files, approaches to documenting research, and ways to maintain the provenance of statistical results.

Prerequisite:

Consent of instructor.

STAT-I 619 - Probability Theory

Credits:

3

Description:

Probability Theory is the foundation of statistical methodologies, which is fundamental in the practice of science. From this course students will get a precise mathematical understanding of probabilities and sigma-algebras, random weak convergence, characteristic functions, the central limit theorem, Lebesgue decomposition, conditioning and martingales.

Prerequisite:

STAT-I 519.

STAT 61900 - Probability Theory

Credits:

3

Description:

Theory Measure theory based course in probability. Topics include Lebesgue measure, measurable functions and integration. Radon-Nikodym Theorem, product measures and Fubini’s Theorem, measures on infinite product spaces, basic concepts of probability theory, conditional probability and expectation, regular conditional probability, strong law of large numbers, martingale theory, martingale convergence theorems, uniform integrability, optional sampling theorems, Kolmogorov’s Three series Theorem, weak convergence of distribution functions, method of characteristic functions, the fundamental weak compactness theorems, convergence to a normal distribution, Lindeberg’s Theorem, infinitely divisible distributions and their subclasses.

Prerequisite:

STAT 51900, 52800.

STAT-S 620 - Introduction to Statistical Theory

Credits:

3

Description:

Fundamental con­cepts and principles of data reduction and statistical inference, including the method of maximum likelihood, the method of least squares, and Bayesian inference. Theoretical justification of statistical procedures introduced in S320.

Prerequisite:

STAT S320 and MATH M463 (or equivalent courses).

STAT-S 625 - Nonparametric Theory and Data Analysis

Credits:

3

Description:

Survey of methods for statistical inference that do not rely on parametric probability models. Statistical functionals, bootstrapping, empirical likelihood. Nonparametric density and curve estimation. Rank and permutation tests.

Prerequisite:

Two statistics courses at the graduate level, or consent of instruc­tor.

STAT-S 626 - Bayesian Theory and Data Analysis

Credits:

3

Description:

Intro­duction to the theory and practice of Bayesian inference. Prior and posterior probability distributions. Data collection, model formulation, computation, model checking, sensitivity analysis.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-I 628 - Advanced Statistical Inference

Credits:

3

Description:

Real analysis for inference, statistics and subfields, conditional expectations and probability distributions, UMP tests with applications to normal distributions and confidence sets, invariance, asymptotic theory of estimation and likelihood based inference, U-statistics, Edgeworth expansions, saddle point method.

Prerequisite:

STAT-I 519 and STAT-I 528.

Corequisite:

STAT-I 619.

STAT 62800 - Advanced Statistical Inference

Credits:

3

Description:

Real analysis for inference, statistics and subfields, conditional expectations and probability distributions, UMP tests with applications to normal distributions and confidence sets, invariance, asymptotic theory of estimation and likelihood based inference, U-statistics, Edgeworth expansions, saddle point method.

Prerequisite:

STAT 51900, 52800, C: STAT 61900.

STAT-S 631 - Applied Linear Models I

Credits:

3

Description:

Part I of a 2-semester sequence on linear models, emphasizing linear regression and the analysis of variance, in­cluding topics from the design of experiments and culminating in the general linear model.

Prerequisite:

STAT S320 and MATH M301 or M303 or S303 (or equivalent courses), or consent of instructor.

STAT-S 632 - Applied Linear Models II

Credits:

3

Description:

Part II of a 2-semester sequence on linear models, emphasizing linear regression and the analysis of variance, in­cluding topics from the design of experiments and culminating in the general linear model.

Prerequisite:

STAT S631, or consent of instructor.

STAT-S 637 - Categorical Data Analysis

Credits:

3

Description:

The analysis of cross classified categorical data. Loglinear models; regression models in which the response variable is binary, ordinal, nomi­nal, or discrete. Logit, probit, multinomial logit models; logistic and Poisson regression. Equivalent to EDUC Y637.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-S 639 - Multilevel Models

Credits:

3

Description:

Introduction to the general multilevel model with an emphasis on applications. Discussion of hierarchical linear models, and generalizations to nonlinear models. How such models are conceptualized, parameters estimated and interpreted. Model fit via software. Major emphasis throughout the course will be on how to choose an appropriate model and computational techniques. Equivalent to EDUC Y639.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-S 640 - Multivariate Data Analysis

Credits:

3

Description:

Elementary treat­ment of multivariate normal distributions, classical inferential techniques for multivariate normal data, including Hotelling’s T² and MANOVA. Discussion of analytic techniques such as principal component analysis, canonical correlation analysis, discriminant analysis, and factor analysis. Equivalent to PSY P654.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-S 645 - Covariance Structure Analysis

Credits:

3

Description:

Path analysis. Introduction to multivariate multiple regression, con­firmatory factor analysis, and latent variables. Structural equa­tion models with and without latent variables. Mean-structure and multi-group analysis. Equivalent to EDUC Y645.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-S 650 - Time Series Analysis

Credits:

3

Description:

Techniques for analyzing data collected at different points in time. Probability models, forecasting methods, analysis in both time and fre­quency domains, linear systems, state-space models, interven­tion analysis, transfer function models and the Kalman filter. Stationary processes, autocorrelations, partial autocorrelations, autoregressive, moving average, and ARMA processes, spectral density of stationary processes, periodograms, estimation of spectral density. Course equivalent to MATH M568.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-S 655 - Longitudinal Data Analysis

Credits:

3

Description:

Introduction to methods for longitudinal data analysis; repeated measures data. The analysis of change—models for one or more response variables, possibly censored. Association of measurements across time for both continuous and discrete responses. Course is equivalent to EDUC Y655.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-S 660 - Sampling

Credits:

3

Description:

Design of surveys and analysis of sample survey data. Simple random sampling, ratio and regression estimation, stratified and cluster sampling, complex surveys, nonresponse bias.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.

STAT-S 670 - Exploratory Data Analysis

Credits:

3

Description:

Numerical and graphical techniques for summarizing and displaying data. Ex­ploration versus confirmation. Connections with conventional statistical analysis and data mining. Applications to large data sets.

Prerequisite:

Two statistics courses at the graduate level, or consent of instructor.