Course Descriptions

STAT 52300 - Categorical Data Analysis Models

Credits:

3

Description:

Generating binary and categorical response data, two way classification tables, measures of association and agreement, goodness-of-fit tests, testing independence, large sample properties. General linear models, logistic regression, probit and extreme value models. Log-linear models in two and higher dimensions; maximum likelihood estimation, testing Goodness-of-fit, partitioning Chi-Square, models for ordinal data. Model-building, selection and diagnostics. Other related topics as time permits. Computer applications using SAS.

Prerequisite:

STAT 52800 or equivalent, or consent of instructor.

STAT-I 524 - Applied Multivariate Analysis

Credits:

3

Description:

Extension of univariate tests in normal populations to the multivariate case, equality of covariance matrices, multivariate analysis of variance, discriminant analysis and misclassification errors, canonical correlation, principal components, and factor analysis. Strong emphasis on the use of existing computer programs.

Prerequisite:

STAT-I 528.

STAT 52400 - Applied Multivariate Analysis

Credits:

3

Description:

Extension of univariate tests in normal populations to the multivariate case, equality of covariance matrices, multivariate analysis of variance, discriminate analysis and misclassification errors, canonical correlation, principal components, factor analysis.

Prerequisite:

STAT 52800 or equivalent, or consent of instructor.

STAT-I 525 - Generalized Linear Models

Credits:

3

Description:

Generalized linear models, likelihood methods for data analysis, and diagnostic methods for assessing model assumptions. Methods covered include multiple regression, analysis of variance for completely randomized designs, binary and categorical response models, and hierarchical loglinear models for contingency tables.

Prerequisite:

STAT-I 528 or equivalent, or consent of instructor.

STAT 52500 - Generalized Linear Model

Credits:

3

Description:

STAT 52501 - Generalized Linear Model

Credits:

3

Description:

Generalized linear models, likelihood methods for data analysis, diagnostic methods for assessing model assumptions. Methods covered include multiple regression, analysis of variance for completely randomized designs, binary and categorical response models, and hierarchical log-linear models for contingency tables.

Prerequisite:

STAT 52800 or equivalent or consent of instructor.

STAT-I 528 - Mathematical Statistics

Credits:

3

Description:

Sufficiency and completeness, the exponential family of distributions, theory of point estimation, Cramer-Rao inequality, Rao-Blackwell Theorem with applications, maximum likelihood estimation, asymptotic distributions of ML estimators, hypothesis testing, Neyman-Pearson Lemma, UMP tests, generalized likelihood ratio test, asymptotic distribution of the GLR test, and sequential probability ratio test.

Prerequisite:

STAT-I 519.

STAT 52800 - Mathematical Statistics I

Credits:

3

Description:

Sufficiency and completeness, the exponential family of distributions, theory of point estimation, Cramer-Rao inequality, Rao-Blackwell Theorem with applications, maximum likelihood estimation, asymptotic distributions of ML estimators, hypothesis testing, Neyman-Pearson Lemma, UMP tests, generalized likelihood ratio test, asymptotic distribution of the GLR test, sequential probability ratio test.

Prerequisite:

STAT 51900.

STAT-I 529 - Applied Decision Theory and Bayesian Analysis

Credits:

3

Description:

Foundation of statistical analysis, Bayesian and decision theoretic formulation of problems; construction of utility functions and quantifications of prior information; methods of Bayesian decision and inference, with applications; empirical Bayes; combination of evidence; and game theory and minimax rules, Bayesian design, and sequential analysis. Comparison of statistical paradigms.

Prerequisite:

STAT-I 528 or equivalent.

STAT 52900 - Bayesian Statistics and Applied Decision Theory

Credits:

3

Description:

Bayesian and decision theoretic formulation of problems; construction of utility functions and quantification of prior information; choice of prior; methods of Bayesian decision and inference,; Bayesian computations; MCMC methods; empirical Bayes; hierarchical models, Bayes factors; combination of evidence; game theory and minimax rules, Bayesian design and sequential analysis.

Prerequisite:

STAT 52800 or equivalent.

STAT-I 532 - Elements of Stochastic Processes

Credits:

3

Description:

A basic course in stochastic models including discrete and continuous time processes, Markov chains, and Brownian motion. Introduction to topics such as Gaussian processes, queues and renewal processes, and Poisson processes. Application to economic models, epidemic models, and reliability problems.

Prerequisite:

STAT-I 519.

STAT 53200 - Elements of Stochastic Processes

Credits:

3

Description:

A basic course in stochastic models including discrete and continuous time processes, Markov chains and Brownian motion. Introduction to topics such as Gaussian processes, queues and renewal processes and Poisson processes. Applications to economics, epidemic models, birth and death processes, point processes, and reliability problems.

Prerequisite:

STAT 51900 or equivalent.

STAT-I 533 - Nonparametric Statistics

Credits:

3

Description:

Binomial test for dichotomous data, confidence intervals for proportions, order statistics, one-sample signed Wilcoxon rank test, two-sample Wilcoxon test, two-sample rank tests for dispersion, and Kruskal-Wallis test for one-way layout. Runs test and Kendall test for independence, one- and two-sample Kolmogorov-Smirnov tests, and nonparametric regression.

Prerequisite:

STAT-I 516 or consent of instructor.

STAT 53300 - Nonparametric Statistics

Credits:

3

Description:

Binomial test for dichotomous data, confidence intervals for proportions, order statistics, one sample signed Wilcoxon rank test, two-sample Wilcoxon test, two-sample rank tests for dispersion, Kruskal-Wallis test for one-way layout. Runs test and Kendall test for independence, one and two sample Kolmogorov-Smirnov tests, nonparametric regression.

Prerequisite:

STAT 51900 or equivalent.

STAT-I 536 - 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, and the Kaplan-Meier estimator; one- and two-sample nonparametric tests for censored data; and semiparametric proportional hazards regression (Cox Regression), parameters' estimation, stratification, model fitting strategies, and model interpretations. Heavy use of statistical software such as R and SAS.

Prerequisite:

STAT-I 517 or equivalent.

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.