STAT- 11300

Statistics and Society

Intended to familiarize the student with basic statistical concepts and some of their applications in public and health policies as well as in social and behavioral sciences. No mathematics beyond simple algebra is needed, but quantitative skills are strengthened by constant use. Involves much reading, writing, and critical thinking through discussions on such topics as data ethics, public opinion polls and the political process, the question of causation the role of government statistics, and dealing with chance in everyday life. Applications include public opinion polls, medical experiments, smoking and health, the consumer price index, state lotteries, and the like. STAT 11300 can be used for general education or as preparation for later methodology courses.

STAT- 30100

Elementary Statistical Methods I

P: MATH 11000 or 11100 or placement. Not open to students in the Department of Mathematical Sciences. Introduction to statistical methods with applications to diverse fields. Emphasis on understanding and interpreting standard techniques. Data analysis for one and several variables, design of samples and experiments, basic probability, sampling distributions, confidence intervals and significance tests for means and proportions, and correlation and regression. Software is used throughout. See Course Web Site for more information.

STAT- 35000

Introduction to Statistics

P: MATH 16500. A data-oriented introduction to the fundamental concepts and methods of applied statistics. STAT 350 is intended primarily for majors in the mathematical sciences mathematics, actuarial sciences, mathematics education. The objective is to acquaint the students with the essential ideas and methods of statistical analysis for data in simple settings. It covers material similar to that of STAT 51100 but with emphasis on more data-analytic material. Includes a weekly computing laboratory using Minitab.

STAT- 37100

Prep for Actuarial Exam I

This course is intended to help actuarial science students prepare for the SOA/CAS Exam P/1.

STAT- 41600

Probability

P: MATH 26100. Not open to students with credit in STAT 31100. An introduction to mathematical probability suitable as preparation for actuarial science, statistical theory, and mathematical modeling. General probability rules, conditional probability, Bayes theorem, discrete and continuous random variables, moments and moment generating functions, continuous distributions and their properties, law of large numbers, and central limit theorem.

STAT- 41700

Statistical Theory

P: STAT 41600. R: STAT 35000. An introduction to the mathematical theory of statistical inference, emphasizing inference for standard parametric families of distributions. Properties of estimators. Bayes and maximum likelihood estimation. Sufficient statistics. Properties of test of hypotheses. Most powerful and likelihood-ratio tests. Distribution theory for common statistics based on normal distributions.

STAT- 47200

Actuarial Models I

P: STAT 41700 or equivalent. Mathematical foundations of actuarial science emphasizing probability models for life contingencies as the basis for analyzing life insurance and life annuities and determining premiums. This course, together with its sequel, STAT 47300, provides most of the background for Exams MLC and MFE of the Society of Actuaries.

STAT- 47300

Actuarial Models II

P: STAT 47200. Continuation of STAT 47200. Together, these courses cover contingent payment models, survival models, frequency and severity models, compound distribution models, simulation models, stochastic process models, and ruin models.

STAT-N 501

Statistical Methods for Health Sciences

P: Math 15300. An introductory statistical methods course, with emphasis on applications in the health sciences. Topics include descriptive statistics, probability distributions, sampling distributions, confidence interval estimation, hypothesis testing, analysis of variance, linear regression, goodness-of-fit tests, and contingency tables. Credit cannot be given for more than one of STAT 30100, 35000 or 51100; or STAT N501.

STAT- 51100

Statistical Methods I

P: MATH 16500. Descriptive statistics; elementary probability; random variables and their distributions; expectation; normal, binomial, Poisson, and hypergeometric distributions; sampling distributions; estimation and testing of hypotheses; one-way analysis of variance; and correlation and regression.

STAT- 51200

Applied Regression Analysis

P: STAT 51100. Inference in simple and multiple linear regression, estimation of model parameters, testing and prediction. Residual analysis, diagnostics and remedial measures. Multicollinearity. Model building, stepwise, and other model selection methods. Weighted least squares. Nonlinear regression. Models with qualitative independent variables. One-way analysis of variance. Orthogonal contrasts and multiple comparison tests. Use of existing statistical computing package.

STAT- 51300

Statistical Quality Control

P: STAT 51100. Control charts and acceptance sampling, standard acceptance plans, continuous sampling plans, sequential analysis, and response surface analysis. Use of existing statistical computing packages.

STAT- 51400

Designs of Experiments

P: STAT 51200. Fundamentals, completely randomized design, and randomized complete blocks. Latin squares, multiclassification, factorial, nested factorial, incomplete blocks, fractional replications, confounding, general mixed factorial, split-plot, and optimum design. Use of existing statistical computing packages.

STAT- 51500

Statistical Consulting Problems

P: consent of advisor. Consultation on real-world problems involving statistical analysis under the guidance of a faculty member. A detailed written report and an oral presentation are required.

STAT- 51600

Basic Probability and Applications

P: MATH 26100. A first course in probability intended to serve as a foundation for statistics and other applications. Intuitive background; sample spaces and random variables; joint, conditional, and marginal distributions; special distributions of statistical importance; moments and moment generating functions; statement and application of limit theorems; and introduction to Markov chains.

STAT- 51700

Statistical Inference

P: STAT 51100 or 51600. A basic course in statistical theory covering standard statistical methods and their applications. Includes unbiased, maximum likelihood, and moment estimation; confidence intervals and regions; testing hypotheses for standard distributions and contingency tables; and introduction to nonparametric tests and linear regression.

STAT- 51900

Probability Theory

P: MATH 26100. Sample spaces and axioms of probability, conditional probability, independence, random variables, distribution functions, moment generating and characteristics functions, special discrete and continuous distributions--univariate and multivariate cases, normal multivariate distributions, distribution of functions of random variables, modes of convergence and limit theorems, including laws of large numbers and central limit theorem.

STAT- 52000

Time Series and Applications

P: STAT 51900. A first course in stationary time series with applications in engineering, economics, and physical sciences. Stationarity, autocovariance function and spectrum; integral representation of a stationary time series and interpretation; linear filtering; transfer function models; estimation of spectrum; and multivariate time series. Use of existing statistical computing packages.

STAT- 52100

Statistical Computing

STAT- 52200

Sampling and Survey Techniques

P: STAT 51200. Survey designs; simple random, stratified, and systematic samples; systems of sampling; methods of estimation; ratio and regression estimates; and costs. Other related topics as time permits.

STAT- 52300

Categorical Data Analysis

P: STAT 52800. Models 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, and probit and extreme value models. Loglinear models in two and higher dimensions; maximum likelihood estimation, testing goodness-of-fit, partitioning chi-square, and models for ordinal data. Model building, selection, and diagnostics. Other related topics as time permits. Computer applications using existing statistical software.

STAT- 52400

Applied Multivariate Analysis

P: STAT 52800. 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.

STAT- 52500

Intermediate Statistical Methodology

C: STAT 52800. 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.

STAT- 52800

Mathematical Statistics

P: STAT 51900. 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.

STAT- 52900

Applied Decision Theory and Bayesian Analysis

C: STAT 52800. 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.

STAT- 53200

Elements of Stochastic Processes MATH 53200

P: STAT 51900. 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.

STAT- 53300

Nonparametric Statistics

P: STAT 51600. 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.

STAT- 53600

Introduction to Survival Analysis

P: STAT 51700. 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 Splus and SAS.

STAT- 59800

Topics in Statistical Methods

P: consent of instructor. Directed study and reports for students who wish to undertake individual reading and study on approved topics.

STAT- 61900

Probability Theory

P: STAT 51900. 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, Lobesgue decomposition, conditioning and martingales.

STAT- 69800

Research M.S. Thesis

P: consent of advisor. M.S. thesis in Applied Statistics.