### Courses

#### Statistics

- STAT 11300 Statistics and Society (3 cr.) Fall, spring. 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 19000 Topics in Statistics for Undergraduates (1-5 cr.) Supervised reading course or special topics course at the freshman level. Prerequisites and course material vary with the topic.
- STAT 29000 Topics in Statistics for Undergraduates (1-5 cr.) Supervised reading course or special topics course at the sophomore level. Prerequisites and course material vary with the topic.
- STAT 30100 Elementary Statistical Methods I (3 cr.) P: MATH 11000 or 11100 (with a minimum grade of C-) or equivalent. Not open to students in the Department of Mathematical Sciences. Fall, spring, summer. 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.
- STAT 35000 Introduction to Statistics (3 cr.) P: MATH 16500 or equivalent. Fall, spring. A data-oriented introduction to the fundamental concepts and methods of applied statistics. The course 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 51100 but with emphasis on more data-analytic material. Includes a weekly computing laboratory using Minitab.
- STAT 37100 Prep for Actuarial Exam I (2 cr.) This course is intended to help actuarial students prepare for the Actuarial Exam P.
- STAT 39000 Topics in Statistics for Undergraduates (1-5 cr.) Supervised reading course or special topics course at the junior level. Prerequisites and course material vary with the topic.
- STAT 41600 Probability (3 cr.) P: MATH 26100 or equivalent. Not open to students with credit in 31100. Fall. 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 (3 cr.) P: 41600. C: 35000 or equivalent. Spring. 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 (3 cr.) P: 41700 or equivalent. Fall. 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, 47300, provides most of the background for Course 3 of the Society of Actuaries and the Casualty Actuarial Society.
- STAT 47300 Actuarial Models II (3 cr.) P: 47200. Spring. Continuation of 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 49000 Topics in Statistics for Undergraduates (1-5 cr.) Supervised reading and reports in various fields.
- STAT 51100 Statistical Methods I (3 cr.) P: MATH 16500. Spring. 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 (3 cr.) P: 51100. Fall. 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 (3 cr.) P: 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 (3 cr.) P: 51200. Spring. Fundamentals, completely randomized design, and randomized complete blocks. Latin squares, multiclassification, factorial, nested factorial, incom-plete blocks, fractional replications, confounding, general mixed factorial, split-plot, and optimum design. Use of existing statistical computing packages.
- STAT 51500 Statistical Consulting Problems (1-3 cr.) 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 (3 cr.) P: MATH 26100 or equivalent. Fall. 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 (3 cr.) P: 51100 or 51600. Spring. 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 Introduction to Probability (3 cr.) P: MATH 26100 or equivalent. Fall. Sample spaces and axioms of probability, conditional probability, independence, random variables, distribution functions, moment generating and characteristics functions, special discrete and continuous distributionsunivariate 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 (3 cr.) P: 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 (3 cr.) C: 51200 or equivalent. A broad range of topics involving the use of computers in statistical methods. Collection and organization of data for statistical analysis; transferring data between statistical applications and computing platforms; techniques in exploratory data analysis; and comparison of statistical packages.
- STAT 52200 Sampling and Survey Techniques (3 cr.) P: 51200 or equivalent. 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 (3 cr.) P: 52800 or equivalent, or consent of instructor. 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 (3 cr.) P: 52800 or equivalent, or consent of instructor. Fall. 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 (3 cr.) C: 52800 or equivalent, or consent of instructor. 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 (3 cr.) P: 51900 or equivalent. Spring. 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 (3 cr.) C: 52800 or equivalent. 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.
- MATH 53200 Elements of Stochastic Processes (3 cr.) P: 51900 or equivalent. 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 (3 cr.) P: 51600 or equivalent. 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 (3 cr.) P: 51700 or equivalent. 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 (1-3 cr.) P: consent of instructor. Directed study and reports for students who wish to undertake individual reading and study on approved topics.
- STAT 61900 Probability (3 cr.) P: STAT 51900, 52800. 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.
- STAT 62800 Advanced Statistical Inference (3 cr.) P: STAT 51900, 52800, C: STAT 61900. 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.
- STAT 63800 Stochastic Processes I (pending approval) (3 cr.) P: STAT 61900. Advanced topics in probability theory which may include stationary processes, independent increment processes, Gaussian processes; martingales, Markov processes, ergodic theory.
- STAT 63900 Stochastic Processes II (pending approval) (3 cr.) P: STAT 63800. This is the continuation of STAT 63800. We will concentrate on specific chapters from the textbook, including Ch VI-IX (Local Times, Generators, Girsanov's theorem, Stochastic Differential Equations). Some material from another textbook (Karatzas and Shreve, Brownian Motion and Stochastic Calculus), and the instructor's own work, may also be used, especially to cover Feynman-Kac formulas and the connection to PDEs and Stochastic PDEs. New topics not treatable using martingales will also be investigated, include stochastic integration with respect to Fractional Brownian Motion and other, more irregular Gaussian processes; anticipative stochastic calculus; Gaussian and non-Gaussian regularity theory.