In the following course list, the Level V statistics prerequisite for some courses may be fulfilled by 16:960:563 or 586 or 593, while the Level IV statistics prerequisite may be fulfilled by 01:960:401 or 484 or 16:960:590 or Level V statistics. Students believing that they have had an experience comparable to that required as a prerequisite, generally through coursework at another university, should contact the graduate director, who will waive the prerequisite when justified.

16:960:501 Statistical Theory for Research Workers I (3) Designed to strengthen the statistical backgrounds of research workers. Concepts of randomness and probability; frequency distributions; expectations; derived distributions and sampling; and estimation and significance testing. Not open to graduate students in statistics.

16:960:502 Statistical Theory for Research Workers II (3) Continuation of 16:960:501. Principles and practices of experimental design as applied to mathematical models; the analysis of variance; factorial designs; analysis of matched groups and repeated measurements on the same group; analysis of qualitative data. Prerequisite: 16:960:501. Not open to graduate students in statistics.

16:960:531,532 Statistical Methods in Education (3,3) First semester: graphing; descriptive measures of central tendency and variability; introduction to correlation and regression; probability theory; the normal curve; sampling; point estimation; interval estimation; and elementary hypothesis testing. Second semester: principles and practices of experimental design; z-test, t-test, chi-square tests, F-test; and analysis of variance. For students in the Graduate School of Education.

16:960:535 Advanced Statistical Methods in Finance (3) Traditional and state-of-the-art statistical methods used in the financial industry for analyzing financial data, developing financial models, searching for arbitrage opportunities, and evaluating and managing risks. Prerequisite: 16:960:563.

16:960:536 Financial Risk Evaluation and Management (3) Methods include statistical methods for value at risk, extreme value theory, pricing of futures and options, credit, and currency and interest rate risk. Prerequisite: 16:960:565.

16:960:540 Statistical Quality Control I (3) Construction and analysis of control charts for variables and attributes; histogram analysis; use and evaluation of Dodge-Romig and Military Standards acceptance sampling plans. Prerequisite: 16:960:580, 582, or 592.

16:960:541 Statistical Quality Control II (3) Introduction to state-of-the-art methods in statistical quality control, including economic design and Bayesian methods in process control, Taguchi's method, and statistical tolerance. Prerequisites: 16:960:540, 590.

16:960:542 Life Data Analysis (3) Statistical methodology for survival and reliability data. Topics include life-table techniques; competing risk analysis; parametric and nonparametric inferences of lifetime distributions; regressions and censored data; Poisson and renewal processes; multistate survival models and goodness-of-fit test. Statistical software used. Prerequisites: One year of calculus and Level V statistics.

16:960:545 Statistical Practice (3) Objectives of statistical collaboration; problem definition; formation of solutions; active consultation; tools of statistical practice; searching literature; data collection form design; codebook development; data entry and cleaning; and documentation and presentation of statistical analysis. Prerequisite: Level IV statistics.

16:960:553 Categorical Data Analysis (3) Two-by-two frequency tables; Fisher's exact test; measures of association; general contingency tables; loglinear models; logistic regression; repeated categorical-response data; maximum likelihood estimation; and tables with ordered categories. Prerequisite: Level V statistics.

16:960:554 Applied Stochastic Processes (3) Markov chains; recurrence; random walk; gambler's ruin; ergodic theorem and stationary distribution; continuous time Markov chains; queuing problems; renewal processes; martingales; Markov processes; Brownian motion; concepts in stochastic calculus; and Ito's formula. Prerequisites: Advanced calculus, and 16:960:580 or 582 or 592.

16:960:555 Nonparametric Statistics (3) Introduction and survey of distribution-free approaches to statistical inference. Fisher's method of randomization; distribution-free test procedures for means, variances, correlations, and trends; rank tests; relative efficiency, asymptotic relative efficiency, and normal-score procedures; binomial, hypergeometric distributions, and combinatorial run theory. Also, tests of goodness-of-fit, including the Kolmogorov-Smirnov and chi-square tests, contingency-table analysis, tolerance sets, and Tchebycheffe-type inequalities. Emphasis on applications. Prerequisites: Level IV statistics, and 16:960:580 or 582 or 592.

16:960:563 Regression Analysis (3) Review of basic statistical theory and matrix algebra; general� regression models; computer application to regression� techniques;� residual analysis; selection of regression models; response surface methodology; experimental design models; and analysis of covariance. Emphasis on applications. Prerequisite: Level IV statistics.

16:960:565 Applied Time Series Analysis (3) Model-based forecasting methods; autoregressive and moving average models; ARIMA, ARMAX, ARCH, and state-space models; estimation, forecasting, and model validation; missing data; irregularly spaced time series; parametric and nonparametric bootstrap methods for time series; multiresolution analysis of spatial and time-series signals; and time-varying models and wavelets. Prerequisite: Level V statistics.

16:960:567 Applied Multivariate Analysis (3) Methods dimension reduction, including principal components, factor� analysis, and multidimensional scaling; correlation techniques,� including partial, multiple, and canonical correlation. Clustering and classification. Emphasis on data analytic issues,� concepts, and methods (e.g., graphical techniques) and on applications� drawn from several areas, including behavioral, management, and physical and engineering sciences. Prerequisite: Level V statistics.

16:960:575 Acceptance Sampling Theory (3) Selection, operation, and statistical behavior of sampling plans. Dodge-Romig plans; continuous, chain, and skip-lot plans; variable sampling plans. Economic analysis and study of sampling systems. Prerequisite: Level IV statistics.

16:960:576 Survey Sampling (3) Introduction to the design, analysis, and interpretation of sample surveys. Sampling types covered include simple random, stratified random, systematical, cluster, and multistage. Methods of estimation described to estimate means, totals, ratios, and proportions. Development of sampling designs combining a variety of types of sampling and methods of estimation, and detailed description of sample size determinations to achieve goals of desired precision at least cost. Prerequisite: 16:960:580, 582, or 592.

16:960:580 Basic Probability (3) Discrete-probability spaces; combinatorial analysis; occupancy and matching problems; basic distributions; probabilities in a continuum; random variables; expectations; distribution functions; conditional probability and independence; coin tossing; weak law of large number; and the deMoivre-Laplace theorem. Prerequisite: 16:640:251. Credit given for only one of 16:960:580, 582, 592.

16:960:582 Introduction to Methods and Theory of Probability (3) Emphasis on methods and problem solving. Topics include probability spaces, basic distributions, random variables, expectations, distribution functions, conditional probability and independence, and sampling distributions. Prerequisite: 16:640:251. Credit given for only one of 16:960:580, 582, 592.

16:960:583 Methods of Inference (3) Theory of point and interval estimation and hypothesis testing. Topics include sufficiency, unbiasedness, and power functions. Emphasis on application of the theory in the development of statistical procedures. Prerequisite: 16:960:580, 582, or 592. Credit not given for both this course and 16:960:593.

19:960:584 Biostatistics I-Observational Studies (3) Statistical techniques for biomedical data. Analysis of observational studies is emphasized. Topics include measures of disease frequency and association; inferences for dichotomous and grouped case-control data; logistic regression for identification of risk factors; Poisson models for grouped data; bioassay. SAS used in analysis of data. Prerequisites: One year of calculus and Level V statistics.

19:960:585 Biostatistics II-Clinical Trials (3) Statistical and practical design, conduct, and analysis of controlled clinical experiments. Topics include introduction to phases of clinical trials; power and sample size estimation; randomization schemes; study design; human subject considerations and recruitment; data collection design and process; data monitoring and interim analysis; baseline covariate adjustment and data analysis; and writing and presenting results. Standard statistical software used for randomization, power/sample size estimation, and data analysis; 16:960:584 Biostatistics I is not required. Prerequisite: Level IV statistics.

16:960:586 Interpretation of Data I (3) Modern methods of data analysis with an emphasis on statistical computing: univariate statistics, data visualization, robust statistics, nonlinear models, logistic regression, generalized linear models (GLM), and smooth regression (including GAM models). Expect to use statistical software packages, such as SAS (or SPSS) and Splus (or R) in data analysis. Prerequisite: Level IV statistics. Corequisite: 16:960:563.

16:960:587 Interpretation of Data II (3) Modern methods of data analysis and advanced statistical computing techniques: Monte-Carlo simulation methods; the EM algorithm; MCMC methods; spatial statistics; longitudinal data analysis/mixed effects models/GEE; latent variable models; hidden Markov models; and Bayesian methods, etc. Expect to use the statistical software package Splus (or R) and to do some Splus (or R) programming for data analysis. Prerequisite: 16:960:586.

16:960:588 Data Mining (3) Databases and data warehousing; exploratory data analysis and visualization; an overview of data mining algorithms; modeling for data mining; descriptive modeling; predictive modeling; pattern and rule discovery; text mining; Bayesian data mining; and observational studies. Prerequisites: 16:960:567 and 587.

16:960:590 Design of Experiments (3) Fundamental principles of experimental design; completely randomized variance component designs; randomized blocks; Latin squares; incomplete blocks; partially hierarchic mixed-model experiments; factorial experiments; fractional factorials; and response surface exploration. Prerequisite: 01:960:484 or 401 or equivalent.

16:960:591 Advanced Design of Experiments (3) Strategy of experimentation; screening designs; factorial designs; response surface methodology; evolutionary operation; mixture designs; incomplete blocking designs; computer-aided experimental designs; and design optimality criteria. Prerequisite: 16:960:590. Recommended: 16:960:563.

16:960:592 Theory of Probability (3) Emphasis on proofs and fundamental concepts. Topics include probability spaces, basic distributions, random variables, expectations, distribution functions, conditional probability and independence, and sampling distributions. Prerequisite: Advanced calculus. Credit given for only one of 16:960:580, 582, 592.

16:960:593 Theory of Statistics (3) Theory of point and interval estimation and hypothesis testing. Topics include sufficiency, unbiasedness, Bayes methods, and power functions. Emphasis on fundamental concepts underlying the theory. Prerequisite: 16:960:592. Credit not given for both 16:960:583 and this course.

16:960:595 Intermediate Probability (3) Central limit theorem. Borel-Cantelli lemma, strong law of large numbers; convolutions, generating functions, recurrent events, random walks on line, plane and 3-space, ruin of a gambler, simple time-dependent processes, and/or Markov chains. Prerequisite: 16:960:592.

18:960:596 Intermediate Statistical Methods (3) An introduction to modern statistical methods for students in the statistics and biostatistics doctoral program. Exploratory methods and linear and nonlinear regression models.
Prerequisite: Admission to the statistics doctoral program or consent of the program director. Credit given for only two of 960:563, 586, 596.

16:960:652 Advanced Theory of Statistics I (3) Theories of statistical inference and their relation to statistical methods; sufficiency, invariance, unbiasedness, decision theory; Bayesian procedures and likelihood procedures. Prerequisites: 16:960:593 and 01:640:412.

16:960:653 Advanced Theory of Statistics II (3) Hypothesis testing, point and confidence estimation robustness, sequential procedures. Prerequisite: 16:960:652.

16:960:654 Stochastic Processes (3) Selected topics from the theory of the Markov processes, queuing theory, birth and death processes, martingale theory, and Brownian motion and related topics. Measure-theoretic notations, as well as ideas from classical analysis used as needed. Prerequisite: 16:960:554 or 16:960:680.

16:960:655 Advanced Nonparametric Statistics (3) Rank-testing and estimation procedures for the one- and two-sample problems; locally most powerful rank tests; criteria for unbiasedness and permutation tests. Exact and asymptotic distribution theory; and asymptotic efficiency. Rank correlation; sequential procedures; and the Kolmogorov-Smirnov test. Emphasis on theory. Prerequisite: 16:960:593.

16:960:663 Regression Theory (3) Least-squares methods of testing and estimation in multiple regression; geometric interpretation of least-squares; and the Gauss-Markov theorem. Confidence, prediction, and tolerance intervals in regression. Orthogonal polynomials; harmonic regression; weighted least-squares; analysis of variance; and simultaneous inference procedures (multiple comparisons). Emphasis on theory. Prerequisites: 16:960:593 and 01:640:350.

16:960:664 (S) Advanced Topics in Regression and ANOVA (3) Development of linear classification models; general results of components of variance for balanced designs; polynomial regression models (response surfaces); crossed models for combined qualitative and quantitative factors; reduced regression models; and nonlinear regression computational and statistical procedures. Prerequisite: 16:960:663.

16:960:667 Multivariate Statistics (3) Multivariate, marginal, and conditional distributions. Multivariate normal; characterizations and parameter estimation. Wishart distribution; Hotelling's T2 statistic; multivariate linear model; and principal component analysis correlations. Multivariate classification; matrices and discriminate methods. Emphasis on theory. Prerequisite: 16:960:663.

16:960:668 Bayesian Data Analysis (3) Bayesian inference, manipulation of joint probability distributions, probability distributions and conditional independence concepts; Monte Carlo methods, static and dynamic methods; predictive approach to Bayesian analysis, exchangeability, and the de Finetti theorem; Bayesian analysis in one-layer problems, including prior, posterior, and predictive distributions; and Monte Carlo methods in advanced modeling and inference problems. Calculations are done in the Splus/R computer language and BUGS, a software package for Bayesian data analysis. Prerequisite: 16:960:593.

16:960:680 Advanced Probability Theory I (3) Measures, measurable functions, and integration; limit theorems; Lebesgue measure; Riemann integral; Lebesgue-Stieltjes integral; measure extension, probability measures, and random variables; expectation, distribution, and independence. Borel-Cantelli lemma; zero-one law; convergence in distribution; convergence in probability; almost sure convergence; law of large numbers; Jensen, Holder, and Minkowski inequalities; convergence in mean; uniform integrability and spaces of functions. Prerequisite: 01:640:412.

16:960:681 Advanced Probability Theory II (3) Characteristic functions; the Lindeberg central limit theorem; Helly's selection theorem; convergence of multivariate distribution functions; conditional probability, the Radon-Nikodym theorem; conditional expectation, martingales, and the optional stopping theorem. Doob's inequalities; martingale convergence theorems; random walk; Markov chains; recurrence and transience; stationary measure and convergence theorems for Markov chains. Product measures; Fubini's theorem; Kolmogorov consistency theorem; weak convergence of stochastic processes; Brownian motion; and the law of the iterated logarithm. Prerequisite: 16:960:680.

16:960:682,683 Individual Studies in Statistics (3,3) Prerequisite: Permission of program director.

16:960:689 Sequential Methods (3) Sequential probability ratio test; approximations for the stopping boundaries, power curve, and expected stopping time; termination with probability one; existence of moments for the stopping time; Wald's lemmas and fundamental identity; and Bayes character and optimality of the SPRT. Composite hypotheses: weight-function and invariant SPRTs. Sequential estimation, including fixed-width confidence intervals and confidence sequences. Prerequisites: 16:960:593 and 680.

16:960:690,691 Special Topics (3,3) Topics, which change on a rotating basis, include large sample theory, time series analysis, Bayesian statistics, robustness, and sequential analysis. Prerequisite: Permission of program director.

16:960:693 Current Topics in Statistics (1) Topics change based on statistical research and applications of faculty in and outside the department. Prerequisite: Permission of program director.

16:960:694,695,696 Special Topics in Statistics (1,1,1) Modern statistics and interdisciplinary topics not regularly covered in the graduate program. Prerequisite: Permission of program director.

16:960:701,702 Research in Statistics (BA,BA)