




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 01:960:484 or 16:960:590 or Level V statistics. 
16:960:501(F) 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; estimation and significance testing. Not open to graduate students in statistics. 
16:960:502(S) 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 or 511. Not open to graduate students in statistics. 
16:960:511(F) Statistical Methods in Social Work (3) Introduction to descriptive and inferential statistics. Frequency distributions and crossclassification techniques; analyzing qualitative and quantitative data; measures of central tendency and dispersion; measures of association, correlation, and regression; probability modeling, sampling distribution, confidence intervals, hypothesis tests. For students in the School of Social Work. 
16:960:531,532Statistical Methods in Education (3,3) First term: 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 term: principles and practices of experimental design; ztest, ttest, chisquare tests, Ftest, and analysis of variance. Penfield. For students in the Graduate School of Education. 
16:960:540(F) Statistical Quality Control I (3) Construction and analysis of control charts for variables and attributes; histogram analysis; use and evaluation of DodgeRomig and Military Standards acceptance sampling plans. Prerequisites: Level IV statistics, 16:960:582 or equivalent. 
16:960:541(S) Statistical Quality Control II (3) Introduction to stateoftheart 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(S) Life Data Analysis (3) Statistical methodology for survival and reliability data. Topics include lifetable techniques; competing risk analysis; parametric and nonparametric inferences of lifetime distributions; regressions and censored data; Poisson and renewal processes; multistate survival models and goodnessoffit test. Statistical software used. Prerequisites: One year of calculus, Level V statistics, or permission of instructor. 
16:960:545Statistical 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, documentation and presentation of statistical analysis. Prerequisite: Level IV statistics. 
16:960:553(F) Categorical Data Analysis (3) Twobytwo frequency tables, Fisher's exact test, measures of association, general contingency tables, loglinear models, logistic regression, repeated categoricalresponse data, maximum likelihood estimation, tables with ordered categories, discriminant analysis. Prerequisite: Level V statistics or permission of instructor. 
16:960:554(S) 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; Ito's formula. Prerequisites: Advanced calculus, 16:960:582 or equivalent. 
16:960:555(F) Nonparametric Statistics (3) Introduction and survey of distributionfree approaches to statistical inference. Fisher's method of randomization, distributionfree test procedures for means, variances, correlations, and trends; rank tests; relative efficiency, asymptotic relative efficiency, and normalscore procedures; binomial, hypergeometric distributions, and combinatorial run theory. Also, tests of goodnessoffit, including the KolmogorovSmirnov and chisquare tests, contingencytable analysis, tolerance sets, and Tchebycheffetype inequalities. Emphasis on applications. Prerequisites: Level IV statistics, 16:960:582, or permission of instructor. 
16:960:563Regression Analysis (3) Review of basic statistical theory and matrix algebra; general regression models, computer application to regression techniques, residual analysis, selection of regression models, responsesurface methodology, nonlinear regression models, experimentaldesign models, analysis of covariance. Emphasis on applications. Prerequisite: Level IV statistics. 
16:960:565 (F) Applied Time Series Analysis (3) Modelbased forecasting methods, autoregressive and moving average models, ARIMA, ARMAX, ARCH, statespace 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 timeseries signals, timevarying models and wavelets. Prerequisite: Level V statistics or permission of instructor. 
16:960:567(S) Applied Multivariate Analysis (3) Methods of reduction of dimensionality, including principal components, factor analysis, and multidimensional scaling; correlation techniques, including partial, multiple, and canonical correlation; classification and clustering methods. Emphasis on dataanalytic 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 or permission of instructor. 
16:960:575(F) Acceptance Sampling Theory (3) Selection, operation, and statistical behavior of sampling plans. DodgeRomig plans; continuous, chain, and skiplot plans; variable sampling plans. Economic analysis and study of sampling systems. Prerequisite: Level IV statistics. 
16:960:576(S) 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: 16:960:582 or equivalent. 
16:960:580(S) Basic Probability (3) Discreteprobability 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, deMoivreLaplace theorem. Prerequisite: One year of calculus. Credit given for only one of 16:960:580, 582, 592. 
16:960:582(F) 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, sampling distributions. Prerequisite: One year of calculus. Credit given for only one of 16:960:580, 582, 592. 
16:960:583(S) 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: 16:960:582. Credit not given for both this course and 16:960:593. 
19:960:584(F) Biostatistics IObservational Studies (3) Statistical techniques for biomedical data. Analysis of observational studies emphasized. Topics include measures of disease frequency and association; inferences for dichotomous and grouped casecontrol 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(S) Biostatistics IIClinical 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; 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. 
16:960:586Interpretation of Data I (3) Modern methods of data analysis with an emphasis on statistical computing: univariate statistics, data visualization, linear models, generalized linear models (GLM), multivariate analysis and clustering methods, treebased methods, and robust statistics. Expect to use statistical software packages, such as SAS (or SPSS) and Splus (or R) in data analysis. Prerequisite: Level IV statistics. Recommended: 16:960: 563. 
16:960:587 (S) Interpretation of Data II (3) Modern methods of data analysis and advanced statistical computing techniques: smooth regression (including GAM models), nonlinear models, MonteCarlo simulation methods, the EM algorithm, MCMC methods, spatial statistics, longitudinal data analysis/mixed effects models/GEE, latent variable models, hidden Markov models, 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 or permission of instructor. 
16:960:588(F) 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, observational studies. Prerequisites: 16:960:567, 587, or permission of instructor. 
16:960:590Design of Experiments (3) Fundamental principles of experimental design; completely randomized variance component designs, randomized blocks, Latin squares, incomplete blocks, partially hierarchic mixedmodel experiments, factorial experiments, fractional factorials, response surface exploration. Prerequisite: 01:960:484 or 401 or equivalent. 
16:960:591(F) Advanced Design of Experiments (3) Strategy of experimentation, screening designs, factorial designs, response surface methodology, evolutionary operation, mixture designs, incomplete blocking designs, computeraided experimental designs, and design optimality criteria. Prerequisite: 16:960:590. Recommended: 16:960:563. 
16:960:592(F) 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 or permission of instructor. Credit given for only one of 16:960:580, 582, 592. 
16:960:593(S) 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 or permission of instructor. Credit not given for both 16:960:583 and this course. 
16:960:595Intermediate Probability (3) Central limit theorem. BorelCantelli lemma, strong law of large numbers; convolutions, generating functions, recurrent events, random walks on line, plane and 3space, ruin of a gambler, simple timedependent processes and/or Markov chains. Prerequisites: Advanced calculus, 16:960:592, or equivalent. 
16:960:652(F) Advanced Theory of Statistics I (3) Theories of statistical inference and their relation to statistical methods. Sufficiency, invariance, unbiasedness, decision theory. Bayesian procedures, likelihood procedures. Prerequisites: 16:960:593, real variables. 
16:960:653(S) Advanced Theory of Statistics II (3) Hypothesis testing, point and confidence estimation robustness, sequential procedures. Prerequisite: 16:960:652. 
16:960:654(F) 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. Measuretheoretic notations, as well as ideas from classical analysis used as needed. Prerequisite: 16:960:554 or 680 or permission of instructor. Offered in alternate years. 
16:960:655(S) Advanced Nonparametric Statistics (3) Ranktesting and estimation procedures for the one and twosample problems; locally most powerful rank tests. Criteria for unbiasedness; permutation tests. Exact and asymptotic distribution theory; asymptotic efficiency. Rank correlation; sequential procedures; the KolmogorovSmirnov test. Emphasis on theory. Prerequisites: 16:960:593, 680, or permission of instructor. 
16:960:663(F) Regression Theory (3) Leastsquares methods of testing and estimation in multiple regression; geometric interpretation of leastsquares; Gauss Markov theorem. Confidence, prediction, and tolerance intervals in regression. Orthogonal polynomials; harmonic regression. Weighted leastsquares. Analysis of variance; simultaneous inference procedures (multiple comparisons). Emphasis on theory. Prerequisites: 16:960:593, vector spaces and matrices. 
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; nonlinear regression computational and statistical procedures. Prerequisite: 16:960:663. 
16:960:667(S) Multivariate Statistics (3) Multivariate, marginal, and conditional distributions. Multivariate normal; characterizations and parameter estimation. Wishart distribution; Hotelling's T2 statistic; multivariate linear model; principal component analysis correlations. Multivariate classification; matrices and discriminate methods. Emphasis on theory. Prerequisites: 16:960:593, vector spaces and matrices, or permission of instructor. Offered in alternate years. 
16:960:668(S) 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 onelayer problems, including prior, posterior, and predictive distributions, 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 or permission of instructor. 
16:960:680(S) Advanced Probability Theory I (3) Measures, measurable functions, integration, limit theorems, Lebesgue measure, Riemann integral, LebesgueStieltjes integral, measure extension, probability measures, random variables, expectation, distribution, independence, BorelCantelli lemma, zeroone law, convergence in distribution, convergence in probability, almost sure convergence, law of large numbers, Jensen, Holder, and Minkowski inequalities, convergence in mean, uniform integrability, spaces of functions. Prerequisite: Real variables or equivalent. 
16:960:681(F) Advanced Probability Theory II (3) Characteristic functions, the Lindeberg central limit theorem, Helly's selection theorem, convergence of multivariate distribution functions, conditional probability, the RadonNikodym theorem, conditional expectation, martingales, the optional stopping theorem, Doob's inequalities, martingale convergence theorems, random walk, Markov chains, recurrence and transience, stationary measure, convergence theorems for Markov chains, product measures, Fubini's theorem, Kolmogorov consistency theorem, weak convergence of stochastic processes, Brownian motion, the law of the iterated logarithm. Prerequisite: 16:960:680 or equivalent. 
16:960:682,683Individual Studies in Statistics (3,3) 
16:960:687,688Seminar in Applied and Mathematical Statistics (3,3) Measure, outer measures, and extensions. Measurable functions. Integration on a measure space. Lebesgue and RadonNikodym theorems, Hahn and Jordan decompositions. Product spaces and Fubini's theorem. Riesz representation theorem Ip spaces. Conditional probability. Topological and especially metric spaces, Euclidean spaces, Banach spaces. Differentiation, Hilbert spaces. Prerequisite: Permission of instructor. 
16:960:689(F) 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; Bayes character and optimality of the SPRT. Composite hypotheses: weightfunction and invariant SPRTs. Sequential estimation, including fixedwidth confidence intervals and confidence sequences. Prerequisites: 16:960:593, 680. 
16:960:690,691Special 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 instructor. 
16:960:693Current Topics in Statistics (1) Topics change based on statistical research and applications of faculty in and outside department. Prerequisite: Permission of program director. 
16:960:694, 695, 696Special Topics in Statistics (3,3,3) Modern statistics and interdisciplinary topics not regularly covered in the graduate program. Prerequisite: Permission of instructor. 
16:960:701,702Research in Statistics (BA,BA) 





