Levels IV and V Statistics: 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 STATISTICAL THEORY FOR RESEARCH WORKERS-I. (Cr. 3)
Prerequisite: 3 credits in statistics or consent of department. Not open to graduate students in Statistics.
An intermediate theory course designed to strengthen the statistical background for research workers. Concepts of randomness and probability; frequency distributions; expectations; derived distributions and sampling; theories of estimation and significance testing; the theoretical structure underlying some common statistical methods.

16:960:502 STATISTICAL THEORY FOR RESEARCH WORKERS-II. (Cr. 3)
Prerequisite: Statistics 501. Not open to graduate students in Statistics.
A continuation and extension of Statistics 501. The principles and practices of experimental design as applied to mathematical models; the analysis of variance; factorial designs; the analysis of matched groups and repeated measurements on the same group; the analysis of qualitative data.

16:960:511 STATISTICAL METHODS IN SOCIAL WORK. (Cr. 2)
For students in the Graduate School of Social Work.
Introduction to descriptive and inferential statistics. Frequency distributions and cross-classification 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. The uses and misuses of statistical techniques and reasoning in social work.

16:960:531-532 STATISTICAL METHODS IN EDUCATION. (Cr. 3, 3)
For students in the Graduate School of Education.
This course includes in the first term, descriptive statistics, introduction to correlation and regression, the normal curve, statistical inference, chi square, the t and F distribution and one-way analysis of variance. Some consideration is given to the presentation and interpretation of statistical data in education literature.
The second term considers the design of experiments, analysis of variance and covariance, trend and discriminant analysis, and the basic multivariate measures, partial and multiple correlation.

16:960:540 STATISTICAL QUALITY CONTROL-I. (Cr. 3)
Prerequisite: Level IV Statistics, 16:960:582 or equivalent.
Construction and analysis of control charts for variables and attributes; histogram analysis; use and evaluation of Dodge-Romig and Military Standards acceptance sampling plans.

16:960:541 STATISTICAL QUALITY CONTROL-II. (Cr. 3)
Prerequisite: 16:960:540, 590.
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.

16:960:542 LIFE DATA ANALYSIS. (Cr. 3)
Prerequisite: One year of Calculus, Level V Statistics or permission of instructor.
Statistical methodology for survival and reliability data. Topics include life table techniques; competing risk analysis; parametric and nonparametric inferences of lifetime distributions; regression on censored data; Poisson and renewal processes; multi-state survival models and goodness of fit test. Statistical softwares will be used.

16:960:545 STATISTICAL PRACTICE. (Cr. 3)
Prerequisite: Level IV Statistics or equivalent.
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.

16:960:553 CATEGORICAL DATA ANALYSIS. (Cr. 3)
Prerequisite: Level V Statistics or permission of instructor.
Two-by-two frequency tables, Fisher's exact test, measures of association, general contingency tables, log-linear models, logistic regression, repeated categorical response data, maximum likelihood estimation, tables with ordered categories, discriminant analysis.

16:960:554 APPLIED STOCHASTIC PROCESSES. (Cr. 3)
Prerequisite: Advanced Calculus, 16:960:582 or equivalent.
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.

16:960:555 NONPARAMETRIC STATISTICS. (Cr. 3)
Prerequisite: Level IV Statistics, Statistics 582 or permission of instructor.
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 are detailed to develop a variety of test and interval estimation procedures. Other topics include tests of goodness of fit including the Kolmogorov-Smirnov and chi-square tests, contingency table analysis, tolerance tests, and Tchebycheff-type inequalities.

16:960:563 REGRESSION ANALYSIS. (Cr. 3)
Prerequisite: Level IV Statistics.
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, nonlinear regression models, experimental design models, analysis of covariance. Emphasis on applications.

16:960:565 APPLIED TIME SERIES ANALYSIS. (Cr. 3)
Prerequisite: Level V Statistics or permission of instructor.
Model based forecasting methods, autoregressive and moving average models, ARIMA, ARMAX, ARCH, state-space models, estimation, forecasting and model validation, missing data, irregularly spaced time series, parametric and non-parametric bootstrap methods for time series, multi-resolution analysis of spatial and time series signals, time-varying models and wavelets.

16:960:567 APPLIED MULTIVARIATE ANALYSIS. (Cr. 3)
Prerequisite: Level V Statistics or permission of instructor.
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 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.

16:960:575 ACCEPTANCE SAMPLING THEORY. (Cr. 3)
Prerequisite: Level IV Statistics.
Selection, operation, and statistical behavior of sampling plans. Dodge-Romig plans; continuous, chain, and skip-lot plans; variables sampling plans. The underlying theory together with applications. Economic analysis and study of sampling systems.

16:960:576 SURVEY SAMPLING. (Cr. 3)
Prerequisite: Statistics 582 or equivalent.
An introduction to the design, analysis, and interpretation of sample surveys. Types of sampling covered include simple random sampling, stratified random sampling, systematic sampling, cluster sampling, and multi-stage sampling. Methods of estimation are 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.

16:960:580 BASIC PROBABILITY. (Cr. 3)
Prerequisite: One year of Calculus. Credit given for only one of 16:960:580, 582, 592.
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 numbers, deMoivre-Laplace theorem.

16:960:582 INTRODUCTION TO METHODS AND THEORY OF PROBABILITY. (Cr. 3)
Prerequisite: One year of Calculus. Credit given for only one of 16:960:580, 582, 592.
Emphasis is on methods and problem solving. Topics include probability spaces, basic distributions, random variables, expectations, distribution functions, conditional probability and independence, sampling distributions.

16:960:583 METHODS OF STATISTICAL INFERENCE. (Cr. 3)
Prerequisite: 16:960:582. Credit not given for both 960:583 and 593.
Theory of point and interval estimation and hypothesis testing. Topics include sufficiency, unbiasedness, and power functions. Emphasis is on application of the theory in the development of statistical procedures.

16:960:584 BIOSTATISTICS I-OBSERVATIONAL STUDIES. (Cr. 3)
Prerequisites: One year of calculus and Level V statistics.
Statistical techniques for biomedical data. Analysis of observational studies 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.

16:960:585 BIOSTATISTICS II-CLINICAL TRIALS. (Cr. 3)
Prerequisite: Level IV Statistics.
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 of 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.

16:960:586 INTERPRETATION OF DATA-I. (Cr. 3)
Prerequisite: Level IV Statistics. Recommended: 16:960:563.
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, tree-based methods, and robust statistics. Expect to use statistical software packages, such as SAS (or SPSS) and Splus (or R) in data analysis.

16:960:587 INTERPRETATION OF DATA-II. (Cr. 3)
Prerequisite: 16:960:586 or permission of instructor.
Modern methods of data analysis and advanced statistical computing techniques: smooth regression (including GAM models), nonlinear models, Monte-Carlo 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.

16:960:588 DATA MINING. (Cr. 3)
Prerequisite: 16:960:567, 587, or permission of instructor.
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.

16:960:590 DESIGN OF EXPERIMENTS. (Cr. 3)
Prerequisite: 01:960:484 or 401 or equivalent.
Fundamental principles of designs; randomized blocks and Latin squares; experimental and sampling errors and components of error; fractional factorials; exploration of response surfaces. Designs for specific problems.

16:960:591 ADVANCED DESIGN OF EXPERIMENTS. (Cr. 3)
Prerequisites: 16:960:590. Recommended: 16:960:563.
Strategy of experimentation, screening designs, factorial designs, response surf. methodology, evolutionary operation, mixture designs, incomplete blocking designs, computer-aided experimental designs, and design optimality criteria.

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

16:960:593 THEORY OF STATISTICS. (Cr. 3)
This course will be the first course in statistical theory required of Ph.D. students.

Prerequisite: 16:960:592 or permission of instructor. Credit not given for both 960:583 and 593.
Theory of point and interval estimation and hypothesis testing. Topics include sufficiency, unbiasedness, Bayes methods and power functions. Emphasis is on fundamental concepts underlying the theory.

16:960:595 INTERMEDIATE PROBABILITY. (Cr. 3)
Prerequisites: Advanced Calculus, 16:960:592 or equivalent.
Central limit theorem, Borel-Cantelli lemma, strong law of large numbers; convolutions, generating functions, recurrent events a la Feller, random walks on line, place and 3-space, ruin of a gambler; simple time dependent processes and/or Markov chains.

16:960:652 ADVANCED THEORY OF STATISTICS-I. (Cr. 3)
Prerequisites: 16:960:593 and a course in real variables.
Theory of statistical inference and their relation to statistical methods. Sufficiency, invariance, unbiasedness, decision theory, Bayesian procedures, likelihood procedures.

16:960:653 ADVANCED THEORY OF STATISTICS-II. (Cr. 3)
Prerequisite: 16:960:652.
Hypothesis testing, point and confidence estimation, robustness, sequential procedures.

16:960:654 STOCHASTIC PROCESSES. (Cr. 3)
Prerequisite: 16:960:554 or 680 or permission of instructor.
Probability models for physical situations. Markov processes; epidemic models; queueing theory; inventory models; birth and death processes; genetic models; theory of dams. Measure theoretic notions as well as ideas from classical analysis will be used as needed.

16:960:655 ADVANCED NON-PARAMETRIC STATISTICS. (Cr. 3)
Prerequisites: 16:960:593, 680, or permission of instructor.
Rank-testing and estimation procedures for the one and two sample problems; locally most powerful rank-tests. Criteria for unbiasedness; permutation tests. Exact and asymptotic distribution theory; asymptotic efficiency. Rank correlation; sequential procedures; the Kolmogorof-Smirnov test.

16:960:663 REGRESSION THEORY. (Cr. 3)
Prerequisites: 16:960:593 and a course in vector spaces and matrices.
Least-squares methods of testing and estimation in multiple regression; geometric interpretation of least-squares; Gauss-Markov theory. Confidence, prediction and tolerance intervals in regression. Orthogonal polynomials; harmonic regression. Weighted least-squares. Analysis of variance; simultaneous inference procedures (multiple comparisons).

16:960:664 ADVANCED TOPICS IN REGRESSION AND ANALYSIS OF VARIANCE. (Cr.3)
Prerequisite: 16:960:663.
Development of linear classification models; general results on 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.

16:960:667 MULTIVARIATE STATISTICS. (Cr. 3)
Prerequisites: 16:960:593 and a course in vector spaces and matrices or permission of instructor.
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 discriminant methods.

16:960:668 BAYESIAN DATA ANALYSIS. (Cr. 3)
Prerequisites: 16:960:593 or permission of instructor.
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, 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.

16:960:680 ADVANCED PROBABILITY THEORY-I. (Cr. 3)
Prerequisites: A course in real variables or equivalent.
Measures, Measurable functions, integration, limit theorems, Lebesgue measure, Riemann integral, Lebesgue-Stieltjes integral, measure extension, probability measures, random variables, expectation, distribution, independence, Borel-Cantelli lemma, 0-1 law, convergence in distribution, convergence in probability, almost sure convergence, law of large numbers, Jensen, Holder and Minkowski inequalities, convergence in mean, uniform integrability, the Lp and lp spaces.

16:960:681 ADVANCED PROBABILITY THEORY-II. (Cr. 3)
Prerequisite: 16:960:680 or equivalent.
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, the optimal 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.

16:960:687, 688 SEMINAR IN APPLIED AND MATHEMATICAL STATISTICS. (Cr. 3, 3)
Prerequisite: Consent of department.
Measures, outer measures and extensions. Measurable function, integration on a measure space. Lebesgue and Radon-Nikodym theorems, Hahn and Jordan decompositions. Product spaces and Fubini's theorem. Riesz representation theorem. Lp-spaces. Conditional probability. Topological and especially metric spaces, Euclidean spaces. Banach spaces. Differentiation, Hilbert spaces.

16:960:689 SEQUENTIAL METHODS. (Cr. 3)
Prerequisites: 16:960:593, 680.
The 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: Weight-function and invariant SPRTs. Sequential estimation, including fixed-width confidence intervals and confidence sequences. Ranking and selection. Some asymptotic considerations.

16:960:690 (F) SPECIAL TOPICS. (3)
Prerequisite: Consent of instructor.
Topics change on a rotating basis. Topics include large sample theory, time series analysis, Bayesian statistics, robustness and sequential analysis.

16:960:691 (S) SPECIAL TOPICS. (3)
Prerequisite: Consent of instructor.
Topics change on a rotating basis. Topics include large sample theory, time series analysis, Bayesian statistics, robustness and sequential analysis.

16:960:693 CURRENT TOPICS IN STATISTICS. (N)
Prerequisite: Consent of department.
Topics change based on statistical research and applications of faculty in and outside department.

7/2005