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. 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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: 16:640:152; effective fall 2009: 16:640:251. Credit given for only one of 16:960:580, 582, 592.
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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: 16:640:152; effective fall 2009: 16:640:251. Credit given for only one of 16:960:580, 582, 592.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
Admission to the statistics doctoral program or consent of the program director.
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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.
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16:960:653
Advanced Theory of Statistics II (3)
Hypothesis testing, point and confidence estimation robustness, sequential procedures.
Prerequisite: 16:960:652.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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16:960:682,683
Individual Studies in Statistics (3,3)
Prerequisite: Permission of program director.
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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.
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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.
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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.
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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.
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16:960:701,702
Research in Statistics (BA,BA)
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