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. Some of the prerequisites come from
the undergraduate math program, with code 640. 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 and biostatistics.

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 and biostatistics.

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; ztest, ttest, chisquare tests, Ftest; and
analysis of variance.
For students in the Graduate School of Education.

16:960:535
Advanced Statistical Methods in Finance (3)
Traditional and stateoftheart 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 DodgeRomig and
Military Standards acceptance sampling plans.
Prerequisite: 16:960:580, 582, or 592.

16:960:541
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 and 590.

16:960:542
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 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)
Twobytwo frequency
tables; Fisher's exact test; measures of association; general contingency
tables; loglinear models; logistic regression; repeated categoricalresponse
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 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, 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
applications of 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)
Modelbased forecasting methods; autoregressive and moving
average models; ARIMA, ARMAX, ARCH, and 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; and timevarying 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. DodgeRomig plans; continuous, chain, and skiplot 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)
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; and the
deMoivreLaplace 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.

16:960:584
Biostatistics IObservational 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 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.

16:960:585
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; 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 and 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: MonteCarlo 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 R and to do some 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 mixedmodel 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; computeraided 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. 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.
Prerequisite: 16:960:592.

16:960:596
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. Measuretheoretic
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)
Ranktesting and estimation procedures for the one and
twosample 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
KolmogorovSmirnov test. Emphasis on theory.
Prerequisite: 16:960:593.

16:960:663
Regression Theory (3)
Leastsquares methods of testing and estimation in multiple
regression; geometric interpretation of leastsquares; and the GaussMarkov
theorem. Confidence, prediction, and tolerance intervals in regression.
Orthogonal polynomials; harmonic regression; weighted leastsquares; 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 onelayer problems, including prior, posterior, and predictive
distributions; and Monte Carlo methods in advanced modeling and inference
problems. Calculations are done in the 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; LebesgueStieltjes integral;
measure extension, probability measures, and random variables; expectation,
distribution, and 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 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 RadonNikodym 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: weightfunction and invariant SPRTs. Sequential estimation,
including fixedwidth 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 (0)
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)
