Graduate Courses

**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.**

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 *T*^{2} 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 *L _{p}* and

**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