Graduate
STAT 401. Basic Statistics for Social and Life Sciences
(3)
Introductory course primarily for graduate students in nursing and the
health sciences. Statistical methods and applications using SPSS software.
Display and summarization of data. Hypothesis testing and interval estimation.
Not for credit toward undergraduate major or minor in statistics, nor
for credit toward any graduate degree in statistics. Credit for only one
of STAT 201, 401.
STAT 412. Statistics for Design and Analysis in
Engineering and Science (3)
For graduate students (primarily) and advanced undergraduates in engineering,
physical sciences, and life sciences. After basic statistical concepts
are reviewed, the remainder of the course consists of a comprehensive
introduction to statistical methods of designing experiments and analyzing
data. The general objective is to train students in statistical modeling
and in the choice of experimental designs to use in scientific investigations.
A variety of experimental designs are covered, and regression analysis
is presented as the primary technique for analyzing data from designed
experiments, and in discriminating between various possible statistical
models. The course is oriented toward graduate students engaged in or
embarking on research. Prerequisite: MATH 122 (an introductory statistics
course is recommended).
STAT 413. Reliability and Calibration (3)
Failure distributions related to life testing; extreme value distributions
and their hazard functions. Static reliability of series, parallel and
mixed systems. Coherent systems and system reliability approximations.
Dynamic reliability models. Linear estimation, maximum likelihood, EM
estimation, estimation from censored data. Calibration procedures. Distributions
from uncalibrated processes, optimization of calibration procedures. Examples
from industrial research and production processes. Prerequisite: one (1)
of: STAT 244, 312, 313, 332, 333 or 433.
STAT 414. Industrial Statistics (3)
Introduction to statistical methods and techniques that are being used
in industry, and especially in various company-wide quality improvement
programs such as Six Sigma. The course covers control charts and process
capability with considerable breadth and depth. The classical and alternative
approaches that have been used in designing industrial experiments are
also covered extensively. Linear regression, analysis of means (ANOM),
and evolutionary operation (EVOP) are other techniques that are covered.
Prerequisite: STAT 312 or equivalent.
STAT 417. Theory of Interest and Life Contingencies
(3)
For graduate students interested in actuarial science. Mathematical
formulation for calculation of compound interest, present and accumulated
values of single investments and of portfolios. Life table analysis for
simple and multiple decrement functions. Life and special annuities; life
insurance and reserves for life insurance. Statistical issues for prediction
from actuarial models. Problem solving using actual insurance record data.
Topics covered include areas examined in the American Society of Actuaries
examination over ASA courses 150 and 160. Additional work is expected
from graduate students. Prerequisite: MATH 223 and STAT 346 or STAT 446.
STAT 425. Data Analysis and Linear Models (3)
Basic exploratory data analysis for univariate response with single or
multiple covariates. Graphical methods and data summarization model-fitting
using S-plus computing language. Linear and multiple regression. Emphasis
on model selection criteria, on diagnostics to assess goodness of fit
and interpretation. Techniques include transformation, smoothing, median
polish, robust/resistant methods. Case studies, and analysis of individual
data sets. Notes of caution and some methods for handling bad/biased data.
Knowledge of regression is helpful. Prerequisite: Permission of Department.
STAT 426. Multivariate Analysis and Data Mining
(3)
Extensions of exploratory data analysis and modeling to multivariate response
observations and to non-Gaussian data. Singular value decomposition and
projection, principal components, factor analysis and latent structure
analysis, discriminant analysis and clustering techniques, cross-validation,
E-M algorithm, and CART. Introduction to generalized linear modeling.
Case studies of complex data sets with multiple objectives for analysis.
Graduate students give both written and oral presentations of data analyses.
Prerequisite: STAT 425.
STAT 427. Statistical Computing (3)
Basic topics in statistical computing: Floating point arithmetic; Seminumerical
computation including generation and tests of random numbers, Monte Carlo
methods, variance reduction methods, stochastic models and simulation
studies; numerical computation including numerical linear algebra, optimization
and root-finding, numerical integration; some graphical and symbolic computations;
special topics in statistical computing: resampling methods, EM algorithms,
Gibbs sampling and projection pursuit. Prerequisite: STAT 345 or STAT
425 or permission of department.
STAT 433. Uncertainty in Engineering and Science
(3)
Phenomena of uncertainty appear in engineering and science for various
reasons and can be modeled in different ways. The course integrates the
mainstream ideas in statistical data analysis with models of uncertain
phenomena stemming from three distinct viewpoints: algorithmic/computational
complexity; classical probability theory; and chaotic behavior of nonlinear
systems. Descriptive statistics, estimation procedures and hypothesis
testing (including design of experiments). Mathematica notebooks and simulations
will be used. Note: Random number generators and their testing. Monte
Carlo methods. Credit given for only on (1) of STAT 312, 313, 333, 133.
Graduate students are required to do an extra project. Prerequisite: MATH
223 or MATH 122.
STAT 437. Stochastic Modeling of Scientific Data
(3)
Introduction to stochastic modeling of data. Emphasis on models and statistical
analysis of data with a significant temporal and/or spatial structure.
Markovian and semi-Markovian models, point processes, point cluster models,
queuing model s, likelihood methods, estimating equations. Note: Restricted
to declared graduate and undergraduate majors and minors in statistics
and biostatistics only. Prerequisite: STAT 333 or STAT 433 (preferred)
or STAT 325, STAT 425 , or STAT 445.
STAT 445. Theoretical Statistics I (3)
Topics provide the background for statistical inference. Random variables;
distribution and density functions; transformations, expectation. Common
univariate distributions. Multiple random variables; joint, marginal and
conditional distributions; hierarchical models, covariance. Distributions
of sample quantities: distributions of sums of random variables, distributions
of order statistics. Methods of statistical inference. Graduate students
are responsible for mathematical derivations, and full proofs of principal
theorems. Prerequisite: MATH 122 or MATH 223. Cross-listed as: EPBI 481.
STAT 446. Theoretical Statistics II (3)
Point estimation: maximum likelihood, moment estimators. Methods of evaluating
estimators including mean squared error, consistency, "best"
unbiased and sufficiency. Hypothesis testing; likelihood ratio and union-intersection
tests. Properties of tests including power function, bias. Interval estimation
by inversion of test statistics, use of pivotal quantities. Application
to regression. Graduate students are responsible for mathematical derivations,
and full proofs of principal theorems. Prerequisite: STAT 445 Cross-listed
as: EPBI 482.
STAT 448. Bayesian Theory with Applications (3)
Principles of Bayesian theory, methodology and applications. Methods for
forming prior distributions using conjugate families, reference priors
and empirically-based priors. Derivation of posterior and predictive distributions
and their moments. Properties when common distributions such as binomial,
normal or other exponential family distributions are used. Hierarchical
models. Computational techniques including Markov chain Monte Carlo and
importance sampling. Extensive use of applications to illustrate concepts
and methodology. Prerequisite: STAT 445.
STAT 453. Time Series, Wavelets I (3)
Stationary discrete-time and continuous-time models. Search for hidden
periodicities in data. Fast Fourier transform; smoothing and filtering;
spectra and periodograms. Multiple series; cross spectra and cross periodograms.
Prediction problems. Time-frequency localization and the uncertainty principle,
windowed Fourier transforms. Introduction to wavelet and multiresolution
analysis. Prerequisite: one (1) of: STAT 333, 346, 433, 446.
STAT 455. Linear Models (3)
Theory of least squares estimation, interval estimation and tests for
models with normally distributed errors. Regression on dummy variables,
analysis of variance and covariance. Variance components models. Model
diagnostics. Robust regression. Analysis of longitudinal data. Prerequisite:
MATH 201 and STAT 346 or STAT 446.
STAT 466. Theory and Methods of Experimental Design
(3)
(Also listed as EPBI 446). Experimental design for polynomial regression
models and for multi-factor models. Theory for construction of increased
efficiency designs including fractional factorials, Latin squares. Designs
for response surfaces. GOSSETT-generated optimal designs for nonstandard
problems. Knowledge of regression required. Prerequisite: STAT 425 Cross-listed
as: EPBI 446.
STAT 468. Sampling from Finite Populations: Theory
and Applications (3)
(Also listed as EPBI 447). Introduction to the theory and methodology
of sampling from finite populations. Simple random, stratified random,
systematic and multistage cluster sampling. Linear, ratio and regression
estimators. Methodology for handling missing data, inference for small
geographical areas or for small subpopulations, inference for quantiles.
Application to large-scale personal interview and telephone surveys. Prerequisite:
STAT 345 or STAT 445 Cross-listed as: EPBI 447.
STAT 471. Special Topics in Statistics (1- 3)
Topics in specialized areas of statistical theory and methodology, with
emphasis on recent advances in theory and development of new methodology.
Topics may change from year to year. Number of credit hours for the class
will be predetermined each semester based on the material to be presented.
Consent of the instructor required.
STAT 476. Advances in Statistics and Modeling (1-
3)
Topics in specialized areas of statistics and stochastic modeling, with
emphasis on recent advances in theory and formulation of models. Investigation
of new areas of application for statistical or stochastic models. Topics
may change from year to year. Number of credit hours for the class will
be predetermined each semester based on the material to be presented.
Consent of the instructor required.
STAT 491. Graduate Student Seminar (1- 2)
Seminar run collaboratively by graduate students to investigate an area
of current research, the topic chosen each semester. All graduate students
participate in presentation of material each semester. Satisfies requirement
for every full-time graduate student to enroll in a participatory seminar
every semester while registered in any graduate degree program. Graduate
standing required.
STAT 495A. Consulting Forum (1-3)
This course examines the principles of statistical consulting. Included
are the views and practices of prominent statistical consultants, as obtained
from the literature and from other sources. This includes responsibilities
of the consultant and of the client. Role playing is used in an attempt
to simulate actual consulting scenarios. The course also serves to unify
what the students have learned in their course work in preparation for
applying their knowledge in consulting work. Prerequisite: STAT 325 or
STAT 425.
STAT 495B. Consulting Forum with Practicum (3)
Graduate students become involved in actual consulting projects under
the guidance of the instructor. The students' involvement can result from
consulting problems presented by guest lecturers, or by assisting the
instructor on projects that have come to the department. The students
gain experience in report writing. The importance of communicating the
results of a study at the appropriate statistical level for the client
is stressed. Prerequisite: STAT 325 or STAT 425.
STAT 525. Advanced Data Analysis (3)
Topics drawn from resampling methods (including bootstrapping), MCMC (Gibbs
sampling), nonparametric curve and surface fitting, kernel density estimation,
projection pursuit, mixture models, time series (time permitting), approaches
to model uncertainty, models for repeated measures and structural-functional
models, statistical inference for large systems, modern data analysis
techniques. Prerequisite: STAT 426 or permission of department.
STAT 527. Advanced Statistical Computing (3)
Special topics drawn from statistical computing, complex system and dynamic
computation. Oriented to research. Prerequisite: STAT 427.
STAT 537. Advanced Stochastic Modeling of Scientific
Data I (3)
Spatial statistics. Theory and techniques for spatial or spatial-temporal
relationships in high dimensional data, point pattern analysis, estimation
of spatial covariance either stationary or non-stationary in space, applications
to environ mental sciences. Characterizations and solutions for mapping
problems, for image reconstruction, for analysis of fractal spatial-temporal
processes with particular application to environmental sciences. Prerequisite:
STAT 446 and STAT 437.
STAT 538. Advanced Stochastic Modeling of Scientific
Data II (3)
Foundations of discrete and continuous-time dynamical systems. Complexity
of nonlinear dynamical systems. Descriptive statistics of dynamical systems,
invariant densities and their estimation. Ergodic properties, space and
time-averaging. Chaotic behavior. Fractals as a signature of chaos. Statistical
estimation of fractal dimension. Asymptotic fluctuations in dynamical
systems. Statistical problems in physical sciences; statistical hydrodynamics.
Statistical problems for hydrological, atmospheric and oceanic models.
Theoretical foundations of simulation of random phenomena. Prerequisite:
STAT 437.
STAT 545. Advanced Theory of Statistics I (3)
A systematic development of advanced statistical theory. Background concepts.
Limits, order comparisons, convergence. Sample moments, quantiles and
other statistics. Transformations. Characterization of distribution functions
and characteristic functions. Normal and other approximations to distributions.
Quadratic forms and other functions of asymptotically normal statistics.
Asymptotic properties of statistics including asymptotic efficiency, consistency.
Admissibility, sufficiency and ancillarity. Nuisance parameters, parameter
orthogonality. Distribution theory in nuisance parameters. Prerequisite:
STAT 446.
STAT 546. Advanced Theory of Statistics II (3)
Estimation: maximum likelihood, minimax, Bayes', empirical Bayes', and
James-Stein estimators. Entropy and information. U-statistics and their
distributions. Von Mises differentiable statistical functions, M, L, R-estimators.
Confidence intervals and regions. Simple and weighted empirical processes.
Convergence and distributions for empirical processes. Prerequisite: STAT
545.
STAT 547. Advanced Theory of Statistics III (3)
Development of empirical process theory with application to censored data
with random, fixed or arbitrary censoring mechanism. Characterization
of quantile processes, spacings and large deviations as empirical processes.
Asymptotic results for nonparametric regression, bootstrap and other resampling
estimators. Prerequisite: STAT 546.
STAT 553. Time Series and Wavelets II (3)
Advanced topics in time series including nonstationary series, nonlinear
models. In-depth development and application of wavelet theory. Wavelets
as computational tool. Extensive use of computing to illustrate and investigate
modeling with wavelets. Prerequisite: STAT 453 and STAT 446 and MATH 491.
STAT 555. Generalized Linear Models (3)
Generalization from linear statistical models to discrete responses and
other non-Gaussian cases. Theory for binomial proportions and logits,
Poisson counts and loglinear models, multinomial response models, models
of survival data. Analysis of deviance, model checking. Conditional, marginal
and quasi-likelihood methods. Inverse linear models. Generalized linear
mixed models. Prerequisite: STAT 455.
STAT 571. Advanced Topics in Statistics (1- 3)
For advanced graduate students. Topics in specialized areas of statistical
theory and methodology, with emphasis on recent advances in theory, developments
of new methodology and definition of new research questions. Topics may
change from year to year. Number of credit hours for the class will be
predetermined each semester based on the material to be presented. Consent
of the instructor required.
STAT 576. Advanced Topics in Modeling (1- 3)
Advanced topics in specialized areas of statistics and stochastic modeling
designed to define new research directions drawing on recent advances
in theory and model formulation. Focus on statistical issues arising in
the application of statistical or stochastic models to new substantive
research efforts. Topics may change from year to year. Number of credit
hours for the class will be predetermined each semester based on the material
to be presented. Consent of the instructor required.
STAT 591. Statistical Research Seminar (1- 3)
Seminar to prepare and explore current research topics presented by faculty
and invited statistics colloquium speakers. Graduate students lecture
on background material for colloquia using recent publications. Following
each colloquium, students lead discussion and clarify further the contributions
of the research. Newer students are paired with senior students; colloquium
assignments coincide with students' research interests insofar as possible.
Attendance at statistics colloquia is required. Satisfies requirement
for every full-time graduate student to enroll in a participatory seminar
every semester while registered in any graduate degree program. Number
of credit hours will be determined by prior agreement with the instructor
and depends on the extent of the student's responsibility. Consent of
the instructor required.
STAT 601. Reading and Research (1- 9)
Individual study and/or project work. Permission of instructor required.
STAT 621. M. S. Research Project (1- 9)
Substantial and/or nonstandard statistical techniques which leads to results
suitable for publication. Written project report must present the context
for the research, justify the statistical methodology used, draw appropriate
inferences and interpret these inferences in both statistical and substantive
scientific terms. Oral presentation of research project may be given in
either graduate student seminar of consulting forum. Permission of instructor
required.
STAT 651. Thesis M.S. (1-36)
(Credit as arranged) May be used as alternative to STAT 621 in fulfillment
of requirements for M.S. degree in statistics. Permission of instructor
required.
STAT 701. Appointed Dissertation Fellowship (1-36)
STAT 702. Appointed Dissertation Fellowship (9)
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