**GRADUATE COURSES IN STATISTICS**

STAT 601 – STATISTICAL ANALYSIS [Fall]

STAT 604 – SPECIAL PROBLEMS IN STATISTICAL COMPUTATIONS AND ANALYSIS [Fall, Spring, Summer]

STAT 605 – ADVANCED TOPICS IN COMPUTATIONAL STATISTICS [Spring]

STAT 607 – SAMPLING [Fall]

STAT 608 – REGRESSION ANALYSIS [Spring, Summer]

STAT 610 – THEORY OF STATISTICS – DISTRIBUTION THEORY [Fall]

STAT 611 – THEORY OF STATISTICS – INFERENCE [Spring]

STAT 612 – THEORY OF LINEAR MODELS [Fall]

STAT 613 – ADVANCED THEORY OF STATISTICAL INFERENCE [Spring]

STAT 614 – STATISTICAL APPLICATIONS IN PROBABILITY [Fall]

STAT 615 – STOCHASTIC PROCESSES [Fall]

STAT 616 – MULTIVARIATE ANALYSIS [Fall]

STAT 618 – STATISTICAL ASPECTS… [Spring]

STAT 620 – STATISTICAL LARGE SAMPLE THEORY [Spring]

STAT 621 – ADVANCED STOCHASTIC PROCESSES [Spring]

STAT 623 – STATISTICAL METHODS FOR CHEMISTRY [As Resources Allow]

STAT 626 – METHODS IN TIME SERIES ANALYSIS [Summer]

STAT 627 – NONPARAMETRIC FUNCTION ESTIMATION [Spring]

STAT 630 – OVERVIEW OF MATHEMATICAL STATISTICS [Fall, Spring, Summer]

STAT 631 – STATISTICAL FINANCE… [Fall]

STAT 632 – STATISTICAL DECISION THEORY [Fall]

STAT 633 – ADVANCED BAYESIAN… [Spring]

STAT 636 – METHODS IN MULTIVARIATE ANALYSIS [Fall]

STAT 638 – INTRODUCTION TO APPLIED BAYESIAN METHODS [Fall]

STAT 641 – THE METHODS OF STATISTICS I [Fall]

STAT 642 – THE METHODS OF STATISTICS II [Spring]

STAT 643 – BIOSTATISTICS I [As Resources Allow]

STAT 644 – BIOSTATISTICS II [As Resources Allow]

STAT 645 – APPLIED BIOSTATISTICS… [Fall]

STAT 646 – STATISTICAL BIOINFORMATICS [Spring]

STAT 647 – SPATIAL STATISTICS [Fall]

STAT 648 – APPLIED STATISTICS… [Fall]

STAT 651 – STATISTICS IN RESEARCH I [Fall, Spring, Summer]

STAT 652 – STATISTICS IN RESEARCH II [Fall, Spring, Summer]

STAT 653 – STATISTICS IN RESEARCH III [Spring]

STAT 656 – APPLIED ANALYTICS… [Spring]

STAT 657 – ADVANCED PROGRAMMING USING SAS [Spring]

STAT 658 – TRANSPORTATION STATISTICS [As Resources Allow]

STAT 659 – APPLIED CATEGORICAL DATA ANALYSIS [Spring, Summer]

STAT 661 – STATISTICAL GENETICS I [As Resources Allow]

STAT 662 – ADVANCED STATISTICAL GENETICS I [As Resources Allow]

STAT 665 – STATISTICAL APPLICATIONS OF WAVELETS [As Resources Allow]

STAT 673 – TIME SERIES ANALYSIS I [Fall]

STAT 674 – TIME SERIES… [Spring]

STAT 681 – SEMINAR [Fall, Spring]

STAT 684 – PROFESSIONAL INTERNSHIP [Fall, Spring, Summer]

STAT 685 – DIRECTED STUDIES [Fall, Spring, Summer]

STAT 689 – SPECIAL TOPICS IN… [As Resources Allow]

STAT 691 – RESEARCH [Fall, Spring, Summer]

601. Statistical Analysis. (3-2). Credit 4.

For students in engineering, physical, and mathematical sciences. Introduction to probability, probability distributions, and statistical inference; hypotheses testing; introduction to methods of analysis such as tests of independence, regression, analysis of variance with some consideration of planned experimentation. Prerequisite: MATH 152 or 172.

604. Topics in Statistical Computations. (3-0). Credit 3.

Efficient uses of existing statistical computer programs (SAS, R, etc.), generation of random numbers; using and creating functions and subroutines; statistical graphics; programming of simulations studies; and data management issues. Prerequisites: MATH 221, 251, or 253.

605. Advanced Statistical Computations. (3-0). Credit 3.

Programming languages, statistical software, and computing environments; development of programming skills using modern methodologies; data extraction and code management; interfacing lower-level languages with data analysis software; simulation; MC integration; MC-MC procedures; permutation tests; bootstrapping. Prerequisite: STAT 612 and STAT 648.

607. Sampling. (3-0). Credit 3.

Planning, execution and analysis of sampling from finite populations; simple, stratified, multistage and systematic sampling; ratio estimates. Prerequisite: STAT 601 or 652 or concurrent enrollment in STAT 641.

608. Regression Analysis. (3-0). Credit 3.

Multiple, curvilinear, nonlinear, robust, logistic and principal components regression analysis; regression diagnostics, transformations, analysis of covariance. Prerequisite: STAT 601 or 641.

610. Theory of Statistics – Distribution Theory. (3-0). Credit 3.

Brief introduction to probability theory; distributions and expectations of random variables, transformations of random variables, and order statistics; generating functions and basic limit concepts. Prerequisite: MATH 409 or concurrent enrollment in MATH 409.

611. Theory of Statistics – Inference. (3-0). Credit 3.

Theory of estimation and hypothesis testing; point estimation, interval estimation, sufficient statistics, decision theory, most powerful tests, likelihood ratio tests, chi-square tests. Prerequisite: STAT 610 or equivalent.

612. Theory of Linear Models. (3-0). Credit 3.

Matrix algebra for statisticians, Gauss-Markov theorem; estimability; estimation subject to linear restrictions; multivariate normal distribution; distribution of quadratic forms; inferences for linear models; theory of multiple regression and AOV; random- and mixed-effects models. Prerequisite: Course in linear algebra.

613. Statistical Methodology I. (3-0). Credit 3.

Elements of likelihood inference; exponential family models; group transformation models; survival data; missing data; estimation and hypothesis testing; nonlinear regression models; conditional and marginal inferences; complex models-Markov chains, Markov random fields, time series, and point processes. Prerequisite: STAT 612.

614. Probability for Statistics. (3-0). Credit 3.

Probability and measures; expectation and integrals, Kolmogorov’s extension theorem; Fubini’s theorem; inequalities; uniform integrability; conditional expectation; laws of large numbers; central limit theorems. Prerequisite: STAT 610 or its equivalent.

615. Stochastic Processes. (3-0). Credit 3.

Survey of the theory of Poisson processes, discrete and continuous time Markov chains, renewal processes, birth and death processes, diffusion processes, and covariance stationary processes. Prerequisites: STAT 611; MATH 409.

616. Statistical Aspects of Machine Learning I: Classical Multivariate Methods. (3-0). Credit 3.

Core methods from traditional multivariate analysis and various extensions. Probability distributions of random vectors and matrices, multivariate normal distributions, model assessment and selection in multiple regression, multivariate regression, dimension reduction, linear discriminant analysis, logistic discriminant analysis, cluster analysis, multidimensional scaling and distance geometry, and correspondence analysis Prerequisites: STAT 611 and 612.

618. Statistical Aspects of Machine Learning II: Modern Techniques. (3-0). Credit 3.

Second course in statistical machine learning. Recursive partition and tree-based methods, artificial neural networks, support vector machines, reproducing kernels, committee machines, latent variable methods, component analysis, nonlinear dimensionality reduction and manifold learning, matrix factorization and matrix completion, statistical analysis of tensors and multi-indexed data. Prerequisites: STAT 610, 611, and 613.

620. Asymptotic Statistics. (3-0). Credit 3.

Review of basic concepts and important convergence theorems; elements of decision theory; delta method; Bahadur representation theorem; asymptotic distribution of MLE and the LRT statistics; asymptotic efficiency; limit theory for U-statistics and differential statistical functionals with illustration from M-,L-,R-estimation; multiple testing. Prerequisite: STAT 614.

621. Advanced Stochastic Processes. (3-0). Credit 3.

Conditional expectation; stopping times; discrete Markov processes; birth-death processes; queuing models; discrete semi-Markov processes; Brownian motion; diffusion processes, Ito integrals, theorem and limit distributions; differential statistical functions and their limit distributions; M-,L-,R-estimation. Prerequisite: STAT 614 or STAT 615.

623. Statistical Methods for Chemistry. (3-0). Credit 3.

Chemometrics topics of process optimization, precision and accuracy; curve fitting; chi-squared tests; multivariate calibration; errors in calibration standards; statistics of instrumentation. Prerequisites: STAT 601 or STAT 652 or STAT 641 or approval of instructor.

626. Methods in Time Series Analysis. (3-0). Credit 3.

Introduction to statistical time series analysis; autocorrelation and spectral characteristics of univariate, autoregressive, moving average models; identification, estimation and forecasting. Prerequisite: STAT 601 or 642 or approval of instructor.

627. Nonparametric Function Estimation. (3-0). Credit 3.

Nonparametric function estimation; kernel, local polynomials, Fourier series and spline methods; automated smoothing methods including cross-validation; large sample distributional properties of estimators; recent advances in function estimation. Prerequisites: STAT 611.

630. Overview of Mathematical Statistics. (3-0). Credit 3.

Basic probability theory including distributions of random variables and expectations. Introduction to the theory of statistical inference from the likelihood point of view including maximum likelihood estimation, confidence intervals, and likelihood ratio tests. Introduction to Bayesian methods. Prerequisites: Math 221, 251, or 253.

631. Statistical Methods in Finance. (3-0). Credit 3.

Regression and the capital asset pricing model, statistics for portfolio analysis, resampling, time series models, volatility models, option pricing and Monte Carlo methods, copulas, extreme value theory, value at risk, spline smoothing of term structure. Prerequisites: STAT 610, 611, 608.

632. Statistical Methodology II-Bayesian Modeling and Inference. (3-0). Credit 3.

Decision theory; fundamentals of Bayesian inference; single and multi-parameter models, Gaussian model; linear and generalized linear models; Bayesian computation; asymptotic methods; non-interative MC; MCMC; hierarchical models; nonlinear models; random effect models; survival analysis; spatial models. Prerequisite: STAT 613.

633. Advanced Bayesian Modeling and Computation. (3-0). Credit 3.

Bayesian methodology, and applications of Bayesian methods in bioinformatics, biostatistics, signal processing, machine learning, and related fields. Prerequisite: STAT 608, 613, 632.

636. Applied Multivariate Analysis. (3-0). Credit 3.

Multivariate extensions of the chi-square and t-tests, discrimination and classification procedures; applications to diagnostic problems in biological, medical, anthropological, and social research; multivariate analysis of variance, principal component and factor analysis, canonical correlations. Prerequisites: MATH 423 and STAT 653 or approval of instructor. Cross-listed with INFO 657.

638. Introduction to Applied Bayesian Methods. (3-0). Credit 3.

Students will learn how uncertainty regarding parameters can be explicitly described as a posterior distribution which blends information from a sampling model and prior distribution Course will emphasize modeling and computations under the Bayesian paradigm. Topics include: prior distributions, Bayes Theorem, conjugate and non-conjugate models, posterior simulation via the Gibbs sampler and MCMC, hierarchical modeling. Prerequisite: STAT 604, 608, 630.

641. The Methods of Statistics I. (3-0). Credit 3.

An application of the various disciplines in statistics to data analysis, introduction to statistical software; demonstration of interplay between probability models and statistical inference. Prerequisites: Concurrent Enrollment in STAT 610 or approval of instructor.

642. The Methods of Statistics II (3-0). Credit 3.

Design and analysis of experiments; scientific method; graphical displays; analysis of nonconventional designs and experiments involving categorical data. Prerequisites: STAT 641.

643. Biostatistics I. (3-0). Credit 3.

Bio-assay for quantitative and quantal responses; statistical analysis of contingency, including effect estimates, matched samples and misclassification. Prerequisites: STAT 608, 630, and 642 or STAT 610.

644. Biostatistics II. (3-0). Credit 3.

Generalized linear models; survival analysis with emphasis on nonparametric models and methods. Prerequisites: STAT 643 or approval of instructor.

645. Applied Biostatistics and Data Analysis. (3-0). Credit 3.

Survey of crucial topics in biostatistics; application of regression in biostatistics; analysis of correlated data; logistic and Poisson regression for binary or count data; survival analysis for censored outcomes; design and analysis of clinical trials; sample size calculation bysimulation; bootstrap techniques for assessing statistical significance; data analysis using R. Prerequisites: STAT 651, 652, and 659, or equivalent or prior approval of instructor.

646. Statistical Bioinformatics. (3-0). Credit 3.

An overview of relevant biological concepts and technologies of genomic/proteomic applications; methods to handle, visualize, analyze, and interpret genomic/proteomic data; exploratory data analysis for genomic/ proteomic data; data preprocessing and normalization; hypotheses testing; classification and prediction techniques for using genomic/ proteomic data to predict disease status. Prerequisites: STAT 604, 651, 652 or equivalent or prior approval of instructor.

647. Spatial Statistics. (3-0). Credit 3.

Spatial correlation and its effects; spatial prediction (kriging); spatial regression; analysis of point patterns (tests for randomness and modelling patterns); sub sampling methods for spatial data. Prerequisite: STAT 601 or STAT 630 and STAT 608 or equivalent.

648. Applied Statistics and Data Analysis. (3-0). Credit 3.

Background to conduct research in the development of new methodology in applied statistics. Topics covered will include: exploratory data analysis; sampling; testing; smoothing; classification; time series; and spatial data analysis. Prerequisite: Approval of instructor.

651. Statistics in Research I. (3-0). Credit 3.

For graduate students in other disciplines; non-calculus exposition of the concepts, methods and usage of statistical data analysis; T-tests, analysis of variance, and linear regression. Prerequisite: MATH 102 or equivalent.

652. Statistics in Research II. (3-0). Credit 3.

Continuation of STAT 651. Concepts of experimental design, individual treatment comparisons, randomized blocks and factorial experiments, multiple regression, chi-square tests and a brief introduction to covariance, non-parametric methods, and sample surveys. Prerequisite: STAT 651.

653. Statistics in Research III. (3-0). Credit 3.

Advanced topics in ANOVA; analysis of covariance; and regression analysis including analysis of messy data; non-linear regression; logistic and weighted regression, diagnostics and model building; emphasis on concepts, computing and interpretation. Prerequisite: STAT 652.

656. Applied Analytics Using SAS Enterprise Miner. (3-0) Credit 3.

Introduction to data mining and will demonstrate the procedures; Optimal prediction decisions; comparing and deploying predictive models; neural networks; constructing and adjusting tree models; the construction and evaluation of multi-stage models. Prerequisite: STAT 657, 659.

657. Advanced Programming Using SAS. (3-0). Credit 3.

Programming with SAS/IML, programming in SAS data step, advanced use of various SAS procedures. Prerequisites: STAT 604, 642.

658. Transportation Statistics. (3-0). Credit 3.

Design of experiments, estimation, hypotheses testing, modeling, and data mining for transportation specialists. Prerequisites: STAT 211 or STAT 651.

659. Applied Categorical Data Analysis. (3-0). Credit 3.

Introduction to analysis and interpretation of categorical data using ANOVA/regression analogs; includes contingency tables, loglinear models, logistic regression; use of computer software such as SAS, GLIM, SPSSX. Prerequisite: STAT 601 or 641 or 652 or equivalent.

661. Statistical Genetics. (3-0), Credit 3.

Basic concepts in human genetics, sampling designs, gene frequency estimation, Hardy-Weinberg equilibrium, linkage disequilibrium, association and transmission disequilibrium test studies, linkage and pedigree analysis, segregation analysis, polygenic models, DNA sequence analysis. Prerequisites: STAT 610 and 611.

662. Advanced Statistical Genetics. (3-0). Credit 3.

This course is a continuation of the course, STAT 661 Statistical Genetics. A strong background in statistics, genetics, and mathematics is required. Topics include counting methods, EM algorithm, Newton’s method, scoring in genetics, genetic identity coefficients, descent graph, molecular phylogeny, models of recombination, sequence analysis, diffusion processes and linkage disequilibrium mappings. Prerequisite: STAT 610, 611, and 661.

665. Statistical Application of Wavelets. (3-0). Credit 3.

This is a course on the use of wavelets methods in statistics. The course introduces wavelet theory, provides an overview of wavelet-based statistical methods. Topics include smoothing of noisy signals, estimation function data and representation of stochastic processes. Some emphasis is given to Bayesian procedures. Prerequisite: STAT 611 or approval by the instructor.

673. Time Series Analysis I. (3-0). Credit 3.

An introduction to diverse modes of analysis now available to solve for univariate time series; basic problems of parameter estimation, spectral analysis, forecasting and model identification. Prerequisite: STAT 611 or equivalent.

674. Time Series Analysis II. (3-0). Credit 3.

Continuation of STAT 673. Multiple time series, ARMA models, test of hypotheses, estimation of spectral density matrix, transfer function and forecasting. Prerequisites: STAT 673.

681. Seminar. Credit 1.

Oral presentations of special topics and current research in statistics. May be repeated for credit. Prerequisite: Graduate classification in statistics.

684. Professional Internship. Credit 1 to 3.

Practicum in statistical consulting for students in Ph.D. program. Students will be assigned consulting problems brought to the Department of Statistics by researchers in other disciplines. Prerequisite: STAT 642 or equivalent.

685. Directed Studies. Credit 1 to 6.

Individual instruction in selected fields in statistics; investigation of special topics not within scope of thesis research and not covered by other formal courses. Prerequisites: Graduate classification and approval of department head.

689. Special Topics in Statistics. Credit 1 to 4.

Selected topics in an identified area of statistics. Open to non-majors. May be repeated for credit. Prerequisite: Approval of instructor.

691. Research. Credit 1 or more.

Research for thesis or dissertation. Prerequisite: Graduate classification.