## Undergraduate Study

For the undergraduate curriculum in liberal arts and sciences, major in statistics, leading to the degree bachelor of science, see Liberal Arts and Sciences, Curriculum.

The curriculum in liberal arts and sciences with a major in statistics is designed to prepare students for (1) entry level statistics positions in business, industry or commerce, nonprofit institutions, and in state or federal government; (2) graduate study in statistics. Entry-level positions include the following types of work: statistical design, data visualization, analysis and interpretation of experiments and surveys; data processing and analysis using modern computation facilities and statistical computing systems; application of statistical principles and methods in commercial areas such as finance, insurance, industrial research, marketing, manufacturing, sports analytics, and quality control and in nonprofit organizations such as large health study institutions.

Students completing the undergraduate degree in statistics should have a broad understanding of the discipline of statistics. They should have a clear comprehension of the theoretical basis of statistical reasoning and should be proficient in the use of modern statistical methods, data visualization, and computing. Such graduates should have an ability to apply and convey statistical concepts and knowledge in oral and written form. They should be aware of ethical issues associated with polling and surveys and in summarizing and displaying the outcomes of statistical studies.

Undergraduate majors in this department usually include in their programs:

STAT 110 | Orientation in Statistics | 1 |

STAT 201 | Introduction to Statistical Concepts and Methods | 4 |

One of the following options | ||

Option I | ||

Calculus I | ||

Calculus II | ||

Calculus III | ||

Option II | ||

Calculus I | ||

Calculus II, Honors | ||

Calculus III, Honors | ||

One of the following | ||

Matrices and Linear Algebra | ||

Theory of Linear Algebra | ||

One of the following | ||

Windows Application Programming | ||

Introduction to Computer Programming | ||

Fundamentals of Computer Programming | ||

Object-oriented Programming | ||

STAT 301 | Intermediate Statistical Concepts and Methods | 4 |

STAT 341 | Introduction to the Theory of Probability and Statistics I | 4 |

STAT 342 | Introduction to the Theory of Probability and Statistics II | 4 |

STAT 471 | Introduction to Experimental Design | 3 |

STAT 475 | Introduction to Multivariate Data Analysis | 3 |

STAT 484 | Computer Processing of Scientific Data | 3 |

STAT 486 | Introduction to Statistical Computing | 3 |

A minimum of 6 credits from the following | ||

Statistical Quality Assurance | ||

Introduction to Time Series | ||

Introduction to Survey Sampling | ||

Introduction to Bayesian Data Analysis | ||

Introduction to Spatial Data Analysis | ||

Introduction to Categorical Data Analysis | ||

Introduction to Stochastic Process Models | ||

Regression for Social and Behavioral Research | ||

Empirical Methods for the Computational Sciences |

English and Speech proficiency requirement: The department requires a passing grade in ENGL 150 Critical Thinking and Communication, completion of ENGL 250 Written, Oral, Visual, and Electronic Composition (or ENGL 250H Written, Oral, Visual, and Electronic Composition: Honors ) with a grade of C or better, and completion of one of ENGL 302 Business Communication or ENGL 314 Technical Communication with a grade of C- or better. The department requires a passing grade in COMST 211 Interpersonal Communication or SP CM 212 Fundamentals of Public Speaking .

It is advisable to have at least a minor in a field of application. Some common minors earned by statistics majors are: Economics, General Business, and Mathematics. Students preparing for positions in data analysis should consider a minor or certificate in Data Science. Students preparing for a career in the field of actuarial science should consider a Certificate in Actuarial Science. Students intending to do graduate work in statistics are strongly advised to complete at least a minor in Mathematics including credit in MATH 414 Analysis I.

Many Statistics majors earn a second major or degree in a field of application or Mathematics. Your academic adviser can assist you in developing your course of study that includes other majors.

### Statistics, B.S.

Freshman | |||
---|---|---|---|

Fall | Credits | Spring | Credits |

ENGL 150 | 3 | MATH 166 or 166H | 4 |

LIB 160 | 1 | STAT 201 | 4 |

STAT 110 | 1 | Social Science Choice | 3 |

MATH 165 | 4 | Humanities Choice | 3 |

Humanities Choice | 3 | ||

Natural Science Choice | 4 | ||

16 | 14 | ||

Sophomore | |||

Fall | Credits | Spring | Credits |

STAT 301 | 4 | STAT 471 | 3 |

MATH 265 or 265H | 4 | MATH 207 or 317 | 3-4 |

ENGL 250 | 3 | Computer Science Choice | 3 |

Natural Science Choice | 4 | Humanities Choice | 3 |

Social Science Choice | 3 | ||

15 | 15-16 | ||

Junior | |||

Fall | Credits | Spring | Credits |

STAT 341 | 4 | STAT 342 | 4 |

STAT 484 | 3 | Statistics Choice | 3 |

SP CM 212 or COMST 211 | 3 | Social Science Choice | 3 |

Foreign Language/Elective | 4 | Foreign Language/Elective | 4 |

Elective | 2 | Elective | 2 |

16 | 16 | ||

Senior | |||

Fall | Credits | Spring | Credits |

STAT 475 | 3 | STAT 486 | 3 |

ENGL 302 or 314 | 3 | Statistics Choice | 3 |

Humanities Choice | 3 | Electives | 9 |

Electives | 6 | ||

15 | 15 |

In order to graduate, all students must complete a three-credit course in U.S. diversity and a three-credit course in international perspectives. Discuss with your adviser how the two courses you select can be applied to your graduation plan. | |

LAS majors require a minimum of 120 credits, | |

You must also complete the LAS foreign language requirement. |

### Minor

The department offers a minor in statistics which may be earned by completing one introductory course in statistics (STAT 101, 104, 105, 201, 226, 231, 305, 322 or 330); STAT 301 or 326; plus at least 9 additional credits from STAT 341, 342, 347, 361, 471, 472, 473, 474, 475, 476, 477, 478, 482, 483, 484, and 486 to yield a total of at least 15 credits in statistics courses. The minor must include at least 9 credits that are not used to meet any other department, college or university requirement.

## Graduate Study

The department offers graduate programs leading to both Master of Science (M.S.) and Doctor of Philosophy (Ph.D.) degrees with a major in statistics. Graduate work leading to a minor in statistics is available for students majoring in other programs, at both the M.S. and Ph.D. levels. The Ph.D. degree is also offered as a co-major with other graduate programs. The department participates in inter-disciplinary graduate programs in Bioinformatics and Computational Biology, Ecology and Evolutionary Biology, Genetics, Human Computer Interaction, Nutritional Sciences, and Wind Energy Science, Engineering, and Policy.

Graduates of the M.S. program have an understanding of basic statistical theory and methods. Elective courses in the M.S. program provide an opportunity for students to emphasize particular areas of statistical methods or application in their program. Students complete a minimum of 34 semester credits, including work on a capstone project resulting in a written creative component under the direction of an individual major professor and presented in a final oral examination.

Graduates of the Ph.D. program in statistics have studied advanced theory and methods, and have demonstrated the ability to conduct independent research resulting in an original contribution to the discipline. Candidates for the Ph.D. degree in statistics complete a minimum of 72 semester credits, including at least 18 credits given for research activity, pass an oral preliminary examination, and submit a written dissertation containing original research that is defended in a final oral examination. Dissertation research is typically conducted in close collaboration with a major professor and usually results in publishable material. The department does not offer specific program tracks or areas of emphasis, but the diversity of elective courses and research areas of faculty allow students to tailor their individual programs to reflect areas of particular interest.

Graduates of co-major Ph.D. programs in statistics and an applied scientific discipline have mastered basic statistical theory and have studied advanced methodology. Students complete a minimum of 72 semester credits for courses in statistics and the chosen scientific discipline. Students conduct research that is a combination of statistical methodology and the scientific discipline. Co-major professors work with the student to prepare for an oral preliminary examination and conduct research leading to a single dissertation project that produces an original contribution to at least one of the two disciplines that is defended in a final oral examination.

Graduates of co-major Ph.D. programs in statistics and an area of theoretical mathematics have mastered basic statistical methods and have studied advanced statistical theory. Students complete a minimum of 72 semester credits. Co-major professors assist the student in preparing a dissertation that represents original research that makes a contribution at the interface of statistical theory and a sub-discipline of mathematics. The dissertation is defended in a final oral examination.

## Courses

**Courses primarily for undergraduates:**

(3-2) Cr. 4. F.S.SS.

*Prereq: 1 1/2 years of high school algebra*

Statistical concepts in modern society; descriptive statistics and graphical displays of data; the normal distribution; data collection (sampling and designing experiments); elementary probability; elements of statistical inference; estimation and hypothesis testing; linear regression and correlation; contingency tables.
Credit for only one of the following courses may be applied toward graduation: STAT 101, STAT 104, STAT 105, STAT 201, or STAT 226.

(2-2) Cr. 3. F.S.SS.

*Prereq: 1 1/2 years of high school algebra*

Statistical concepts and their use in science; collecting, organizing and drawing conclusions from data; elementary probability; binomial and normal distributions; regression; estimation and hypothesis testing. For students in the agricultural and biological sciences.
Credit for only one of the following courses may be applied toward graduation: STAT 101, STAT 104, STAT 105, STAT 201, or STAT 226.

(1-0) Cr. 1. F.

Opportunities, challenges, and the scope of the curriculum in statistics. For students planning or considering a career in this area.

(3-2) Cr. 4. S.

*Prereq: Credit or enrollment in MATH 165*

Statistical thinking and applications of statistical concepts and methods in modern society. Display and summary of categorical and numerical data. Exploring relationships between variables, association, correlation, and regression. Observational studies and experiments. Probability concepts, random variables, discrete and continuous distributions. Elements of statistical inference; estimation and hypothesis testing.
Credit for only one of the following courses may be applied toward graduation: STAT 101, STAT 104, STAT 105, STAT 201, or STAT 226.

(Cross-listed with MATH). Cr. 1. S.

Career development in the mathematics and statistics disciplines with an emphasis on contemporary social issues. Presentations by professionals in STEM fields about occupations, decision-making strategies, and career goal implementation; development of job searching, resume writing, negotiating, and interviewing techniques.
Offered on a satisfactory-fail basis only.

(3-0) Cr. 3. F.S.SS.

*Prereq: MATH 150 or MATH 165*

Obtaining, organizing, and presenting statistical data; measures of location and dispersion; the Normal distribution; sampling and sampling distribution of the sample mean; elements of statistical inference; confidence intervals and hypothesis testing for the mean; describing bivariate relationships and inference for simple linear regression analysis; use of computers to visualize and analyze data.
Credit for only one of the following courses may be applied toward graduation: STAT 101, STAT 104, STAT 105, STAT 201, or STAT 226.

(4-0) Cr. 4. F.S.

*Prereq: Credit or enrollment in MATH 265 (or MATH 265H)*

Emphasis on engineering applications. Basic probability; random variables and probability distributions; joint and sampling distributions. Descriptive statistics; confidence intervals; hypothesis testing; simple linear regression; multiple linear regression; one way analysis of variance; use of statistical software.

(3-2) Cr. 4. F.S.

*Prereq: STAT 101 or STAT 104 or STAT 105 or STAT 201*

Statistical concepts and methods used in the analysis of observational data. Analysis of single sample, two sample and paired sample data. Simple and multiple linear regression including polynomial regression and use of indicator variables. Model building and analysis of residuals. Introduction to one-way ANOVA, tests of independence for contingency tables, and logistic regression.
Credit for only one of the following courses may be applied toward graduation: STAT 301, STAT 326, STAT 401, or STAT 587.

(3-0) Cr. 3. F.S.SS.

*Prereq: MATH 165*

Statistics for engineering problem solving. Principles of engineering data collection; descriptive statistics; elementary probability distributions; principles of experimentation; confidence intervals and significance tests; one-, two-, and multi-sample studies; regression analysis; use of statistical software.
Credit for both STAT 105 and STAT 305 may not be applied toward graduation.

(Cross-listed with E E). (3-0) Cr. 3. F.S.

*Prereq: E E 224*

Introduction to probability with applications to electrical engineering. Sets and events, probability space, conditional probability, total probability and Bayes' rule. Discrete and continuous random variables, cumulative distribution function, probability mass and density functions, expectation, moments, moment generating functions, multiple random variables, functions of random variables. Elements of statistics, hypothesis testing, confidence intervals, least squares. Introduction to random processes.

(2-2) Cr. 3. F.S.SS.

*Prereq: STAT 226*

Multiple regression analysis; regression diagnostics; model building; applications in analysis of variance and time series; random variables; distributions; conditional probability; use of computers to visualize and analyze data.
Credit for only one of the following courses may be applied toward graduation: STAT 301, STAT 326, STAT 401, or STAT 587.

(3-0) Cr. 3. F.S.SS.

*Prereq: MATH 166*

Topics from probability and statistics applicable to computer science. Basic probability; Random variables and their distributions; Stochastic processes including Markov chains; Queuing models; Basic statistical inference; Introduction to regression.

(Cross-listed with ENGL). (3-0) Cr. 3.

*Prereq: STAT 101, STAT 104, STAT 201 or STAT 226; ENGL 250*

Communicating quantitative information using visual displays; visualizing data; interactive and dynamic data displays; evaluating current examples in the media; color, perception, and representation in graphs; interpreting data displays.

(Cross-listed with MATH). (3-2) Cr. 4. F.S.

*Prereq: MATH 265 (or MATH 265H)*

Probability; distribution functions and their properties; classical discrete and continuous distribution functions; multivariate probability distributions and their properties; moment generating functions; transformations of random variables; simulation of random variables and use of the R statistical package.
Credit for only one of the following courses may be applied toward graduation: STAT 341, STAT 347, STAT 447, or STAT 588.

(Cross-listed with MATH). (3-2) Cr. 4. F.S.

*Prereq: STAT 201 or equivalent; STAT 341; MATH 207 or MATH 317*

Sampling distributions; confidence intervals and hypothesis testing; theory of estimation and hypothesis tests; linear model theory; resampling methods; introduction to Bayesian inference; use of the R statistical package for simulation and data analysis.

Cr. 4. F.

*Prereq: MATH 207 or MATH 317; MATH 265; STAT 301 or STAT 326*

Introduction to probability; distribution functions and their properties; classical discrete and continuous distributions; sampling distributions; theory of estimation; theory of inference; use of R statistical package for simulation and data analysis.
Credit for only one of the following courses may be applied toward graduation: STAT 341, STAT 347, STAT 447, or STAT 588.

(Cross-listed with I E). (2-2) Cr. 3. F.S.

*Prereq: STAT 231, STAT 301, STAT 326, STAT 401, or STAT 587*

Statistical methods for process improvement. Simple quality assurance principles and tools. Measurement system precision and accuracy assessment. Control charts. Process capability assessment. Experimental design and analysis for process improvement. Significant external project in process improvement.

Cr. R. F.S.SS.

*Prereq: Permission of department chair*

Off-campus work periods for undergraduate students in a field of statistics.

(Dual-listed with STAT 571). (3-0) Cr. 3. F.S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

The role of statistics in research and the principles of experimental design. Concepts of experimental and observational units, randomization, replication, blocking, subdividing and repeatedly measuring experimental units; factorial treatment designs and confounding; common designs including randomized complete block design, Latin square design, split-plot design, and analysis of data from such common designs; extensions of the analysis of variance to cover variance components. Determining sample size.
Credit in only one of STAT 402, STAT 471, or STAT 571 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 572). (3-0) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Methods for analyzing data collected over time; review of multiple regression analysis. Elementary forecasting methods: moving averages and exponential smoothing. Autoregressive-moving average (Box-Jenkins) models: identification, estimation, diagnostic checking, and forecasting. Transfer function models and intervention analysis. Introduction to multivariate time series methods.
Credit for only one of STAT 451, STAT 472, or STAT 572 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 573). (2-2) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; STAT 341 or STAT 347 or STAT 447 or STAT 588*

Concepts of sample surveys and the survey process; methods of designing sample surveys, including: simple random, stratified, systematic, probability proportional to size, and multistage sampling designs; methods of analyzing sample surveys including ratio, regression, domain estimation and nonresponse.

(Dual-listed with STAT 574). (2-2) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; STAT 342 or STAT 447 or STAT 588.*

Probability models and prior distributions; updating priors through the likelihood function. Computational and simulation-based methods for deriving posterior distributions and for estimating parameters. Basic statistical and hierarchical models. Model adequacy and posterior predictive checks. Markov Chain Monte Carlo methods and introduction to WinBUGS or similar software. Emphasis on applications and examples from the social, biological and physical sciences.
Credit for only one of STAT 444, STAT 474, or STAT 574 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 575). (2-2) Cr. 3. F.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; knowledge of matrix algebra*

Techniques for displaying and analyzing multivariate data including plotting high-dimensional data using interactive graphics; comparing group mean vectors using Hotelling's T2; multivariate analysis of variance; reducing variable dimension with principal components; identifying factors with exploratory factor analysis; grouping observations with multidimensional scaling and cluster analysis; and classification using discriminant analysis, logistic regression, classification trees, and random forests. Introduction to the R statistical software package.
Credit for only one of STAT 407, STAT 475, or STAT 575 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 576). (3-0) Cr. 3. Alt. S., offered even-numbered years.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; STAT 341 or STAT 447 or STAT 588 or permission of instructor.*

The analysis of spatial data; geostatistical methods, mapping and spatial prediction; methods for areal data; models and methods for spatial point processes. Emphasis on application and practical use of spatial statistical analysis. Use of R and R packages for spatial data analysis.
Credit for only one of STAT 406, STAT 476, or STAT 576 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 577). (3-0) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Statistical methods for the analysis of categorical data: graphical summaries, estimation and inference for proportions, sample size determination, chi-square tests, measures of relative risk, odds and association, analysis of paired data and measures of agreement, logistic regression models, log-linear models.
Credit for only one of STAT 457, STAT 477, or STAT 577 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 578). (3-0) Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 231 or STAT 341 or STAT 347 or STAT 447 or STAT 588*

Probabilistic models in biological, engineering and the physical sciences. Markov chains; Poisson, birth-and-death, renewal, branching and queuing processes; applications to bioinformatics and other quantitative problems.
Credit for only one of STAT 432, STAT 478, or STAT 578 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 582). (2-2) Cr. 3. F.S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Applications of generalized linear regression models to social science data. Assumptions of regression; diagnostics and transformations; analysis of variance and covariance; logistic, multinomial and Poisson regression.
Credit for only one of STAT 404, STAT 482, or STAT 582 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 583). (3-0) Cr. 3. F.

*Prereq: STAT 330 or an equivalent course, MATH 166, knowledge of linear algebra.*

Statistical methods for research involving computers; exploratory data analysis; selected topics from analysis of designed experiments - analysis of variance, hypothesis testing, interaction among variables; linear regression, logistic regression, Poisson regression; parameter estimation, prediction, confidence regions, dimension reduction techniques, model diagnostics and sensitivity analysis; Markov chains and processes; simulation techniques and bootstrap methods; applications to computer science, bioinformatics, computer engineering - programs, models and systems as objects of empirical study; communicating results of empirical studies. Statistical software: R.
Credit for only one of STAT 430, STAT 483, or STAT 583 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 584). (3-0) Cr. 3. F.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Structure, content and programming aspects of modern statistical software packages. Advanced techniques for data management, graphics, exploratory data analysis, and generalized linear models.
Credit for only one of STAT 479, STAT 484, or STAT 584 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 586). (3-0) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Modern statistical computing. Topics may include: data management; spread sheets; verifying data accuracy; transferring data between software packages; data and graphical analysis with statistical software packages; algorithmic programming concepts and applications; simulation studies and resampling methods; software reliability; statistical modeling and machine learning.
Credit for only one of STAT 480, STAT 486, or STAT 586 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

Cr. arr. Repeatable, maximum of 9 credits.

*Prereq: 10 credits in statistics*

No more than 9 credits in Stat 490 may be counted toward graduation.

Cr. arr. Repeatable, maximum of 9 credits.

*Prereq: 10 credits in statistics*

No more than 9 credits in Stat 490 may be counted toward graduation.

**Courses primarily for graduate students, open to qualified undergraduates:**

(3-2) Cr. 4. F.

*Prereq: STAT 447 or STAT 588 or current enrollment in STAT 542; knowledge of matrix algebra.*

Analysis of data from designed experiments and observational studies. Randomization-based inference; inference on group means; nonparametric bootstrap; pairing/blocking and other uses of restricted randomization. Use of linear models to analyze data; least squares estimation; estimability; sampling distributions of estimators; general linear tests; inference for parameters and contrasts. Model assessment and diagnostics; remedial measures; alternative approaches based on ranks.

(3-0) Cr. 3. S.

*Prereq: STAT 500; STAT 542; STAT 579 or equivalent; knowledge of matrix algebra.*

Statistical methods for analyzing and displaying multivariate data; the multivariate normal distribution; inference in multivariate populations, simultaneous analysis of multiple responses, multivariate analysis of variance; summarizing high dimensional data with principal components, factor analysis, canonical correlations, classification methods, clustering, multidimensional scaling; introduction to basic nonparametric multivariate methods. Statistical software: SAS or R.

(3-0) Cr. 3. Alt. S., offered even-numbered years.

*Prereq: STAT 500, STAT 542, STAT 579.*

A Statistics-MS-level introduction to Modern Multivariate Statistical Learning. Theory-based methods for modern data mining and machine learning, inference and prediction. Variance-bias trade-offs and choice of predictors; linear methods of prediction; basis expansions; smoothing, regularization, kernel smoothing methods; neural networks and radial basis function networks; bootstrapping, model averaging, and stacking; linear and quadratic methods of classification; support vector machines; trees and random forests; boosting; prototype methods; unsupervised learning including clustering, principal components, and multi-dimensional scaling; kernel mechanics. Substantial use of R packages implementing these methods.

(2-2) Cr. 3. Alt. S., offered irregularly.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; STAT 341 or STAT 347 or STAT 447 or STAT 542 or STAT 588; STAT 480 or STAT 486 or STAT 579 or STAT 586*

Approaches to finding the unexpected in data; exploratory data analysis; pattern recognition; dimension reduction; supervised and unsupervised classification; interactive and dynamic graphical methods; computer-intensive statistical techniques for large or high dimensional data and visual inference. Emphasis is on problem solving, topical problems, and learning how so-called black-box methods actually work.

(3-0) Cr. 3.

*Prereq: STAT 447 or STAT 542 or STAT 588; STAT 401 or STAT 500 or STAT 587*

Statistical methods and models for environmental applications. Emphasis on environmental toxicology. Analysis of data with below detection-limit values. Dose-response curve modeling, including overdispersion and estimation of safe doses. Trend analysis; analysis of autocorrelated data. Equivalence testing.

(3-0) Cr. 3. S.

*Prereq: STAT 500; STAT 447 or STAT 588 or credit/enrollment in STAT 543*

Linear models and analysis of variance for multifactor experiments with balanced and unbalanced data. Likelihood analysis for general linear models and models with non-normal random components; linear model results in the context of likelihood; linear mixed models and their application; estimation, inference, and prediction. Introduction to generalized linear models and generalized linear mixed models. Case studies of applications including problem formulation, exploratory analysis, model development, estimation and inference, and model assessment.

(3-0) Cr. 3. F.

*Prereq: STAT 510*

Basic techniques of experimental design developed in the context of the general linear model; completely randomized, randomized complete block, and Latin Square designs; factorial experiments, confounding, fractional replication; split-plot and incomplete block designs.

(3-0) Cr. 3.

*Prereq: STAT 402 or STAT 471 or STAT 512 or STAT 571; knowledge of elementary matrix theory and matrix formulation of regression*

Analysis techniques for locating optimum and near-optimum operating conditions: standard experimental designs for first- and second-order response surface models; design performance criteria; use of data transformations; mixture experiments; optimization for multiple-response problems. Requires use of statistical software with matrix functions.

(3-0) Cr. 3.

*Prereq: STAT 447 or STAT 543 or STAT 588; STAT 510*

Construction of nonlinear statistical models; random and systematic model components, additive error nonlinear regression with constant and non-constant error variances, generalized linear models, transform both sides models. Iterative algorithms for estimation and asymptotic inference. Basic random parameter models, beta-binomial and gamma-Poisson mixtures. Requires use of instructor-supplied and student-written R functions.

(3-0) Cr. 3.

*Prereq: STAT 500; STAT 447 or STAT 542 or STAT 588*

Introduction to high-throughput technologies for gene expression studies (especially RNA-sequencing technology): the role of blocking, randomization, and biological and technical replication in the design of gene expression experiments; normalization methods; methods for identifying differentially expressed genes including mixed linear model analysis, generalized linear model analysis, generalized linear mixed model analysis, quasi-likelihood methods, and empirical Bayes analysis; procedures for controlling false discovery rate for multiple testing; clustering problems for gene expression data; testing gene categories; emphasis on current research topics for statistical analysis of high dimensional gene expression data.

(3-0) Cr. 3. F.

*Prereq: STAT 510; STAT 447 or STAT 543 or STAT 588*

Nonlinear regression; generalized least squares; asymptotic inference. Generalized linear models; exponential dispersion families; maximum likelihood and inference. Designing Monte Carlo studies; bootstrap; cross-validation. Fundamentals of Bayesian analysis; data models, priors and posteriors; posterior prediction; credible intervals; Bayes Factors; types of priors; simulation of posteriors; introduction to hierarchical models and Markov Chain Monte Carlo methods.

(3-0) Cr. 3. S.

*Prereq: STAT 401 or STAT 500 or STAT 587; STAT 447 or STAT 542 or STAT 588*

Practical aspects and basic theory of design and estimation in sample surveys for finite populations. Simple random, systematic, stratified, cluster multistage and unequal-probability sampling. Horvitz-Thompson estimation of totals and functions of totals: means, proportions, regression coefficients. Linearization technique for variance estimation. Model-assisted ratio and regression estimation. Two-phase sampling and sampling on two occasions. Non-response effects. Imputation.

(3-0) Cr. 3. Alt. F., offered irregularly.

*Prereq: STAT 421 or STAT 473 or STAT 521 or STAT 573*

Advanced topics in survey sampling and methodology: clustering and stratification in practice, adjustments and imputation for missing data, variance estimation in complex surveys, methods of panel and/or longitudinal surveys, procedures to increase response rates, and computing. Examples are taken from large, well-known surveys in various subject areas.

(6-0) Cr. 6.

*Prereq: STAT 341 or equivalent*

Descriptive statistics; data collection through experimentation and sampling; univariate statistical inference; contingency tables; design of experiments and ANOVA; simple linear regression; logistic regression; multiple linear regression; statistics pedagogy. (Offered on a 3-year cycle; offered SS 2020.).
May not be used for graduate credit in the Statistics program. Credit in STAT 410 or STAT 525, but not both, may be applied toward graduation.

Cr. 3. F.

*Prereq: Admission to Master of Business Analytics program*

Probability concepts and distributions used in statistical decision-making for business applications. Least-squares and maximum likelihood estimation, sampling distributions of estimators, formal statistical inference, analysis of variance, multiple regression models and strategies for model selection, logistic regression, and Poisson regression. Applications implemented with the R statistical package. Simulations used to investigate properties of inferential procedures and to assist in data analysis.
May not be used for graduate credit in the Statistics program.

Cr. 3. F.

*Prereq: Admission to the Master of Business Analytics Program*

Types of data displays; numerical and visual summaries of data; data structures for data displays; data vs info graphics; good practices of displaying data; human perception and cognition in data displays; graphics as tools of data exploration; graphical diagnostics of statistical models and machine learning procedures; strategies and techniques for data visualizations; basics of reproducibility and repeatability; web-based interactive applets for visual presentation of data and results; programming in R.
May not be used for graduate credit in the Statistics program.

(Cross-listed with I E). (3-0) Cr. 3.

*Prereq: STAT 401 or STAT 587; STAT 342 or STAT 447 or STAT 588*

Statistical methods and theory applicable to problems of industrial process monitoring and improvement. Statistical issues in industrial measurement; Shewhart, CUSUM, and other control charts; feedback control; process characterization studies; estimation of product and process characteristics; acceptance sampling, continuous sampling and sequential sampling; economic and decision theoretic arguments in industrial statistics.

(Cross-listed with I E). (3-0) Cr. 3. Alt. S., offered even-numbered years.

*Prereq: STAT 342 or STAT 432 or STAT 447 or STAT 478 or STAT 578 or STAT 588*

Probabilistic modeling and inference in engineering reliability; lifetime models, product limit estimator, probability plotting, maximum likelihood estimation for censored data, Bayesian methods in reliability, system reliability models, competing risk analysis, acceleration models and analysis of accelerated test data; analysis of recurrence and degradation data; planning studies to obtain reliability data.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

*Prereq: STAT 447 or STAT 542 or STAT 588*

Statistical methods for non-standard problems, illustrated using questions and data from ecological field studies. Estimation of abundance and survival from mark-recapture studies, deterministic and stochastic matrix models of population trends, integral projection models, and hierarchical modeling, especially of population dynamics. Additional topics vary based on student interest.

(Cross-listed with GDCB). (3-0) Cr. 3.

*Prereq: STAT 401 or STAT 587; STAT 447 or STAT 588; GEN 320 or BIOL 313*

Statistical models and methods for genetics covering models of population processes: selection, mutation, migration, population structure, and linkage disequilibrium, and inference techniques: genetic mapping, linkage analysis, and quantitative trait analysis. Applications include genetic map construction, gene mapping, genome-wide association studies (GWAS), inference about population structure, phylogenetic tree construction, and forensic and paternity identification.

(4-0) Cr. 4. F.

*Prereq: MATH 414.*

Sample spaces, basic probability results, conditional probability. Random variables, univariate distributions, moment generating functions. Joint distributions, conditional distributions and independence, correlation and covariance. Probability laws and transformations. Introduction to the multivariate normal distribution. Sampling distributions, normal theory, sums and order statistics. Convergence concepts, the law of large numbers, the central limit theorem and delta method. Basics of stochastic simulation.

(3-0) Cr. 3. S.

*Prereq: STAT 542.*

Point estimation including method of moments, maximum likelihood and Bayes. Properties of point estimators, mean squared error, unbiasedness, consistency, loss functions. Large sample properties of maximum likelihood estimators. Exponential families, sufficiency, completeness, ancilarity, Basu's theorem. Hypothesis tests, Neyman-Pearson lemma, uniformly most powerful tests, likelihood ratio tests, Bayes tests. Interval estimation, inverting tests, pivotal quantities. Nonparametric theory, bootstrap.

(3-0) Cr. 3. S.

*Prereq: Credit or concurrent enrollment in STAT 543*

Specification of probability models; subjective, conjugate, and noninformative prior distributions; hierarchical models; analytical and computational techniques for obtaining posterior distributions; model checking, model selection, diagnostics; comparison of Bayesian and traditional methods.

(3-0) Cr. 3. Alt. S., offered even-numbered years.

*Prereq: STAT 543, STAT 510*

Theory and methods for analyzing functional data, which are high dimensional data resulted from discrete, error-contaminated measurements on smooth curves and images. The topics include kernel and spline smoothing, basis expansion, semiparametric regression, functional analysis of variance, covariance modeling and estimation, functional principal component analysis, functional generalization linear models, joint modeling, dimension reduction, classification and clustering functional data.

(3-0) Cr. 3. F.

*Prereq: STAT 447 or STAT 542 or STAT 588*

Concepts of trend and dependence in time series data; stationarity and basic model structures for dealing with temporal dependence; moving average and autoregressive error structures; analysis in the time domain and the frequency domain; parameter estimation, prediction and forecasting; identification of appropriate model structure for actual data and model assessment techniques. Possible extended topics include dynamic models and linear filters.

(Cross-listed with MATH). (3-0) Cr. 3. F.

*Prereq: STAT 542*

Markov chains on discrete spaces in discrete and continuous time (random walks, Poisson processes, birth and death processes) and their long-term behavior. Optional topics may include branching processes, renewal theory, introduction to Brownian motion.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

*Prereq: STAT 401 or STAT 500 or STAT 587; STAT 447 or STAT 543 or STAT 588*

Statistical methods for analyzing simple random samples when outcomes are counts or proportions; measures of association and relative risk, chi-squared tests, loglinear models, logistic regression and other generalized linear models, tree-based methods. Maximum likelihood estimation and large sample theory. Extensions to longitudinal studies and complex survey designs, models with fixed and random effects. Use of statistical software: SAS or R.

Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 401 or STAT 500 or STAT 587*

Statistical methods for analysis of binary and polytomous data using latent trait models. Application and theory of model selection and fit, dimensionality, differential item functioning and test development. Use of appropriate statistical software.

(Cross-listed with TOX). (3-0) Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 401 or STAT 500 or STAT 587; STAT 447 or STAT 543 or STAT 588*

Statistical methods commonly used in epidemiology and human and animal health studies. Overview of cohort studies, case-control studies and randomized clinical trials. Topics include inference procedures for disease risk factors, analysis of time-to-event and survival data, analysis of longitudinal studies of disease progression and health status, diagnostic test evaluation, and meta-analysis. Examples will come from recent studies of physical and mental health, nutrition and disease progression in human and animal populations. Use of statistical software: SAS or R.

(Cross-listed with BCB, COM S, GDCB). (3-0) Cr. 3. S.

*Prereq: BCB 567 or (BIOL 315 and one of STAT 430 or STAT 483 or STAT 583), credit or enrollment in GEN 409*

Statistical models for sequence data, including applications in genome annotation, motif discovery, variant discovery, molecular phylogeny, gene expression analysis, and metagenomics. Statistical topics include model building, inference, hypothesis testing, and simple experimental design, including for big data/complex models.

(Cross-listed with BCB, COM S, CPR E, GDCB). (3-0) Cr. 3. S.

*Prereq: BCB 567 or COM S 311, COM S 228, GEN 409, STAT 430 or STAT 483 or STAT 583*

Algorithmic and statistical approaches in computational functional genomics and systems biology. Analysis of high throughput biological data obtained using system-wide measurements. Topological analysis, module discovery, and comparative analysis of gene and protein networks. Modeling, analysis, and inference of transcriptional regulatory networks, protein-protein interaction networks, and metabolic networks. Dynamic systems and whole-cell models. Ontology-driven, network based, and probabilistic approaches to information integration.

(Dual-listed with STAT 471). (3-0) Cr. 3. F.S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

The role of statistics in research and the principles of experimental design. Concepts of experimental and observational units, randomization, replication, blocking, subdividing and repeatedly measuring experimental units; factorial treatment designs and confounding; common designs including randomized complete block design, Latin square design, split-plot design, and analysis of data from such common designs; extensions of the analysis of variance to cover variance components. Determining sample size.
Credit in only one of STAT 402, STAT 471, or STAT 571 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 472). (3-0) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Methods for analyzing data collected over time; review of multiple regression analysis. Elementary forecasting methods: moving averages and exponential smoothing. Autoregressive-moving average (Box-Jenkins) models: identification, estimation, diagnostic checking, and forecasting. Transfer function models and intervention analysis. Introduction to multivariate time series methods.
Credit for only one of STAT 451, STAT 472, or STAT 572 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 473). (2-2) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; STAT 341 or STAT 347 or STAT 447 or STAT 588*

Concepts of sample surveys and the survey process; methods of designing sample surveys, including: simple random, stratified, systematic, probability proportional to size, and multistage sampling designs; methods of analyzing sample surveys including ratio, regression, domain estimation and nonresponse.

(Dual-listed with STAT 474). (2-2) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; STAT 342 or STAT 447 or STAT 588.*

Probability models and prior distributions; updating priors through the likelihood function. Computational and simulation-based methods for deriving posterior distributions and for estimating parameters. Basic statistical and hierarchical models. Model adequacy and posterior predictive checks. Markov Chain Monte Carlo methods and introduction to WinBUGS or similar software. Emphasis on applications and examples from the social, biological and physical sciences.
Credit for only one of STAT 444, STAT 474, or STAT 574 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 475). (2-2) Cr. 3. F.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; knowledge of matrix algebra*

Techniques for displaying and analyzing multivariate data including plotting high-dimensional data using interactive graphics; comparing group mean vectors using Hotelling's T2; multivariate analysis of variance; reducing variable dimension with principal components; identifying factors with exploratory factor analysis; grouping observations with multidimensional scaling and cluster analysis; and classification using discriminant analysis, logistic regression, classification trees, and random forests. Introduction to the R statistical software package.
Credit for only one of STAT 407, STAT 475, or STAT 575 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 476). (3-0) Cr. 3. Alt. S., offered even-numbered years.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587; STAT 341 or STAT 447 or STAT 588 or permission of instructor.*

The analysis of spatial data; geostatistical methods, mapping and spatial prediction; methods for areal data; models and methods for spatial point processes. Emphasis on application and practical use of spatial statistical analysis. Use of R and R packages for spatial data analysis.
Credit for only one of STAT 406, STAT 476, or STAT 576 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 477). (3-0) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Statistical methods for the analysis of categorical data: graphical summaries, estimation and inference for proportions, sample size determination, chi-square tests, measures of relative risk, odds and association, analysis of paired data and measures of agreement, logistic regression models, log-linear models.
Credit for only one of STAT 457, STAT 477, or STAT 577 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 478). (3-0) Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 231 or STAT 341 or STAT 347 or STAT 447 or STAT 588*

Probabilistic models in biological, engineering and the physical sciences. Markov chains; Poisson, birth-and-death, renewal, branching and queuing processes; applications to bioinformatics and other quantitative problems.
Credit for only one of STAT 432, STAT 478, or STAT 578 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(0-2) Cr. 1. F.

*Prereq: Enrollment in STAT 500*

An introduction to the logic of programming, numerical algorithms, and graphics. The R statistical programming environment will be used to demonstrate how data can be stored, manipulated, plotted, and analyzed using both built-in functions and user extensions. Concepts of modularization, looping, vectorization, conditional execution, and function construction will be emphasized.

(3-0) Cr. 3. S.

*Prereq: STAT 579; STAT 447 or STAT 588 or STAT 542*

Introduction to scientific computing for statistics using C: Introduction to C for computing and memory efficiency; design of statistical algorithms; use of algorithms in modern libraries, parallel computing. Interfacing R with C. Building statistical libraries. Statistical computing: solving nonlinear equations; optimization; integration; simulation methods, inversion of probability integral transformations, rejection sampling, importance sampling.

(3-0) Cr. 3. S.

*Prereq: STAT 401 or STAT 587*

Introduction to high-throughput technologies for gene expression studies (especially RNA-sequencing technology): the role of blocking, randomization, and biological and technical replication in the design of gene expression experiments; normalization methods; methods for identifying differentially expressed genes including mixed linear model analysis, generalized linear model analysis, generalized linear mixed model analysis, quasi-likelihood methods, empirical Bayes analysis, and resampling based approaches; procedures for controlling false discovery rate for multiple testing; clustering and classification problems for gene expression data; testing gene categories; emphasis on practical use of methods.
May not be used for graduate credit in the Statistics MS and PhD degree programs. Credit in STAT 416 or STAT 581, but not both, may be applied toward graduation.

(Dual-listed with STAT 482). (2-2) Cr. 3. F.S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Applications of generalized linear regression models to social science data. Assumptions of regression; diagnostics and transformations; analysis of variance and covariance; logistic, multinomial and Poisson regression.
Credit for only one of STAT 404, STAT 482, or STAT 582 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 483). (3-0) Cr. 3. F.

*Prereq: STAT 330 or an equivalent course, MATH 166, knowledge of linear algebra.*

Statistical methods for research involving computers; exploratory data analysis; selected topics from analysis of designed experiments - analysis of variance, hypothesis testing, interaction among variables; linear regression, logistic regression, Poisson regression; parameter estimation, prediction, confidence regions, dimension reduction techniques, model diagnostics and sensitivity analysis; Markov chains and processes; simulation techniques and bootstrap methods; applications to computer science, bioinformatics, computer engineering - programs, models and systems as objects of empirical study; communicating results of empirical studies. Statistical software: R.
Credit for only one of STAT 430, STAT 483, or STAT 583 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(Dual-listed with STAT 484). (3-0) Cr. 3. F.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Structure, content and programming aspects of modern statistical software packages. Advanced techniques for data management, graphics, exploratory data analysis, and generalized linear models.
Credit for only one of STAT 479, STAT 484, or STAT 584 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

Cr. 3. Alt. S., offered odd-numbered years.

*Prereq: STAT 579.*

Introduction to computational methods for data analysis. Accessing and managing data formats: flat files, databases, web technologies based on mark-up languages (SML, KML, HTML), netCDF. Elements of text processing: regular expressions for cleaning data. Working with massive data, handling missing data, scaled computing. Efficient programming, reproducible code.

(Dual-listed with STAT 486). (3-0) Cr. 3. S.

*Prereq: STAT 301 or STAT 326 or STAT 401 or STAT 587*

Modern statistical computing. Topics may include: data management; spread sheets; verifying data accuracy; transferring data between software packages; data and graphical analysis with statistical software packages; algorithmic programming concepts and applications; simulation studies and resampling methods; software reliability; statistical modeling and machine learning.
Credit for only one of STAT 480, STAT 486, or STAT 586 may be applied to graduation. May not be used for graduate credit in the Statistics MS and PhD degree programs.

(3-2) Cr. 4. F.S.SS.

*Prereq: An applied statistics course at the undergraduate level, such as STAT 101, 104, 105, 201, or 226. Students without an equivalent course should contact the department.*

A first course in statistics for graduate students from the applied sciences. Principles of data analysis and scientific inference, including estimation, hypothesis testing, and the construction of interval estimates. Statistical concepts and models, including group comparison, blocking, and linear regression. Different sections are designed for students in various disciplines, and additional methods covered may depend on the target audience. Topics covered may include basic experimental designs and analysis of variance for those designs, analysis of categorical data, logistic and log-linear regression, likelihood-based inference, and the use of simulation. Equivalent to STAT 401 in previous catalogs.
May not be used for graduate credit in the Statistics MS and PhD degree programs. Credit in STAT 401 or STAT 587, but not both, may be applied toward graduation.

(4-0) Cr. 4. F.S.SS.

*Prereq: MATH 151 and permission of instructor, or MATH 265*

Provides an introduction to the theoretical basis of fundamental statistical methods for graduate students in the applied sciences. Probability and probability distributions, moments and moment generating functions, conditional expectation, and transformation of random variables. Estimation based on loss functions, maximum likelihood, and properties of estimators. Sampling distributions, exact and asymptotic results, and the development of intervals. Principles of Bayesian analysis, inference from posterior distributions, and optimal prediction. Uses simulation to verify and extend theoretical results. Equivalent to STAT 447 in previous catalogs.
May not be used for graduate credit in the Statistics MS and PhD degree programs. Credit in STAT 447 or STAT 588, but not both, may be applied toward graduation.

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*Prereq: Permission of the department chair*

Off-campus work periods for graduate students in a field of statistics.

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**Courses for graduate students:**

(3-0) Cr. 3. S.

*Prereq: STAT 520, STAT 543 and MATH 414 or enrollment in STAT 641*

Methods of constructing complex models including adding parameters to existing structures, incorporating stochastic processes and latent variables. Use of modified likelihood functions; quasi-likelihoods; profiles; composite likelihoods. Asymptotic normality as a basis of inference; Godambe information. Sample reuse; block bootstrap; resampling with dependence. Simulation for model assessment. Issues in Bayesian analysis.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

*Prereq: STAT 520, STAT 543, STAT 579*

Statistical theory and methods for modern data mining and machine learning, inference, and prediction. Variance-bias trade-offs and choice of predictors; linear methods of prediction; basis expansions; smoothing, regularization, and reproducing kernel Hilbert spaces; kernel smoothing methods; neural networks and radial basis function networks; bootstrapping, model averaging, and stacking; linear and quadratic methods of classification; support vector machines; trees and random forests; boosting; prototype methods; unsupervised learning including clustering, principal components, and multi-dimensional scaling; kernel mechanics.

(3-0) Cr. 3. Alt. F., offered irregularly.

*Prereq: STAT 506, STAT 543*

Consideration of advanced topics in spatial statistics, including areas of recent development in modern spatial statistics. Topics may include spatial sampling design; spatial Markov random fields; non-Gaussian spatial models, including spatial generalized linear mixed effects model; spatial Bayesian hierarchical models, simulation of random fields; spatial-temporal process models; non-stationary process models; multivariate spatial process models; spectral methods for spatial data; computational methods for large spatial data, spatial models for stream networks. Use of R to analyze various real spatial data.

(3-0) Cr. 3. F.

*Prereq: STAT 510; STAT 542 or STAT 447 or STAT 588; a course in matrix algebra*

Matrix preliminaries, estimability, theory of least squares and of best linear unbiased estimation, analysis of variance and covariance, distribution of quadratic forms, extension of theory to mixed and random effects models, restricted maximum likelihood estimation and inference for variance components.

(3-0) Cr. 3. Alt. S., offered irregularly.

*Prereq: STAT 512*

General theory of factorial experiments. Design optimality criteria, approximate design and general equivalence theory, computational approaches to constructing optimal designs for linear models, and extensions to nonlinear models. Advanced topics of current interest in the design of experiments, including one or more of: distance based design criteria and construction of spatial process models, screening design strategies for high-dimensional problems, and design problems associated with computational experiments.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

*Prereq: STAT 544 and STAT 601*

Complex hierarchical and multilevel models, dynamic linear and generalized linear models, spatial models. Bayesian nonparametric methods. Specialized Markov chain Monte Carlo algorithms and practical approaches to increasing mixing and speed convergence. Summarizing posterior distributions, and issues in inference. Model assessment, model selection, and model averaging.

(3-0) Cr. 3. Alt. F., offered irregularly.

*Prereq: STAT 521*

Advanced topics of current interest in the design of surveys and analysis of survey data, including: asymptotic theory for design and model-based estimators, use of auxiliary information in estimation, variance estimation techniques, small area estimation, non-response modeling and imputation.

(Cross-listed with MATH). (3-0) Cr. 3. F.

*Prereq: MATH 414 or MATH 501 or equivalent course.*

Sequences and set theory; Lebesgue measure, measurable functions. Absolute continuity of functions, integrability and the fundamental theorem of Lebesgue integration. General measure spaces, probability measure, extension theorem and construction of Lebesgue-Stieljes measures on Euclidean spaces. Measurable transformations and random variables, induced measures and probability distributions. General integration and expectation, Lp-spaces and integral inequalities. Uniform integrability and absolute continuity of measures. Probability densities and the Radon-Nikodym theorem. Product spaces and Fubini-Tonelli theorems.

(Cross-listed with MATH). (3-0) Cr. 3. S.

*Prereq: STAT 641, or STAT 543 and MATH 515.*

Probability spaces and random variables. Kolmogorov's consistency theorem. Independence, Borel-Cantelli lemmas and Kolmogorov's 0 - 1 Law. Comparing types of convergence for random variables. Sums of independent random variables, empirical distributions, weak and strong laws of large numbers. Convergence in distribution and its characterizations, tightness, characteristic functions, central limit theorems and Lindeberg-Feller conditions. Conditional probability and expectation. Discrete parameter martingales and their properties and applications.

(3-0) Cr. 3. F.

*Prereq: STAT 543, STAT 642*

Sufficiency and related concepts, completeness, exponential families and statistical information. Elements of decision theory, decision rules, invariance and Bayes rule. Maximum likelihood and asymptotic inference. Generalized estimating equations and estimating functions, M-estimation, U-statistics. Likelihood ratio tests, simple and composite hypotheses, multiple testing. Bayesian inference. Nonparametric inference, bootstrap, empirical likelihood, and tests for nonparametric models.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 544 and STAT 642*

Exchangeability, parametric models, consistency and asymptotic normality of posterior distributions, posterior robustness, selection of priors using formal rules, improper priors and posterior propriety, Bayes factors, model selection, MCMC theory, irreducibility, Harris recurrence, regeneration, minorization and drift conditions, ergodicity, central limit theorems, Gibbs samplers, Metropolis Hastings samplers, techniques for speeding up convergence of certain MCMC algorithms.

(Cross-listed with MATH). (3-0) Cr. 3. S.

Weak convergence. Random walks and Brownian motion. Martingales. Stochastic integration and Ito's Formula. Stochastic differential equations and applications.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 543, knowledge of matrix algebra*

Multivariate normal distribution, estimation of the mean vector and the covariance matrix, multiple and partial correlation, Hotelling's T2 statistic, Wishart distribution, multivariate regression, principle components, discriminant analysis, high dimensional data analysis, latent variables.

Cr. arr. Alt. F., offered irregularly.

*Prereq: STAT 543.*

Seminar topics change with each offering.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 551, STAT 642*

Stationary and nonstationary time series models, including ARMA, ARCH, and GARCH. Covariance and spectral representation of time series. Fourier and periodogram analyses. Predictions. CLT for mixing processes. Estimation and distribution theory. Long range dependence.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

*Prereq: STAT 543 and STAT 580*

Normal approximations to likelihoods. The delta-method and propagation of errors. Topics in the use of the E-M algorithm including; its use in the exponential family, computation of standard errors, acceleration. Resampling methods: brief theory and application of the jackknife and the bootstrap. Randomization tests. Stochastic simulation: Markov Chain, Monte Carlo, Gibbs' sampling, Hastings-Metropolis algorithms, critical slowing-down and remedies, auxiliary variables, simulated tempering, reversible-jump MCMC and multi-grid methods.

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*Prereq: Permission of instructor*

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*Prereq: Permission of instructor*

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*Prereq: Permission of instructor*

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*Prereq: Permission of instructor*

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*Prereq: Permission of instructor*

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*Prereq: Permission of instructor*

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