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# Courses in Statistics

This page was created at 6:19 PM on Wed, Jan 21, 2004.

## Winter Academic Term 2004 (January 6 - April 30)

### STATS 400. Applied Statistical Methods.

#### Instructor(s): Bendek B Hansen (bbh@umich.edu)

Prerequisites: High School Algebra. (4). May not be repeated for credit. No credit granted to those who have completed or are enrolled in ECON 404 or 405, or STATS 250, 265, 350, 405, or 412.

Credits: (4).

Course Homepage: http://coursetools.ummu.umich.edu/2004/winter/stats/400/001.nsf

Statistics and the scientific method; observational study versus designed experiment; visualization; introduction to probability; statistical inference; confidence intervals; one-sample tests of hypothesis; two-sample problems; analysis of variance (ANOVA); blocked designs; tests for association and independence (chi-square tests); regression and correlation; and non-parametric tests. Course format includes lectures (3 hours per week) and a laboratory (1.5 hours per week).

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### STATS 401(403). Applied Statistical Methods II.

#### Instructor(s): Kerby A Shedden (kshedden@umich.edu)

Prerequisites: MATH 115, and STATS 350 or 400. (4). May not be repeated for credit. No credit granted to those who have completed or are enrolled in STATS 413.

Credits: (4).

Course Homepage: http://www.stat.lsa.umich.edu/~kshedden/Courses/Stat401/index.html

An intermediate course in applied statistics, covering a range of topics in modeling and analysis of data including: review of simple linear regression, two-sample problems, one-way analysis of variance; multiple linear regression, diagnostics and model selection; two-way analysis of variance, multiple comparisons, and other selected topics. Three hours of lecture supplemented by one and one-half hours of laboratory.

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### STATS 405 / ECON 405. Introduction to Statistics.

#### Instructor(s): Elizaveta Levina (elevina@umich.edu)

Prerequisites: MATH 116. Juniors and seniors may elect this course concurrently with ECON 101 or 102. (4). May not be repeated for credit. No credit granted to those who have completed or are enrolled in IOE 265, STATS 265, 400 or 412. Students with credit for ECON 404 can only elect STATS 405 for 2 credits and must have permission of instructor.

Credits: (4).

Course Homepage: http://www.stat.lsa.umich.edu/~elevina/stat405/index.html

The purpose of this course is to provide students with an understanding of the principles of statistical inference. Topics include probability, experimental and theoretical derivation of sampling distributions, hypothesis testing, estimation, and simple regression. (Students are advised to elect the sequel, ECON 406.)

TEXTBOOK: Statistics: Theory and Methods, Berry/Lindgren, 2nd Edition.

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### STATS 408. Statistical Principles for Problem Solving: A Systems Approach.

#### Instructor(s): Edward Rothman (erothman@umich.edu)

Prerequisites: High school algebra. (4). May not be repeated for credit. No credit granted to those who have completed or are enrolled in STATS 170.

Credits: (4).

Course Homepage: http://coursetools.ummu.umich.edu/2004/winter/stats/408/001.nsf

Our purpose is to help students use quantitative reasoning to facilitate learning. Specifically, we introduce statistical and mathematical principles, and then use these as analogues in a variety of real world situations. The notion of a system, a collection of components that come together repeatedly for a purpose, provides an excellent framework to describe many real world phenomena and provides a way to view the quality of an inferential process.

Evaluation is focused on clear writing that illustrates understanding of the theory by providing new applications of the theory. Points are obtained from four activities: a journal (max 20 points); test score (max 30 points); and discussion section leader bonus (max 5 additional points).

TEXTBOOKS:

• Theory of Constraints, E. Goldratt, Northriver Press;
• The Goal, E. Goldratt, Northriver Press;
• The Fifth Discipline, Peter M. Senge, Doubleday Currency; and
• The New Economics for Industry Government Education, W. Edwards Deming, 2nd Edition, MIT.

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### STATS 412. Introduction to Probability and Statistics.

#### Instructor(s): Elizaveta Levina (elevina@umich.edu)

Prerequisites: Prior or concurrent enrollment in MATH 215 and EECS 183. (3). May not be repeated for credit. No credit granted to those who have completed or are enrolled in ECON 405, STATS 265, 400, or 405, or IOE 265. One credit granted to those who have completed or are enrolled in STATS 350.

Credits: (3).

Course Homepage: http://www.stat.lsa.umich.edu/~elevina/stat412/index.html

The objectives of this course are to introduce students to the basic ideas of probability and statistical inference and to acquaint students with some important data analytic techniques, such as regression and the analysis of variance. Examples will emphasize applications to the natural sciences and engineering. There will be regular homework, two midterms, and a final exam.

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### STATS 413. The General Linear Model and Its Applications.

#### Instructor(s): Yongyun Shin (choil@umich.edu)

Prerequisites: STATS 350 and MATH 217; concurrent enrollment in STATS 425. Students who have not taken MATH 217 should elect STATS 401. (4). May not be repeated for credit. Two credits granted to those who have completed STATS 403. Graduate credit for students outside the Stat. department.

Credits: (4).

Course Homepage: No homepage submitted.

This course will introduce students to the general linear model and its assumptions, and will cover topics such as the geometry of the model projections, least squares estimation, residuals, normal distribution theory results, inference on parameters, diagnostic tools, and applications in analysis of variance, design, and the series. Three hours of lecture and 1.5 hours of lab per week. Regular homework and a final exam.

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### STATS 425 / MATH 425. Introduction to Probability.

#### Instructor(s): Statistics faculty

Prerequisites: MATH 215, 255, or 285. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

Basic concepts of probability; expectation, variance, covariance; distribution functions; and bivariate, marginal, and conditional distributions.

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### STATS 425 / MATH 425. Introduction to Probability.

#### Instructor(s): Mathematics faculty

Prerequisites: MATH 215, 255, or 285. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

See MATH 425.

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### STATS 425 / MATH 425. Introduction to Probability.

#### Instructor(s): Sergey Fomin (fomin@umich.edu)

Prerequisites: MATH 215, 255, or 285. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: http://www.math.lsa.umich.edu/~fomin/425w04.html

See MATH 425.003.

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### STATS 426. Introduction to Theoretical Statistics.

#### Instructor(s): Moulinath Banerjee (moulib@umich.edu)

Prerequisites: STATS 425. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

This course covers the basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric testing, and Bayesian inference. The sequence of STATS 425/426 serves as a prerequisite for more advanced Statistics courses. Regular homework and a final exam.

Topic covered include:

 Random Variables Joint Distributions Induced Distributions Expectation The Law of Large Numbers The Central Limit Theorem Simulation Populations and Samples The Chi-squared, t, and F Distributions Estimation: The Method of Moments Maximum Likelihood Estimation Bias, Variance, and MSE The Cramer Rao Inequality Exponential Families and Sufficiency Confidence Intervals Approximate Confidence Intervals The Bootstrap Asymptotics of the MLE Tests and Confidence Intervals Neyman Pearson Likelihood Ratio Tests Chi-Squared Tests Goodness of Fit Tests The Sample Distribution Function Decision Analysis Bayesian Inference The Two Sample Problem More on the Two Sample Problem Rank Tests One Way ANOVA Simultaneous Confidence Two Way ANOVA Categorical Data Simple Linear Regression Multiple Regression

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### STATS 430. Applied Probability.

#### Instructor(s): George Michailidis (gmichail@umich.edu)

Prerequisites: STATS 425. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

Review of probability theory; introduction to random walks; counting and Poisson processes; Markov chains in discrete and continuous time; equations for stationary distributions; introduction to Brownian motion. Selected applications such as branching processes, financial modeling, genetic models, the inspection paradox, inventory and queuing problems, prediction, and/or risk analysis. Selected optional topics such as hidden Markov chains, martingales, renewal theory, and/or stationary process.

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### STATS 466 / IOE 466 / MFG 466. Statistical Quality Control.

#### Instructor(s): Justin Wayne Kile

Prerequisites: STATS 265 and 401 or IOE 366. (4). May not be repeated for credit. CAEN lab access fee required for non-Engineering students.

Credits: (4).

Lab Fee: CAEN lab access fee required for non-Engineering students.

Course Homepage: http://coursetools.ummu.umich.edu/2004/winter/ioe/466/001.nsf

Quality improvement philosophies; Modeling process quality, statistical process control, control charts for variables and attributes, CUSUM and EWMA, short production runs, multivariate quality control, auto correlation, engineering process control economic design of charts, fill control, precontrol, adaptive schemes, process capability, specifications and tolerances, gage capability studies, acceptance sampling by attributes and variables, international quality standards.

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### STATS 470. Introduction to the Design of Experiments.

#### Instructor(s): Nancy S Boudreau (nboudre@umich.edu)

Prerequisites: STATS 401. (4). May not be repeated for credit.

Credits: (4).

Course Homepage: No homepage submitted.

This course will introduce students to basic principles in classical experimental design, including randomization, replication, confounding, interaction, covariates, and use of the general linear model. Students will be introduced to the following designs: completely randomized, randomized blocks, Latin squares, incomplete blocks, factorial, split plot, Taguchi, response surface, and optimal. There will be regular assignments and a final exam. Class format is 3 hours of lecture and 1.5 hours of laboratory per week.

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### STATS 501. Applied Statistics II.

#### Instructor(s): Julian J Faraway (faraway@umich.edu)

Prerequisites: STATS 500. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: http://www.stat.lsa.umich.edu/~faraway/stat501/

Generalized Linear Models, Analysis of binary and categorical data, Log-linear models, Random and mixed effects models, Smoothing and non-parametric regression, Generalized Additive models, Regression and classification trees, Neural Networks.

Course pack.

The following books are recommended

• Generalized Linear Models by Nelder & McCullagh (2nd Ed, Chapman Hall),
• Applying Generalised Linear Models by Lindsey (Springer),
• Modelling Binary Data by Collett (Chapman Hall)
• Categorical Data Analysis by Agresti (Wiley),
• Generalized Additive Models by Hastie & Tibshirani (Chapman Hall)

Assessment: Assignments worth 30%; Midterm worth 30%; Final worth 40%. All examinations are open book.

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### STATS 503. Applied Multivariate Analysis.

#### Instructor(s): George Michailidis (gmichail@umich.edu)

Prerequisites: STATS 500. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

Topics in applied multivariate analysis including Hotelling's T2 multivariate ANOVA, discriminant functions, factor analysis, principal components, canonical correlations, and cluster analysis. Selected topics from: maximum likelihood and Bayesian methods, robust estimation and survey sampling. Applications and data analysis using a computer will be stressed.

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### STATS 525 / MATH 525. Probability Theory.

#### Instructor(s): Gautam Bharali

Prerequisites: MATH 451 (strongly recommended) or 450. STATS 425 would be helpful. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

See MATH 525.001.

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### STATS 526 / MATH 526. Discrete State Stochastic Processes.

#### Instructor(s): Charles R Doering

Prerequisites: STATS 525 or EECS 501. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

Review of discrete distributions; generating functions; compound distributions, renewal theorem; modeling of systems as Markov chains; first properties; Chapman-Kolmogorov equations; return and first passage times; classification of states and periodicity; absorption probabilities and the forward equation; stationary distributions and the backward equation; ergodicity; limit properties; application to branching and queueing processes; examples from engineering, biological, and social sciences; Markov chains in continuous time; embedded chains; the M/G/1 queue; Markovian decision processes; application to inventory problems; other topics at instructor's discretion.

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### STATS 531 / ECON 677. Analysis of Time Series.

#### Instructor(s): Edward L Ionides

Prerequisites: STATS 426. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: http://www.stat.lsa.umich.edu/~ionides/531/

See ECON 677.001.

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### STATS 545 / BIOINF 545 / BIOSTAT 646. Data Analysis in Molecular Biology.

#### Instructor(s): Zhaohui Qin

Prerequisites: STAT 400 and graduate standing. Students should have a strong preparation in either biology or some branch of quantitative analysis (mathematics, statistics, or computer science), but not necessarily in both domains. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

This course will cover statistical methods used to analyze data in experimental molecular biology, with an emphasis on gene and protein expression array data. Topics: data acquisition, databases, low level processing, normalization, quality control, statistical inference (group comparisons, cyclicity, survival), multiple comparisons, statistical learning algorithms, clustering visualization, and case studies.

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### STATS 547 / MATH 547 / BIOINF 547. Probabilistic Modeling in Bioinformatics.

#### Instructor(s): Daniel M Burns Jr

Prerequisites: STATS 425 or MCDB 427 or BIOLCHEM 415; basic programming skills desirable. Graduate standing and permission of instructor. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: http://www.math.lsa.umich.edu/~dburns/547/547syll.html

See MATH 547.001.

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### STATS 548 / MATH 548. Computations in Probabilistic Modeling in Bioinformatics.

#### Instructor(s):

Prerequisites: STATS 425 or MCDB 427 or BIOLCHEM 415; basic programming skills desirable. Graduate standing and permission of instructor. (1). May not be repeated for credit.

Credits: (1).

Course Homepage: http://www.math.lsa.umich.edu/~dburns/547/547syll.html

See MATH 548.

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### STATS 553 / PHIL 553. Conceptual Foundations of Statistical Inference.

#### Instructor(s): James M Joyce (jjoyce@umich.edu) , Michael B Woodroofe (michaelw@umich.edu)

Prerequisites: A course in statistical theory (STAT 405, PSYCH 613, ECON 405) and upperclass standing. (3-4). May not be repeated for credit.

Credits: (3-4).

Course Homepage: https://coursetools.ummu.umich.edu/2004/winter/phil/553/001.nsf

See PHIL 553.001.

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### STATS 575 / ECON 678. Econometric Theory I.

#### Instructor(s): Atsushi Inoue (inoue@umich.edu)

Prerequisites: ECON 671, 672, and 600. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

See ECON 678.001.

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### STATS 606. Statistical Computing.

#### Instructor(s): Kerby A Shedden (kshedden@umich.edu)

Prerequisites: Calculus, Linear Algebra, some knowledge of Probability and Statistics. Graduate standing. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: http://www.stat.lsa.umich.edu/~kshedden/Courses/Stat606/index.html

This course aims to give an overview of techniques in numerical analysis that are useful in the advanced practice of statistics. The course is roughly divided into three parts:

1. evaluation of special functions, numerical linear algebra (linear solvers, matrix factorizations, eigenvalue problems),
2. optimization (unconstrained methods, simplex method, active set methods, penalty function methods, combinatorial optimization), and
3. simulation (importance and rejection sampling, Markov chain methods, exact methods).

The course will cover some theoretical issues, but primarily will focus on the design and implementation of algorithms.

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### STATS 611(511) Mathematical Statistics II.

#### Instructor(s): Robert W Keener (keener@umich.edu)

Prerequisites: STAT 610. Graduate standing. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

More on the theory of estimation including: minimax, Bayes and James-Stein estimators. The theory of hypothesis testing including: tests significance levels, power, the Neyman-Pearson lemma, uniformly most powerful unbiased tests, monotone likelihood ratios, locally best tests, similar tests, likelihood ratio tests and the associated large sample theory, sequential tests, goodness of fit tests, and tests in contingency tables. Other topics include: confidence regions, introduction to the general linear model, and non-parametric methods.

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### STATS 617. Advanced Topic in Quantitative Methodology.

#### Instructor(s): Bendek B Hansen (bbh@umich.edu)

Prerequisites: Graduate standing. (3). May be repeated for credit for a maximum of 6 credits.

Credits: (3).

Course Homepage: No homepage submitted.

This course explores and critiques advanced methods for conducting quantitative research in the social sciences. A special topic is chosen for a particular semester, with relevant methods drawn from a wide variety of disciplines, including economics, education, epidemiology, psychology, sociology, and statistics. Particular attention is paid to quasi-experimental and observational research designs.

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### STATS 621. Theory of Probability II.

#### Instructor(s): Anna Amirdjanova (anutka@umich.edu)

Prerequisites: STATS 620. Graduate standing. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

A continuation of STATS 620. Topics covered include: weak convergence, characteristic functions, inversion, unicity and continuity, the central limit theorem for sequences and arrays aud, extensions to higher dimensions. Also: the renewal theorem, conditional probability and expectation, regular conditional distributions, stationary sequences aud the bergodic theorem, martingales, and the optimal stopping theorem. The course will also cover: the Poisson process, Brownian motion, the strong Markov property and the invariance principle.

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### STATS 640 / BIOSTAT 890. Multivariate Statistical Models.

#### Instructor(s): Anant M Kshirsagar

Prerequisites: MATH 417 and either STATS 511 or BIOSTAT 602; Graduate standing and permission of instructor. (3). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

Wishart distribution, multivariate linear models, multivariate regression, Hotelling's T-square and its applications, discriminant analysis, canonical correlations, principal components analysis, growth curves.

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#### Instructor(s):

Prerequisites: Graduate standing and permission of instructor. (1-6). (INDEPENDENT). May be elected for a maximum of 5 credits. May be elected more than once in the same term.

Credits: (1-6).

Course Homepage: No homepage submitted.

Designed for individual students who have an interest in a specific topic (usually that has stemmed from a previous course). An individual instructor must agree to direct such a reading, and the requirements are specified when approval is granted.

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### STATS 809. Seminar in Applied Statistics II.

#### Instructor(s): Moulinath Banerjee (moulib@umich.edu)

Prerequisites: Graduate standing. (1). May not be repeated for credit.

Credits: (1).

Course Homepage: No homepage submitted.

No Description Provided. Contact the Department.

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### STATS 811. Literature Proseminar II.

#### Instructor(s): George Michailidis (gmichail@umich.edu)

Prerequisites: Graduate standing and permission of instructor. (2). May not be repeated for credit.

Credits: (2).

Course Homepage: No homepage submitted.

This course is designed to acquaint students with classical papers in mathematical and applied statistics and probability theory, to encourage them in critical independent reading, and to permit them to gain pedagogical experience during the course of their graduate training.

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### STATS 816. Interdisciplinary Seminar in the Physical Sciences.

#### Instructor(s): Michael B Woodroofe (michaelw@umich.edu)

Prerequisites: STATS 426; Graduate standing. (1-4). May be repeated for credit for a maximum of 12 credits.

Credits: (1-4).

Course Homepage: No homepage submitted.

The seminar will consider statistical questions that arise in the physical sciences. Topics will be drawn from current research projects, will vary each semester. Meetings will feature lectures by faculty from the University and selected visitors. Students will be expected to complete a course project and present to group.

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### STATS 990. Dissertation/Precandidate.

#### Instructor(s):

Prerequisites: Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing. (1-8). (INDEPENDENT). May be repeated for credit. This course has a grading basis of "S" or "U."

Credits: (1-8; 1-4 in the half-term).

Course Homepage: No homepage submitted.

Election for dissertation work by doctoral student not yet admitted as a candidate.

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### STATS 993. Graduate Student Instructor Training Program.

#### Instructor(s): Brenda K Gunderson (bkg@umich.edu)

Prerequisites: Graduate standing. (1). May not be repeated for credit. This course has a grading basis of "S" or "U."

Credits: (1).

Course Homepage: No homepage submitted.

A seminar for all beginning graduate student instructors, consisting of a two-day orientation before the term starts and periodic workshops/meetings during the term. Beginning graduate student instructors are required to register for this course.

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### STATS 995. Dissertation/Candidate.

#### Instructor(s):

Prerequisites: Graduate School authorization for admission as a doctoral Candidate (Prerequisites enforced at registration). (8). (INDEPENDENT). May be repeated for credit. This course has a grading basis of "S" or "U."

Credits: (8; 4 in the half-term).

Course Homepage: No homepage submitted.

Graduate school authorization for admission as a doctoral candidate. N.B. The defense of the dissertation (the final oral examination) must be held under a full term candidacy enrollment period.

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### Undergraduate Course Listings for STATS.

This page was created at 6:19 PM on Wed, Jan 21, 2004.