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# Courses in Statistics

This page was created at 9:28 AM on Thu, Oct 11, 2001.

## Fall Academic Term, 2001 (September 5 – December 21)

Open courses in Statistics
(*Not real-time Information. Review the "Data current as of: " statement at the bottom of hyperlinked page)

Wolverine Access Subject listing for STATS

Fall Term '01 Time Schedule for Statistics.

To see what graduate courses have been added to or changed in Statistics this week go to What's New This Week.

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### STATS 400. Applied Statistical Methods.

#### Instructor(s): Derek R. Bingham (dbingham@umich.edu)

Prerequisites: High School Algebra. No credit granted to those who have completed or are enrolled in Econ. 404 or 405, or Stats. 350, 350, 265, 402, 405, or 412. (4).

Credits: (4).

Course Homepage: http://www.stat.lsa.umich.edu/~dbingham/Stat400/index.html

This course is aimed at advanced undergraduate students and graduate students from disciplines outside of Statistics. The course will introduce students to a broad range of applied statistical methods involved in data collection, analysis and visualization. Emphasis will be placed on using statistical methods to answer real-world problems. 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 405 / ECON 405. Introduction to Statistics.

#### Instructor(s):

Prerequisites: Math. 116 or 118. Juniors and seniors may elect this course concurrently with Econ. 101 or 102. No credit granted to those who have completed or are enrolled in Stats. 265, 311, 400 or 412. Students with credit for Econ. 404 can only elect Stats. 405 for 2 credits and must have permission of instructor. (4).

Credits: (4).

Course Homepage: http://coursetools.ummu.umich.edu/2001/fall/econ/405/001.nsf

Principles of statistical inference, including: probability, experimental and theoretic derivation of sampling distributions, hypothesis testing, estimation, and simple regression.

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### STATS 406. Introduction to Statistical Computing.

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

Prerequisites: One of Stats. 205 (or 402), 405, 412, or 425. (4). Graduate credit for students outside the Stat. department.

Credits: (4).

Course Homepage: http://www.stat.lsa.umich.edu/~kshedden/Courses/Stat406/index.html

Acquaints students with selected topics in statistical computing, including basic numerical aspects, iterative statistical methods, principles of graphical analyses, simulation and Monte Carlo methods, generation of random variables, stochastic modeling, importance sampling, numerical and Monte Carlo integration. Three hours of lecture and one and one-half hour laboratory session each week.

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

#### Instructor(s):

Prerequisites: Prior or concurrent enrollment in Math. 215 and CS 183. No credit granted to those who have completed or are enrolled in Econ. 405, or Stats. 265, 311, 350, 400, or 405. One credit granted to those who have completed Stats. 350 or 402. (3).

Credits: (3).

Course Homepage: No homepage submitted.

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):

Prerequisites: Stats. 350 (or 402) and Math. 217; concurrent enrollment in Stat. 425. Students who have not taken Math. 217 should elect Stat. 401. Two credits granted to those who have completed Stats. 403. (4). 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): Sergey Fomin (fomin@umich.edu)

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

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

See Mathematics 425.001.

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

#### Instructor(s): Jeganathan

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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

#### Instructor(s): Brent Carswell (carswell@umich.edu)

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

Course Homepage: http://www.math.lsa.umich.edu/~carswell/math425/

See Mathematics 525.003.

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

#### Instructor(s): Stephen S Bullock (stephns@umich.edu)

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

Course Homepage: http://www.math.lsa.umich.edu/~stephnsb/cur425/math425005.html

See Mathematics 425.005.

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

#### Instructor(s): Amirdjanova

Prerequisites: Math. 215, 255, or 285. (3).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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### STATS 426. Introduction to Theoretical Statistics.

#### Instructor(s):

Prerequisites: Stats. 425. (3).

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 Statistics 425/426 serves as a prerequisite for more advanced Statistics courses, regular homework and a final exam.

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
More on 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).

Credits: (3).

Course Homepage: http://www.stat.lsa.umich.edu/~gmichail/stat430-F01/

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.

Book: Introduction to Probability Models (7th ed.), by Sheldon Ross. Assignments: 6 homework assignments. Grading: – homeworks 45% . – midterm 20% – final 35%

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

#### Instructor(s): Shi

Prerequisites: Stats. 265 and Stats. 401 or IOE 366. (4). CAEN lab access fee required for non-Engineering students.

Credits: (4).

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

Course Homepage: No homepage submitted.

Design and analysis of procedures for forecasting and control of production processes. Topics include: attribute and variables sampling plans; sequential sampling plans; rectifying control procedures; charting, smoothing, forecasting, and prediction of discrete time series.

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

#### Instructor(s):

Prerequisites: Stats. 350. (4).

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, 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, 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 500. Applied Statistics I.

#### Instructor(s):

Prerequisites: Math. 417, and Stats. 350 (or 402) or 426. (3).

Credits: (3).

Course Homepage: No homepage submitted.

Course outline:

Linear Models: Definition, fitting, inference, interpretation of results, meaning of regression coefficients, identifiablity, lack of fit, multicollinearity, ridge regression, principal components regression, partial least squares, regression splines, Gauss-Markov theorem, variable selection, diagnostics, transformations, influential observations, robust procedures, ANOVA and analysis of covariance, . Randomised block, factorial designs.

Computing: The software I will be using for the course is R. R is very similar to S+, the software I have used for this course in the past. R is free with Windows and Unix versions. You can download your own copy and use it wherever you find convenient.

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### STATS 503. Applied Multivariate Analysis.

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

Prerequisites: Stats. 500. (3).

Credits: (3).

Course Homepage: http://www.stat.lsa.umich.edu/~gmichail/stat503-F01/

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 504. Statistical Consulting.

#### Instructor(s):

Prerequisites: Stats. 401 or 500. (3). May be elected for a total of nine credits.

Credits: (3).

Course Homepage: No homepage submitted.

Applications of statistics to problems in engineering, physical and social sciences; students will be expected to analyze data and write reports.

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### STATS 505 / ECON 671. Econometric Analysis I.

#### Instructor(s): Howrey

Prerequisites: Permission of instructor. (3).

Credits: (3).

Course Homepage: No homepage submitted.

This course is designed for first-year graduate students in economics, business, and related subjects. It involves a fairly rigorous development of statistical reasoning and methods relating to hypothesis testing, estimation, and regression analysis. Students are supposed to have had a course in calculus and in introductory statistics. Knowledge of matrix algebra is required. Evaluation of students is based on midterm and final examinations and weekly assignments. Students taking this course are expected to take Economics 674 – Econometric Analysis II in the following term.

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### STATS 510. Mathematical Statistics I.

#### Instructor(s):

Prerequisites: Math. 450 or 451, and a course in probability or statistics. (3).

Credits: (3).

Course Homepage: No homepage submitted.

Review of probability, exponential families, sufficiency, completeness, Basu's Theorem, unbiased estimation, curved exponential families, information inequalities, conditional probability, Bayesian estimation, large sample theory.

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

#### Instructor(s):

Prerequisites: Math. 450 or 451. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 525 for only one credit. (3).

Credits: (3).

Course Homepage: No homepage submitted.

See Mathematics 525.001.

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### STATS 550 / IOE 560 / SMS 603. Bayesian Decision Analysis.

#### Instructor(s):

Prerequisites: Stats. 425. (3). CAEN lab access fee required for non-Engineering students.

Credits: (3).

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

Course Homepage: No homepage submitted.

This course covers advanced aspects of Bayesian models and inference. Topics include a selection of the following: axiomatic development of subjective probability and utility; interpretation and assessment of personal probability and utility; formulation of Bayesian decision problems; risk functions and admissibility; likelihood principle and properties of likelihood functions; natural conjugate prior distributions; improper and finitely additive prior distributions; examples of posterior distributions, including the general regression model and contingency tables; Bayesian credible intervals and hypothesis tests; applications to a variety of decision-making situations; and numerical methods including importance sampling and Markov chain Monte Carlo.

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

#### Instructor(s): Shinichi Sakata (ssakata@umich.edu)

Prerequisites: Math. 417 and 425, or Econ. 671, 672, and 600. (3).

Credits: (3).

Course Homepage: http://coursetools.ummu.umich.edu/2001/fall/econ/678/001.nsf02.nsf

The purpose of this course is to develop the results of asymptotic distribution theory needed for statistical inference in econometrics and to use these results to derive the properties of various estimators and test procedures used in econometrics. The course is a prerequisite for Statistics 576 (Econometric Theory II).

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### STATS 580 / SOC 717 / BIOSTAT 617. Methods and Theory of Sample Design.

#### Instructor(s):

Prerequisites: Three or more courses in statistics and preferably a course in methods of survey sampling. (3).

Credits: (3).

Course Homepage: http://coursetools.ummu.umich.edu/2001/fall/biostat/617/001.nsf

Methods and Theory of Sample Design is concerned with the theory underlying the methods of survey sampling widely used in practice. It covers the basic techniques of simple random sampling, stratification, systematic sampling, cluster and multi-stage sampling, and probability proportional to size sampling. It also examines methods of variance estimation for complex sample designs, including the Taylor series expansion method, balanced repeated replications, and jackknife methods. It will cover several specialized topics, including stratification and subclasses, multi-phase or double sampling, ratio estimation, selection with unequal probabilities without replacement, non-response adjustments, imputation, and small area estimation. The course will examine both the practical applications of the sampling techniques presented as well as the theory supporting the methods.

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### STATS 600. Advanced Topics in Applied Statistics I and II.

#### Instructor(s):

Prerequisites: Stat. 501 and Graduate standing. (3).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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### STATS 610. Mathematical Statistics I.

#### Instructor(s):

Prerequisites: Math. 601 and 625. Graduate standing. (3).

Credits: (3).

Course Homepage: No homepage submitted.

Review of probability theory including: probability, conditioning, independence, random variables, standard distributions, exponential families, inequalities and a central limit theorem. Introduction to decision theory including: models, parameter spaces, decision rules, risk functions, Bayes versus classical approaches, admissibility, minimax rules, likelihood functions and sufficiency. Estimation theory including unbiasedness, complete sufficient statistics, Lehmann-Scheffe and Rao-Blackwell theorems and various types of estimators.

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### STATS 620. Theory of Probability I.

#### Instructor(s):

Prerequisites: Math. 451 or the equivalent. Graduate standing. (3).

Credits: (3).

Course Homepage: No homepage submitted.

Basics of probability at an advanced level. Specific topics include: discrete probability spaces, the weak law of large numbers, the de Moivre-Laplace theorems, classes of sets, algebras, measures, extension of measures, countable additivity and Lebesgue and product measures. Also: measurable functions, random variables, conditional probability, independence, the Borel-Cantelli lemmas and the zero-one law. The course will additionally cover: integration, convergence theorems, inequalities, Fubini's theorem, the Radon-Nikodym theorem, distribution functions, expectations, and the strong law of large numbers.

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### STATS 625 / MATH 625. Probability and Random Processes I.

#### Instructor(s): Joseph Conlon (conlon@umich.edu)

Prerequisites: Math. 597. Graduate standing. (3).

Credits: (3).

Course Homepage: http://www.math.lsa.umich.edu/~conlon/math625.html

See Mathematics 625.001.

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### STATS 642 / BIOSTAT 851. Linear Statistical Models.

#### Instructor(s):

Prerequisites: Math. 417 and either Stat. 511 or Biostat. 602. Graduate standing. (3).

Credits: (3).

Course Homepage: No homepage submitted.

General linear model, estimability,Gauss-Markov theorem, general linear hypothesis, analysis of variance and covariance, multiple comparisons, variance components.

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### STATS 670. Intermediate Sampling Theory.

#### Instructor(s):

Prerequisites: Stat. 426 and 575 and Graduate standing. (3).

Credits: (3).

Course Homepage: http://www.stat.lsa.umich.edu/~jeffwu/stat670.htm

Recent developments in the foundations and methodology of sampling finite populations. Identifiability of units, likelihood of units, likelihood functions, admissibility of standard estimators, randomization, use of prior information in design and inference. Models for non-sampling errors including bias, response error and non-response. Other topics of current interest.

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

Credits: (1-6).

Course Homepage: http://www.stat.lsa.umich.edu/~gmichail/stat700-F01/

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 808. Seminar in Applied Statistics I.

#### Instructor(s): Bingham

Credits: (1).

Course Homepage: No homepage submitted.

No Description Provided.

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### STATS 810. Literature Proseminar I.

#### Instructor(s): Woodroofe

Prerequisites: Graduate standing and permission of instructor. (2).

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 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.

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)

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 Winter Academic Term. Beginning graduate student instructors are required to register for this class.

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### STATS 995. Dissertation/Candidate.

#### Instructor(s):

Prerequisites: Graduate School authorization for admission as a doctoral Candidate. Graduate standing. (8). (INDEPENDENT). May be repeated for credit.

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 9:28 AM on Thu, Oct 11, 2001.