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# Courses in Statistics

This page was created at 7:05 PM on Wed, Oct 10, 2001.

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

Open courses in Statistics
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Wolverine Access Subject listing for STATS

Fall Term '01 Time Schedule for Statistics.

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### STATS 100. Introduction to Statistical Reasoning.

#### Instructor(s):

Prerequisites & Distribution: No credit granted to those who have completed or are enrolled in Soc. 210, Stats. 350, 350, 402, 405, or 412, or Econ. 404 or 405. (4). (MSA). (BS). (QR/1).

Credits: (4).

Course Homepage: http://www.stat.lsa.umich.edu/~bkg/stat100/

Provides an overview of the field of statistics, including methods of summarizing and analyzing data, statistical reasoning for learning from observations (experimental or sample), and techniques for dealing with uncertainties in drawing conclusions from collected data. Emphasis is on presenting underlying concepts rather than covering a variety of different methodologies. Course evaluation is based on a combination of a Thursday evening midterm examination, a final examination, and GSI input. The course format includes lectures and a discussion section (1 hour per week).

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### STATS 265 / IOE 265. Probability and Statistics for Engineers.

#### Instructor(s):

Prerequisites & Distribution: Math. 116 and Engin. 101. No credit granted to those who have completed or are enrolled in Stats. 311, 400, 405, or 412, or Econ. 405. (4). (Excl). (BS). 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.

Engineering is divided into two worlds: deterministic and probabilistic. Your math, physics, and chemistry course preparation to date has concentrated on "deterministic" models: a given set of inputs or conditions repeatedly produce a fixed, completely predictable output. IOE 265 launches your modeling skills into a totally new dimension ... the much more realistic situation wherein a given set of inputs or conditions produce random (or "chance" or "probabilistic" or "stochastic" ) outcomes! Examples include the characteristics of products leaving manufacturing lines (e.g. lifetime of a bulb, concentration of a therapeutic drug), results of laboratory experiments (e.g., growth rates of microorganisms) or processes observed over space or time (e.g. spatial distribution of soil contaminants or time series of rainfall amounts). The field of statistics deals with the collection, presentation, analysis and use of data to make decisions, solve problems and design products and processes.

The first part of the class will be devoted to the presentation of probabilistic concepts which are the building blocks of all statistical procedures that will be introduced in the second (more applied) part of the class. Homeworks and labs will allow students to apply these concepts and learn how to use basic statistical Excel functions to solve problems.

The course prerequisites are Math 116 and Engin 101. IOE 265 is a prerequisite for many undergraduate IOE courses (e.g., 316, 366, 421, 425, 432, 441, 447, 449, 452, 460, 463, 465, 466, 474, 424/491).

Applied Statistics and Probability for Engineers by Douglas C. Montgomery and George C. Runger, Second Edition, 1998. Chapters 1 to 9 will be covered in this course.

• Homeworks: 30% Homeworks will typically be assigned on a Wednesday and are due on Friday the next week, see schedule below. A dropping time and place will be specified later. Solutions to homework problems will be posted on this Website and CAEN Website the day after the due date, hence late homeworks will receive no credit. According to the Engineering Honor Code, all homework assignments are to be completed on your known, without using solutions prepared in prior years. Two lab sessions will be devoted to Technical communication and the related assignment will be graded and counted as homework #11.
• 2 midterm Exams: 40%
• Final Exam: 30% All exams will be closed-book and will consist of a set of multiple choice questions and problems covering both theory and applications. For each midterm, you may use, however, 1 crib sheet (two sides) including all information that you think may be helpful in the examination. The final exam will be comprehensive and 3 double-sided crib sheets will be permitted.

Course outline:

• Data Summary and Presentation
• Concepts of sample and population
• Type of data
• Descriptive statistics
• Data summary and display
• Probabilistic Concepts
• Sample spaces and events
• Axioms of probability
• Conditional probability and independence
• Random variables: discrete and continuous
• Probability Distributions
• Probability mass(density) functions and cumulative distribution functions
• Mean and variance of a random variable (RV)
• Examples of probability distributions
• Discrete RV: uniform, binomial, (hyper)geometric, Poisson
• Continuous RV: Normal, exponential, Gamma, Weibull
• Joint probability distributions
• Parameter Estimation
• Properties of estimators
• Estimation methods
• Sampling distributions & confidence intervals
• Statistical inference
• Hypothesis testing
• Inference on the mean and variance
• Inference on a population proportion
• Goodness of Fit
• Inference for two samples

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### STATS 350(250/402). Introduction to Statistics and Data Analysis.

#### Instructor(s):

Prerequisites & Distribution: No credit granted to those who have completed or are enrolled in Econ. 404 or 405, or Stats. 350, 265, 311, 400, 402, 405, or 412. (4). (NS). (BS). (QR/1).

Credits: (4).

Course Homepage: http://www.stat.lsa.umich.edu/~bkg/stat350/

In this course students are introduced to the concepts and applications of statistical methods and data analysis. Statistics 350 has no prerequisite and has been elected by students whose mathematics background includes only high school algebra. Examples of applications are drawn from virtually all academic areas and some attention is given to statistical process control methods. The course format includes lectures (3 hours per week) and a laboratory (l.5 hours per week). The laboratory section deals with the computational aspects of the course and provides a forum for review of lecture material. For this purpose, students are introduced to the use of a statistical analysis-computer package. Course evaluation is based on a combination of two examinations, a final examination, weekly homework, and lab participation.

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### STATS 400. Applied Statistical Methods.

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

Prerequisites & Distribution: 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). (Excl). (BS).

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 & Distribution: 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). (Excl). (BS). (QR/1).

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 & Distribution: One of Stats. 205 (or 402), 405, 412, or 425. (4). (Excl). (BS).

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 & Distribution: 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). (Excl). (BS).

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 & Distribution: 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). (Excl). (BS).

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 & Distribution: Math. 215, 255, or 285. (3). (Excl). (BS).

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 & Distribution: Math. 215, 255, or 285. (3). (Excl). (BS).

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 & Distribution: Math. 215, 255, or 285. (3). (Excl). (BS).

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 & Distribution: Math. 215, 255, or 285. (3). (Excl). (BS).

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 & Distribution: Math. 215, 255, or 285. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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### STATS 426. Introduction to Theoretical Statistics.

#### Instructor(s):

Prerequisites & Distribution: Stats. 425. (3). (Excl). (BS).

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 & Distribution: Stats. 425. (3). (Excl). (BS).

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 & Distribution: Stats. 265 and Stats. 401 or IOE 366. (4). (Excl). (BS). 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 & Distribution: Stats. 350. (4). (Excl). (BS).

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 499. Honors Seminar.

#### Instructor(s):

Prerequisites & Distribution: Permission of departmental Honors advisor. (2-3). (Excl). (INDEPENDENT).

Credits: (2-3).

Course Homepage: No homepage submitted.

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### STATS 500. Applied Statistics I.

#### Instructor(s):

Prerequisites & Distribution: Math. 417, and Stats. 350 (or 402) or 426. (3). (Excl). (BS).

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 & Distribution: Stats. 500. (3). (Excl). (BS).

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 & Distribution: Stats. 401 or 500. (3). (Excl). (BS). 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 & Distribution: Permission of instructor. (3). (Excl). (BS).

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 & Distribution: Math. 450 or 451, and a course in probability or statistics. (3). (Excl). (BS).

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

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 & Distribution: Stats. 425. (3). (Excl). (BS). 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 & Distribution: Math. 417 and 425, or Econ. 671, 672, and 600. (3). (Excl). (BS).

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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### Graduate Course Listings for STATS.

This page was created at 7:05 PM on Wed, Oct 10, 2001.