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# Courses in Statistics

This page was created at 1:26 PM on Thu, Mar 13, 2003.

## Fall Academic Term, 2003 (September 2 - December 19)

Search the LS&A Course Guide

### STATS 100. Introduction to Statistical Reasoning.

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

Prerequisites & Distribution: (4). (MSA). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in SOC 210, STATS 265, 350, 400, 405, or 412, IOE 265, or ECON 404 or 405.

Credits: (4).

Course Homepage: No homepage submitted.

This course will provide an overview of the field of Statistics. It will expose students to statistical reasoning and concepts for dealing with uncertainty, visualizing and analyzing data, and drawing conclusions from experimental or observational data. Emphasis is on presenting underlying concepts rather than covering a variety of different methodologies. Course evaluation is based on a combination of in-class quizzes, weekly homework, a Thursday evening midterm examination, a final examination, and GSI input. The course format includes lectures and a discussion section (1 hour per week) Homework There will be weekly homework assignments, available each Monday on the web, which will be collected and graded. Problems assigned (and their corresponding solutions) will be posted on the web for viewing and printing. There will be four in-class quizzes during the semester.

Textbook:
Interactive Statistics
Aliaga/Gunderson
Prentice-Hall

Student Solutions Manual

TI-83 Calculator *Required.*

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

#### Instructor(s):

Prerequisites & Distribution: MATH 116 and ENGR 101. (4). (Excl). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in STATS 311, 400, 405, or 412, or ECON 405. 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., IOE 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: (4). (NS). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in ECON 404 or 405, or IOE 265 or STATS 265, 400, 405, or 412.

Credits: (4).

Course Homepage: No homepage submitted.

In this course students are introduced to the concepts and applications of statistical methods and data analysis. STATS 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 (1.5 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): Bendek B Hansen

Prerequisites & Distribution: High School Algebra. (4). (Excl). (BS). (QR/1). 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: No homepage submitted.

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): Kirsten T Namesnik

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

Credits: (4).

Course Homepage: No homepage submitted.

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.

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

#### Instructor(s): Sarah L Senesky

Prerequisites & Distribution: MATH 116. Juniors and seniors may elect this course concurrently with ECON 101 or 102. (4). (Excl). (BS). (QR/1). 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: No homepage submitted.

No Description Provided. Contact the Department.

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

#### Instructor(s):

Prerequisites & Distribution: MATH 116. Juniors and seniors may elect this course concurrently with ECON 101 or 102. (4). (Excl). (BS). (QR/1). 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: No homepage submitted.

See Economics 405.001.

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### STATS 406. Introduction to Statistical Computing.

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

Prerequisites & Distribution: One of STATS 401, 412, or 425. (4). (Excl). (BS). May not be repeated for credit.

Credits: (4).

Course Homepage: No homepage submitted.

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, and 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): Elizaveta Levina

Prerequisites & Distribution: Prior or concurrent enrollment in MATH 215 and EECS 183. (3). (Excl). (BS). 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: 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 425 / MATH 425. Introduction to Probability.

#### Instructor(s): Statistic faculty

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

Credits: (3).

Course Homepage: No homepage submitted.

See Mathematics 425.

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### STATS 426. Introduction to Theoretical Statistics.

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

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

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

Prerequisites & Distribution: STATS 265 and 401 or IOE 366. (4). (Excl). (BS). 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: No homepage submitted.

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): Derek R Bingham (dbingham@umich.edu)

Prerequisites & Distribution: STATS 401. (4). (Excl). (BS). 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 499. Honors Seminar.

#### Instructor(s):

Prerequisites & Distribution: Permission of departmental Honors advisor. (2-3). (Excl). (INDEPENDENT). May not be repeated for credit.

Credits: (2-3).

Course Homepage: No homepage submitted.

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### STATS 500. Applied Statistics I.

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

Prerequisites & Distribution: MATH 417, and STATS 350 or 426. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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, and 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). 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 504. Statistical Consulting.

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

Prerequisites & Distribution: STATS 401 or 500. (3). (Excl). (BS). May be repeated for credit for a maximum of 9 credits.

Credits: (3).

Course Homepage: No homepage submitted.

Applications of statistics to problems in engineering, physical sciences, 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): Lutz Kilian (lkilian@umich.edu)

Prerequisites & Distribution: Permission of instructor. (3). (Excl). (BS). May not be repeated for credit.

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 575 / ECON 678. Econometric Theory I.

#### Instructor(s):

Prerequisites & Distribution: MATH 417 and 425, or ECON 671, 672, and 600. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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 1:26 PM on Thu, Mar 13, 2003.