# Courses in Statistics (Division 489)

300. Introduction to Statistical Reasoning. (3). (NS).

This course is designed to provide an overview of the field of statistics. Course topics include approaches to the collection of numerical data, methods of analyzing and summarizing such data, statistical reasoning as a means of learning from observations (experimental or sample), and techniques for dealing with uncertainties in drawing conclusions from collected data. Basic fallacies in common statistical analyses and reasoning are discussed and proper methods indicated. Alternative approaches to statistical inference are also discussed. The course emphasis is on presenting basic underlying concepts rather than on covering a wide variety of different methodologies. Applications are drawn from a wide variety of other disciplines. Evaluation is based upon class examinations, a final examination, and weekly assignments. The course format is lecture with some discussion. (Hammerstrom and Staff)

310. Elements of Probability. Prior or concurrent enrollment in Math. 215. (3). (NS).

This course covers the main ideas and uses of probability: expectation, variance, covariance, distribution functions, bivariate, marginal and conditional distributions, the binomial and related distributions, the Poisson process, the exponential and gamma distributions, the normal sample statistics, the law of large numbers, the central limit theorem. There are regularly assigned homework exercises, two in-class examinations, and a final examination. The emphasis is on problem solving and applications. (Kuo)

311/I.O.E. 365. Engineering Statistics. Math. 215 and Eng. 102, or equivalent. No credit granted to those who have completed 412. (4). (Excl).

This course provides an analysis of engineering data associated with stochastic industrial processes. Topics include: fundamentals of distribution analysis; process model identification, estimation, testing of hypotheses, validation procedures. Students are required to use the MTS computer system for problem solving. The course format includes three lectures and a lab. There are regularly assigned homework exercises, two hour examinations, and a final examination. Applications are mainly drawn from problems in engineering. (Hoppe)

402. Introduction to Statistics and Data Analysis. No credit granted to those who have completed 412. (4). (NS).

This course is designed for students with an interest in the application of the scientific method and in the use of Michigan Interactive Data Analysis System (MIDAS). Statistics 402 has no prerequisite and has been elected by many students whose mathematics background includes only high school algebra. The course is "applications oriented" and is appropriate for students from all academic areas. The course focuses on the general problems associated with conclusions drawn on the basis of observation. Examples which reflect student interests are chosen, and all concepts are illustrated via these examples. The course format includes three lectures and a laboratory (1.5 hours) each week. The laboratory introduces the use of MIDAS and serves as a recitation section. Course evaluation is based upon a combination of class examinations, a midterm, a final, and class discussion. (Rothman and staff)

403. Introduction to Statistics and Data Analysis II. Stat. 402. (4). (NS).
Applied Regression and Analysis of Variance.
This course surveys some intermediate topics in multiple linear regression and the analysis of variance and covariance, stressing applications rather than theory. We particularly emphasize residual analysis in multiple regression and cover such topics as the least squares estimation and tests of hypotheses, prediction analysis, multicollinearity and variable selection. Fixed, random, and mixed models are all discussed in the analysis of variance. Experimental designs studied include randomized complete block, hierarchial or nested designs and the latin square. Three hours of lecture and one and one-half hours of lab per week. (Smith)

405/Econ. 405. Introduction to Statistics. Math. 115 or permission of instructor. Juniors and seniors may elect concurrently with Econ. 201 and 202. No credit granted to those who have completed Econ. 404. (4). (SS).

This course has originally been designed for economics concentrators but the discussion is sufficiently general to serve noneconomics concentrators just as well. The emphasis is on understanding rather than on "cookbook" applications. Students are expected to know basic algebra and to have some understanding of the concept of derivatives and integrals. Since the content of the course does not extend much beyond establishing the foundations of statistical inference, it is recommended that after finishing the course students elect to take Economics 406 or a similar course in the Statistics Department to learn some applications and get some experience with computer work. While Economics 405 is not required for an economics concentration, it is difficult to see how anyone today can be regarded as an economist without some knowledge of statistics. Employers typically ask for some training in statistics, and letters from graduates often express regret for not having had more statistics. (Starr)

412. Introduction to Probability and Statistics. Prior or concurrent enrollment in Math. 215 and either CCS 274 or Engin. 102. No credit granted to those who have completed 311 or 402. (3). (NS).

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, including assignments which require the use of MTS, two midterms, and a final exam. (Woodroofe)

425/Math. 425. Introduction to Probability. Math. 215. (3). (N.Excl).

426. Introduction to Mathematical Statistics. Stat. 425. (3). (NS).

This course covers the basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric test, and Bayesian inference. The sequence of Statistics 425/426 serves as a prerequisite for more advanced Statistics courses. Weekly problem sets, one or two hourly exams, and one final exam. (Muirhead)

510, 511. Probability and Mathematical Statistics I and II. Math. 450 or 451 and a course in probability or statistics; or permission of instructor. (3 each). (NS).

Statistics 511 is offered Winter Term, 1982.

Statistics 511 covers topics in mathematical statistics including an introduction to decision theory, estimation, sufficiency, completeness, maximum likelihood and Bayes estimators, internal estimation, UMP tests unbiased tests, sequential tests, Bayes tests, likelihood ratio tests, and introductions to the analysis of variance and regression. (Keener)

551. Bayesian Inference. Stat. 550. (3). (NS).

The foundations of Statistics, from the Bayesian point of view, followed by special topics in Bayesian inference and decision theory – for example: the Bayesian view of the Stein paradox; Bayesian analysis of contingency tables; Bayesian analysis of nonparametric problems; the species sampling problems; and interesting recent articles.

552. Sequential Analysis and Design. Stat. 426 or equivalent. (3). (NS).

Models for sequential sampling and sequential design; potential advantages and disadvantages of sequential methods, including their increased efficiency, ethical considerations, and the effect on significance levels; the insensitivity of the likelihood function and posterior distributions to sequential sampling; fixed width confidence intervals; the Robbins-Munro and related processes; some common sequential tests, including the sequential probability ratio test and restricted sequential procedures; decision theoretic formulation of sequential problems; Bayesian solutions of sequential problems by dynamic programming; applications to quality control and clinical trials; special topics.

576/Econ. 776. Econometric Theory II. Econ. 775 or equivalent. (3). (NS).

This is a course in advanced econometrics. It includes a thorough treatment of statistical problems in dealing with time series and cross-section data, a development of simultaneous equation techniques, and formulation and estimation of special models. Other topics may also be included depending on time and interest. (Kmenta)