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, Keener)
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.
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. Section 003 is open to CEW evening students.
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.
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. (Kramer)
425/Math. 425. Introduction to Probability. Math. 215. (3). (N.Excl).
See Mathematics 425.
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)
526/Math. 526/C.I.C.E. 516. Discrete State Stochastic Processes. Math. 525; or Stat. 510; or C.I.C.E. 512. (3). (N.Excl).
Generating functions; recurrent events and the renewal theorem; random walks; Markov chains; branching processes; limit theorems; Markov chains in continuous time with emphasis on birth and death processes and queueing theory. An introduction to Brownian notion, stationary processes, or martingales. (Keener)
531. Statistical Analysis of Time Series. Stat. 426. (3). (NS).
The purpose of this course is to introduce students to both time- and frequency-domain approaches to time series analysis. The use of covariance and spectral density functions to characterize stationary stochastic processes is considered. Identification and estimation of autoregressive, moving-average, and mixed models is covered. Practical aspects of applied time series analysis are covered. Students are expected to complete a short paper. (Howrey)
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)
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