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 disciplines. Evaluation is based upon class examinations, a final examination, and weekly assignments. The course format is lecture with some discussion.

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).

Analysis of engineering data associated with stochastic industrial processes. Topics include: fundamentals of distribution analyses; process model identification, estimation, testing of hypothesis, validation procedures, and evaluation of models by regression and correlation. Students are required to use the MTS computer system for problem solving.

402. Introduction to Statistics and Data Analysis. No credit granted to those who have completed 412. (4). (NS).
Section 00l.
In this course students are introduced to the concepts and applications of statistical methods and data analysis. Statistics 402 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. The course format includes three lectures and a laboratory (l.5 hours per week). The laboratory section covers some of the data analysis material and introduces the use of interactive computing through the use of MIDAS. Course evaluation is based on a combination of three examinations given Wednesday evenings, a final examination and teaching fellow input.

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, multicolinearity 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.

404. Problem Solving in Medical Statistics. Enrollment in Inteflex or permission of instructor. (3). (Excl).

This course is intended to introduce students in the medical sciences to the measurement and interpretation of clinically relevant variables. Applications to the design and analysis of clinical trials and diagnosis are presented. The methodology includes some probability theory, classical inference, and curve fitting. Many of the topics are illustrated through current problems in medicine. (Rothman)

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).

See Economics 405 for description. (Kmenta)

412. Introduction to Probability and Statistics. Prior or concurrent enrollment in Math. 215 and either CS 283 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.

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

See Mathematics 425 for description.

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 testing, and Bayesian inference. The sequence of Statistics 425/426 serves as a prerequisite for more advanced Statistics courses. Weekly problem sets, two hourly exams, and one final exam.

500. Applied Statistics I. Math. 417 and a course in statistics (Stat. 402 or 426); or permission of instructor. (3). (NS).

Review of matrices, multivariate normal and related distributions. Regression and general least squares theory, Gauss-Markov theorem, estimation of regression coefficients, polynomial regression, step-wise regression, residuals. ANOVA models, multiple comparisons, analysis of covariance, Latin square designs, random and mixed-effect models. Applications and real data analysis will be stressed, with students using the computer to perform statistical analysis.

505/Econ. 673. Econometric Analysis. Permission of instructor. (3). (Excl.)

This is a one-term course in probability and statistics whose purpose is to provide the needed background for econometrics and other non-experimental sciences. The prerequisites for the course are Mathematics 115 and 116 or equivalent. The course includes the theory and practice of testing hypotheses (including the Neyman-Pearson lemma and the likelihood ratio test) and statistical estimation theory (including properties of estimators and estimation methods). It is a required course for all doctoral students in the Department of Economics.

510/Math. 525. Probability Theory. Math. 450 or 451; or permission of instructor. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 510 for one credit. (3). (N.Excl).

See Mathematics 525 for description.

550/SMS 576/I.O.E. 560. Bayesian Decision Analysis. Stat. 425 or permission of instructor. (3). (NS).

Axiomatic foundations for personal probability and utility; interpretation and assessment of personal probability and utility; formulation of Bayesian decision problems; risk functions, 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; application to a variety of decision-making situations. There will be assigned homework exercises, a midterm and a final examination.

560/Biostat. 685 (Public Health). Introduction to Nonparametric Statistics. Stat. 426 or permission of instructor. (3). (NS).

The course will cover the basic linear rank statistics for one sample, two sample, one and two way ANOVA, and regression problems. Tests and their power functions, point and interval estimates are covered. Efficiencies of rank and parametric tests are computed.

575/Econ. 775. Econometric Theory I. Math. 417 and 425 or Econ. 653, 654, 673, and 674. (3). (Excl).

This course involves a derivation of the required theory in mathematical statistics, and of the main results needed for statistical inference associated with the linear model. The emphasis is on the asymptotic distribution theory as it is applied to the methods of estimation used in econometrics. The course is a prerequisite for Statistics 576 (Econometric Theory II).


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