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 and some attention is given to statistical process control methods. 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. (Section 001 Rothman; Section 002 Ericson)

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.

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).

Principles of statistics inference, including: probability, experimental and theoretic derivation of sampling distributions, hypothesis testing, estimation, and simple regression.

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 Math 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 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.

466/IOE 466. Statistical Quality Control. Statistics 311 or IOE 365. (3). (Excl).

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. (Field)

502. Analysis of Categorical Data. Stat. 426. (3). (NS).

Models for contingency tables, including the Poisson, multinomial, and hypergeometric models; additive and loglinear models for cell probabilities; estimation of parameters, exact and asymptotic sampling distributions, and sufficient statistics, tests of hypotheses, including likelihood ratio tests.

504. Seminar on Statistical Consulting. Stat. 403 or 500. (1-4). (Excl). Offered mandatory credit/no credit. May be repeated for a total of 8 credits.

Applications of statistics to problems in the sciences and social sciences; students will be expected to analyze data and write reports.

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 Math 525.

511. Mathematical Statistics. Stat. 510 or Math. 525; or permission of instructor. (3). (N.Excl).

TOPICS IN MATHEMATICAL STATISTICS WILL INCLUDE: Introduction to decision theory, estimation, sufficiency, completeness, maximum likelihood, and Bayes estimators, interval estimation UMP tests, unbiased tests and introductions to the analysis of variance and regression.

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).

Review of discrete distributions, generating functions, compound distributions, renewal theorem, systems as Markov chains. Properties of Markov chains: Chapman-Kolmogorov equations, return and first passage times, classification of states and periodicity, absorption probabilities, forward equations, stationary distributions, backward equation, ergodicity, limit properties. Branching and queueing processes: examples from engineering, biological and social sciences; continuous time Markov chains, embedded chains, the M/G/1 queue, Markovian decision processes, inventory problems.

531. Statistical Analysis of Time Series. Stat. 426. (3). (NS).

The major topics include time- and frequency-domain characteristics of stationary discrete time series, autoregressive and moving average models, prediction theory, estimation and hypothesis testing, and computer applications. Special topics might include vector autoregression, cross-spectral analysis, causality testing or other issues of current interest. Statistics 511 or Economics 775 is the standard prerequisite. Student evaluation is based on exams, homework, and a term paper. Lectures and problem sets including computer exercises are the main methods of instruction.

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.

570. Experimental Design. Stat. 426 and a basic knowledge of matrix algebra; or permission of instructor. (3). (NS).

Basic topics and ideas in the design of experiments: randomization and randomization tests; the validity and analysis of randomized experiments; randomized blocks; Latin and Graeco-Latin squares; plot techniques; factorial experiments; the use of confounding and response surface methodology; weighing designs, lattice and incomplete block and partially balanced incomplete block designs.

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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