100(300). Introduction to Statistical Reasoning. No credit granted to those who have completed or are enrolled in Soc. 210, Poli.Sci. 280, Stat. 402, 311, 405, or 412, or Econ. 404. (4). (NS).

This course is designed to provide an overview of the field of statistics. Course topics include methods of analyzing and summarizing 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. Course evaluation is based on a combination of two Thursday evening midterm examinations, a final examination and teaching fellow input. The course format includes three lectures and a laboratory (1 hour per week). Cost:2 WL:3 (Hardwick, Gunderson, Aliaga)

170(270). The Art of Scientific Investigation. (4). (NS).

The objective of this course is to introduce students to the learning process in a non-deterministic environment. An appreciation for measurement, bias and variation is essential to formulate questions and learn about things. Underlying this course is the Edwards Deming philosophy. Deming, an American statistician, was invited to Japan in the early 1950's to help improve the quality of mass produced items. His success in Japan is, in part, responsible for our current balance of trade deficit; and here the Ford Motor Co., has also attained a larger market share as a result of his ideas. Implementation of the Deming message requires a critical appreciation of variation and the scientific method. Specifically, we will discuss: (1)Historical attempts to learn and the advent of the modern scientific method. (2)The differences between special or assignable causes and common causes of variation. Before we can learn how a process operates, the process must be stable. (3) Differences between observational and controlled randomized studies and associated ethical issues. (4) The 'what' and 'how' of measurement and the quantification of uncertainty-subjective and frequency notions of probability. (5) Understanding bias and variation. (6) How to use bias to design efficient studies. (7) Differences between enumerative and analytic studies. Many of the ideas will be introduced through experimentation (e.g., the red bead and funnel experiments) and the mathematical level will not require more than a modest background in high school algebra. The course format includes 3 lectures and a laboratory. (1.5 hours per week). Cost:2 WL:3 (Rothman)

290. The History of Chance. (3). (NS).

This course will acquaint students with the evolution of some of the main ideas of probability and statistics in an historical context. This evolution will be depicted from the earliest evidences of chance in ancient cultures and continues with the description of problems appearing in the Renaissance that prompted leading mathematical thinkers to attempt the measurement of uncertainty. Beginning then with the famous Pascal-Fermat correspondence and the resulting books of Huygens, de Montmort, Jacob Bernoulli and de Moivre on the one hand, and Bayes' essays on inverse probability on the other, the transformation of the concepts in the measurement of uncertainty during the Enlightenment will be followed against the changing background of mathematical, natural philosophical, general intellectual and scientific as well as religious thought, thus arriving at the monumental treatise of Laplace. The goal of the rest of the lectures is to understand what has recently been described as the probabilistic revolution. This refers to the fact that while in 1800, say, "the world was deemed to be governed by stern necessity and universal laws", as Ian Hacking writes, "shortly after 1930 it became virtually certain that at bottom our world is run at best by laws of chance." Some basic concepts, technical rules and ideas of probabilistic and statistical reasoning will be introduced and used on an elementary level of mathematical sophistication, as required by the historical development. Grading will be based on one or two midterm tests and a final examination. A smaller part of each of these will be concerned with knowledge on a technical level, while the rest will be a short, non-technical essay on a given historical topic. There is no formal text-book, essentially important readings will be organized in a course pack. Students having an interest in both the history of science and the study of randomness are encouraged to elect the course. (Csörgo)

311/I.O.E. 365. Engineering Statistics. Math. 215 or equivalent. No credit granted to those who have completed or are enrolled in Stat. 405 or 412. One credit granted to those who have completed Stat. 402. (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. (Sun)

402. Introduction to Statistics and Data Analysis. No credit granted to those who have completed or are enrolled in Econ. 404 or Stat. 311, 405, or 412. (4). (NS).

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 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 micro-computer package and the Macintosh computer. Course evaluation is based on a combination of three examinations GIVEN WEDNESDAY EVENINGS, a final examination and teaching fellow input. Cost:2 WL:3 (Bélisle, Gunderson, Hydorn)

403. Introduction to Statistics and Data Analysis II. Stat. 402. (4). (Excl).

Intermediate topics in multiple linear regression, and the analysis of covariance, stressing applications: least squares estimates, test of hypotheses, prediction analysis, residual analysis, multicollinearity, and the variable selection techniques; fixed and random effects models in ANOVA; multiple comparisons, randomized blocks, Latin squares, nested, and hierarchical designs; and robust procedures, as time permits. Three hours of lecture supplemented by one and one-half hours of laboratory. Cost:2 WL:3 (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 or are enrolled in Stat. 311 or 412. Students with credit for Econ. 404 can only elect Stat. 405 for 2 credits and must have permission of instructor. (4). (Excl).

Principles of statistical inference, including: probability, experimental and theoretic derivation of sampling distributions, hypothesis testing, estimation, and simple regression. Cost:2 WL:3 (Woodroofe)

412. Introduction to Probability and Statistics. Prior or concurrent enrollment in Math. 215 and CS 183. No credit granted to those who have completed or are enrolled in 311 or 405. One credit granted to those who have completed Stat. 402. (3). (Excl).

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. Cost:3 WL:3 (Mielniczuk)

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. WL:3 (Sun)

470. The Design of Scientific Experiments. Stat. 311, 402, 412, or 426; or permission of instructor. (4). (Excl).

The objective of this course is to introduce students to the process of planning, designing and implementation of a study. Includes enumerative, Monte Carlo, observational and controlled randomized experimentation. Emphasis is on the conceptual framework not on the mathematical theory of design (e.g., Statistics 570). Cost:3 WL:3 (Lawoko)

501. Applied Statistics II. Stat. 500 or permission of instructor. (3). (Excl).

A variety of topics in applied statistics will be covered in the course. The main topics are survey sampling methods including: simple random sampling, stratification, cluster sampling, systematic sampling and multistage sampling methods. Survival analysis including: hazard and survival functions, censoring, Kaplan-Meier estimation, graphical methods and proportional hazards models. Bootstrap and jackknife methods and their uses. Topics in time series analysis including: autocorrelation functions, stationarity, identification, estimation and forecasting with ARIMA models and spectra. Non-parametric density estimation including: kernels, cross validation, splines and the penalized maximum likelihood estimators. Discriminant analysis including: linear and quadratic discriminators, relation to regression and non-parametric approaches. Cost:4 WL:3 (Faraway)

504. Seminar on Statistical Consulting. Stat. 403 or 500. (1-4). (Excl). 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. Cost:2 WL:3 (Ericson)

511. Mathematical Statistics II. Stat. 510. (3). (Excl).

More on theory of estimation including: minimax, Bayes, and James-Stein estimators. The theory of hypothesis testing including: tests, significance levels, power, the Neyman-Pearson lemma, uniformly most powerful unbiased tests, monotone likelihood ratios, locally best tests, similar tests, likelihood ratio tests and the associated large sample theory, sequential tests, goodness of fit tests, and tests in contingency tables. Other topics include: confidence regions, introduction to the general linear model, and non-parametric methods. Cost:3 WL:3 (Jeganathan)

525/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. 525 for only 1 credit. (3). (Excl).

See Mathematics 525 for description.

531/Econ. 677. Analysis of Time Series. Stat. 426. (3). (Excl).

Decomposition of series; trend and regression as a special case of time series; cyclic components; smoothing techniques; the variate difference method; representations including spectogram, periodogram, etc., stochastic difference equations, autoregressive schemes, moving averages; large sample inference and predictions; covariance structure and spectral densities; hypothesis testing and estimation; applications and other topics. Cost:3 WL:3 (Howrey)

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

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 exam. Cost:3 WL:3 (Hill)

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