**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 a Thursday evening midterm examination, a final examination and teaching fellow input. The course format includes three lectures and a laboratory (1 hour per week). Cost:2 WL:3

**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)

**311/I.O.E. 365. Engineering Statistics. *** Engin. 103, Math. 215, and I.O.E 315 or Stat 310. 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). *

Collection and analysis of engineering data associated with stochastic industrial processes. Topics include: exploratory data analysis, describing relationships, importance of experimentation, applications of sampling distribution theory, test of hypotheses, experiments with one or more factors, and regression analysis. Students are required to use statistical packages on CAEN for problem solving. (Nair)

**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

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

APPLIED REGRESSION. The course will also cover various topics associated with the general linear model emphasizing applications. Topics include: multiple regression, variable selection, stepwise regression, residual analysis, analysis of variance models, covariance analysis and principal components. OTHER TOPICS. As time allows, the course may cover some aspects of probit and logic analyses, analysis of time series data, reliability analysis, and topics in experimental design. Three hours of lecture and one and one-half hours of lab per week. Cost:2 WL:3

**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 (Hill)

**406. Introduction to Statistical Computing. *** Stat. 425 and 402.
(4). (Excl). *

Acquaints students with selected topics in statistical computing, including basic numerical aspects, iterative statistical methods, principles of graphical analyses, simulation and Monte Carlo methods, generation of random variables, stochastic modeling, importance sampling, numerical and Monte Carlo integration. Three hours lecture and one and one-half hour laboratory session each week. (Sun)

**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 (Hardwick)

**425/Math. 425. Introduction to Probability. *** Math. 215. (3). (N.Excl).
Sections 001 and 002. * See Mathematics
425 for description.

* Sections 003 and 004. * Sample spaces and axiomatic probability; elementary combinatorics; conditional probability
and independence; random variables; probability distributions, including
binomial, Poisson, Gamma, and normal; expectation, mean and variance; moment
generating functions; the law of large numbers; central limit theorem. Cost:2
WL:3

**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. Cost:2 or 3 WL:3 (Muirhead)

**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. Cost:2 WL:3 (Herrin)

**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:3 WL:3 (Faraway)

**503. Applied Multivariate Analysis. *** Stat. 500 or permission of
instructor. (3). (Excl). *

Topics in applied multivariate analysis including Hotelling's T^{2}
multivariate ANOVA, discriminant functions, factor analysis, principal components, canonical correlations, and cluster analysis. Selected topics from: maximum
likelihood and Bayesian methods, robust estimation and survey sampling.
Applications and data analysis using a computer will be stressed. (Coad)

**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

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

This is a course in advanced econometrics. It includes a thorough treatment of the general linear model, a development of simultaneous equation techniques, and an introduction to nonlinear models. Maximum likelihood and generalized method-of-moments estimators are rigorously treated. Cost:3 WL:4 (Lee)

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