**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 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. Evaluation is based upon three hourly in-class examinations and a final examination. The course format is lecture with some discussion. Cost:2 WL:3

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

This is a Collegiate Fellows course; see page 3 for a complete list of Collegiate Fellows courses and the Time Schedule for details of time and place.

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. *** 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. [Cost:2] [WL:3] (Belisle)

**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] (Ericson)

**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 Econ. 404 or Stat. 311 or 412. (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] (Sarkar)

**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] (Jeganathan)

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

See Math 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 (Jeganathan)

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

Topics in applied multivariate analysis including Hotelling's T2 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 the computer will be stressed. Cost:2 WL:3 (Ericson)

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

Topics covered will include: hypothesis testing and related topics such as size, power, similarity and optimality properties. Likelihood ratio tests, generalized likelihood ratio tests, decision theory and Bayes approaches. Sequential procedures, large sample theory and various other topics. [Cost:2] [WL:3] (Keaner)

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

See Math 525 for description.

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

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. 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. WL:3

**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). [Cost:4] (Genius)

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