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

The objective of this course is to introduce students to learning 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). (Rothman)

**300. Introduction to Statistical Reasoning. *** (3). (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. Evaluation is based upon a midterm and a final examination. The course format is lecture with some discussion.

**402. Introduction to Statistics and Data Analysis. *** No credit granted
to those who have completed 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 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). (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 logit 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.

**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.

**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. (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). (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.

**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.

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

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.

**502. Analysis of Categorical Data. *** Stat. 426. (3). (Excl). *

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

**510. Mathematical Statistics I. *** Math. 450 or 451, and a course
in probability or statistics; or permission of instructor. (3). (Excl). *

Review of probability theory including: conditioning, independence, random variables, standard distributions, exponential families, inequalities and a central limit theorem. Introduction to decision theory including: models, parameter spaces, decision rules, risk functions, Bayes versus classical approaches, admissibility, minimax rules, likelihood functions and sufficiency. Estimation theory including unbiasedness, complete sufficient statistics, Lehmann-Scheffe and Rao-Blackwell theorems, and various types of estimators.

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

See Math 525 for description.

**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.

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

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.

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