**100. 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). (BS). (QR/1). *

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. The Art of Scientific Investigation. *** (4). (NS). (BS). (QR/1). *

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 three lectures
and a laboratory (1.5 hours per week). Cost:2 WL:3 (Gunderson)

**190(290). The History of Chance. *** (3). (NS). (BS). *

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 textbook, 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/IOE 365. Engineering Statistics. *** Engin. 103, Math. 215, and IOE 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). (BS). *

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). (BS). (QR/1). *

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). (BS). *

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 (Kuhn)

**405/Econ. 405. Introduction to Statistics.
*** Math. 115 or permission of instructor. Juniors and seniors may elect
concurrently with Econ. 101 and 102. 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). (BS). (QR/1). *

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). (BS). *

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 of lecture and one and one-half hour laboratory session each week. (Gu)

**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). (BS). *

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, two midterms, and a final exam. Cost:2 WL:3 (Hardwick)

**414. Topics in Applied Statistics. *** Stat 413 or 403; prior or concurrent
enrollment in 426; and permission of instructor. (4). (Excl). (BS). *

Topics in applied statistics, including random and mixed effects ANOVA models, analysis of covariance and repeated measures designs, ridge regression, splines, logit-probit analysis, log-linear models, topics in multivariate analysis (MANOVA, discriminant analysis, profile analysis) topics in time series analysis, and basics of survival analysis. (Faraway)

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

* 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 (003:Csörgo; 004:Woodroofe)

**426. Introduction to Mathematical Statistics. *** Stat. 425. (3).
(NS). (BS). *

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 (Jeganathan)

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

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 (Shi)

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

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 (Hardwick)

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

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. (Coleman)

**504. Seminar on Statistical Consulting. *** Stat. 403 or 500. (1-4).
(Excl). (BS). 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 (Nair)

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

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 (Sun)

**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). (BS). *

See Mathematics 525.

**526/Math. 526. Discrete State Stochastic Processes. *** Math. 525, or Stat. 525, or EECS 501. (3). (Excl). (BS). *

See Mathematics 526.

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

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)

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

Order statistics and confidence intervals for quantiles; rank tests for the 1, 2, and k-sample problems; asymptotic distributions of rank statistics; asymptotic efficiency; randomization as a basis for inference; permutation tests; the sample distribution function and goodness of fit tests. Cost:4 WL:3

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

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. Cost:3 or 4 WL:3 (Wu)

**575/Econ. 775. Econometric Theory I. *** Math. 417 and 425 or Econ.
653, 654, 673, and 674. (3). (Excl). (BS). *

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:2 or 3 WL:3

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

This is a course of advanced econometrics. The quasi-maximum likelihood and generalized method-of-moment estimators are rigorously examined. Statistical inference based on these estimators are also considered. Cost:3 WL:4 (Sakata)

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