Courses in Statistics (Division 489)

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 (Rothman)

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.

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 (Deshpande)

405/Econ. 405. Introduction to Statistics. Math. 116 or 118. 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 (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). (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. Cost:2 WL:3 (Hardwick)

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:Jeganathan; 004:Kou)

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 (Woodroofe)

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)

480. Survey Sampling Techniques. Stat. 402. (4). (Excl). (BS).

Motivating examples, abstraction to: populations, variables, parameters, etc.; samples and sample designs, probability versus convenience samples, target versus sampled populations, frames, inclusion probabilities, joint inclusion probabilities, statistics, sampling distributions, and Horvitz-Thompson estimators; simple random samples (with and without replacement), binomial and hypergeometric distributions, sample size determinations; cluster sample designs; systematic sample designs; stratified sample designs, including sample size determination, Neyman allocation, proportional allocation, etc.; two and multiple stage designs, estimation and optimal design; combination designs, e.g., stratified cluster samples, etc.; non-sampling errors and biases, non-response (unit and item), response bias and error, and possible preventatives and cures; and special topics as time allows: e.g., capture-recapture sampling, Bayesian views, area sampling, etc. There will be weekly assignments and a final exam. Class format is 3 hours of lecture and 1.5 hours of laboratory per week. Cost:2 WL:3 (Hamada)

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 (Faraway)

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

Models for contingency tables, including the Poisson, multinomial, and hypergeometric models; additive and loglinear models for cell probabilities; estimation of parameters, exact and asymptotic sampling distributions, and sufficient statistics, test of hypotheses, including likelihood ratio tests. Cost:2 or 3 WL:3 (Kou)

504. Seminar on Statistical Consulting. Stat. 403 or 500. (1-4). (Excl). (BS). May be repeated for a total of 8 credits.
(3 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 (Gillespie)

506. Statistical Computing. Stat. 426 or 500, and CS 380 or 283, or permission of instructor. (3). (Excl). (BS).

Selected topics in statistical computing, including: Monte Carlo procedures, generation of random numbers, computation of estimators, linear and non-linear problems, resampling algorithms, splines, other special topics. Cost:2 or 3 WL:3 (Y. Wu)

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 (Keener)

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 (Wang)

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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