# 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

125. Games, Gambling and Coincidences. (3). (Excl). (QR/1).

This course will emphasize problem solving and modeling. To achieve this end, students will work together in class attempting to solve various problems posed by the instructor. Hopefully with a bit of gentle guidance, the students will be able to create models and deduce the basic concepts necessary for solution. Students will be asked to write up solutions and work on a project. Grades will be determined from this work and class participation. Problems from the course will be drawn primarily from Markov chains with a finite state space, dynamic programming, again with a finite state space, and game theory. Possible examples include: gambler's ruin; expected run lengths in coin tossing until a specified string is obtained and chances that one string will occur before another; optimal strategies in sports and gambling; optimal replacement strategies; minimax solutions for finite state two-person zero sum games. Cost:2 WL:3 (Keener)

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. Cost:2 WL:1 (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

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).

See Economics 405. (Howrey)

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, including assignments which require the use of MTS, two midterms, and a final exam. Cost:2 WL:3

413. The General Linear Model and Its Applications. Stat. 402 and Math. 217; concurrent enrollment in Stat. 425. Students who have not taken Math. 217 should elect Stat. 403. Two credits granted to those who have completed Stat. 403. (4). (Excl). (BS).

Some motivating real examples – regression, ANOVA, time series - abstraction into a common model; statement of the model and assumptions; description of the design matrix including dummy variables; discussion of the error vector and assumptions regarding those errors; geometry of the GLM, including projections, Pythagorus, least squares estimation, residuals, predicted values, Gauss-Markov result, etc.; normal distribution theory results; confidence and predictive intervals, F and t tests, the extra sum of squares principle; multiple and partial correlations with geometry; checking for violations of the assumptions, normal probability plots, outliers, influence functions, problems of multicollinearity or near collinearity; cures for violations, transforms, weighting, etc. Multiple regression applications; choice of independent variables, principal components, all possible regressions, stepwise procedures, use of data subsamples (validation); polynomial regression, orthogonal polynomials. Use of dummy variables and ANOVA applications, fixed effect completely crossed ANOVA cases, balanced versus unbalanced designs, contrasts, interactions, multiple inference procedures including at least Scheffe, studentized range and Bonferroni; nested designs, etc. Time series applications, use of polynomial regression, deseasonalization, leads, lags and autoregressive models, serial correlation, Durbin-Watson test, ARIMA models, etc. Real applications will be stressed. There will be weekly assignments and a final exam. Class format is 3 hours of lecture and 1.5 hours of laboratory per week. Note: This course is designed primarily for Statistics Undergraduate Concentrators; other students, without the Mathematics 217 prerequisite, should elect Statistics 403. Cost:2 WL:3

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

Sections 001 and 002. 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

Sections 003 and 004. See Mathematics 425 for description.

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

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 or 3 WL:3

470. Experimental Design. Stat. 402. (4). (Excl). (BS).

This course will introduce students to basic principles in classical experimental design, including randomization, replication, confounding, interaction, covariates, use of the general linear model. Students will be introduced to the following designs: completely randomized, randomized blocks, Latin squares, incomplete blocks, factorial, split plot, Taguchi, response surface, optimal. 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

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

500. Applied Statistics I. Math. 417, and Stat. 402 or 426; or permission of instructor. (3). (Excl). (BS).

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 squares, 26 p designs, random and mixed-effects models. Applications and real data analysis will be stressed, with students using a computer to perform statistical analyses. Cost:2 WL:3

505/Econ. 673. Econometric Analysis. Permission of instructor. (3). (Excl). (BS).

This course is designed for first-year graduate students in economics, business, and related subjects. It involves a fairly rigorous development of statistical reasoning and methods relating to hypothesis testing, estimation, and regression analysis. Students are supposed to have had a course in calculus and in introductory statistics. Knowledge of matrix algebra is required. Evaluation of students is based on midterm and final examinations and weekly assignments. Students taking this course are expected to take Economics 674 – Econometric Analysis II in the following term. Cost:2 WL:3 (Howrey)

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

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

Review of probability theory including: probability, conditioning, independence, random variables, standard distributions, exponential families, inequalities and the 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. Cost:3 WL:3

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).

550/SMS 576 (Business Administration)/IOE 560. Bayesian Decision Analysis. Stat. 425 or permission of instructor. (3). (Excl). (BS).

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

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