YALE UNIVERSITY

Department of Statistics Graduate Course List for 1994-95

Organizational Meeting for all Fall term courses whose times are not listed below: Tuesday, 30 August at 10:00, Room 107, 24 Hillhouse Avenue. Those interested in attending one of the courses but unable to be present at this meeting should inform Mrs. Amato beforehand and submit their schedules.

Statistics 523a, Introduction to Statistical Methods and Probabilistic Reasoning.

(Also Statistics 123a.)

Mr. W. Sudderth. Basic concepts of statistical methods shown through examples of statistical practice. Introduction to probabilistic reasoning, hypothesis testing, regression. Some use of computers for data analysis.

Tue., Thu., 1:00-2:15; Lab session Monday afternoon; begins Thursday, September 1.

Statistics 530b, Introductory Data Analysis.

(Also Statistics 230b, PLSC 530b.)

Mr. J. Hartigan. Survey of statistical methods: plots, transformations, regression, analysis of variance, clustering, principal components, contingency tables, and time series analysis. Some sessions are used to demonstrate techniques on the computers. After or concurrent with Statistics 123a or Psychology 200a or b or equivalent.

Tue., Thu., 2:30-3:45

Statistics 541a, Probability Theory

(Also Statistics/Mathematics 241a.)

Mr. N. Hengartner. A ﬁrst course in probability theory: probability spaces, random variables, expectations and probabilities, conditional probability, independence, some discrete and continuous distributions, central limit theorem, Markov chains, probabilistic modeling. After or concurrent with Mathematics 120a or b or equivalents.

Mon., Wed., Fr., 9:30-10:20.

Statistics 542b, Theory of Statistics.

(Also Statistics/Mathematics 242b.)

Mr. A. Barron. Principles of statistical analysis: maximum likelihood, sampling distributions, estimation, conﬁdence intervals, tests of signiﬁcance, regression, analysis of variance, and the method of least squares. After Statistics 241a; after or concurrent with Mathematics 222; or equivalents.

Mon., Wed., Fri., 9:30-10:20.

Statistics 551b: Stochastic Processes.

(Also Statistics 251b.)

Mr. J. Chang. A study of random processes, including Markov chains, Markov random ﬁelds, martingales, random walks, Brownian motion and diﬀusions. Introduction to certain modern techniques in probability such as coupling and large deviations. Applications to image reconstruction, Bayesian statistics, ﬁnance, probabilistic analysis of algorithms, genetics and evolution. After Statistics 241 or equivalent.

Mon., Wed., 2:30-3:45.

Statistics 600b, Advanced Probability.

Mr. D. Pollard. Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is

assumed. Probability at the level of Statistics 600b will be a prerequisite for a course on Stochastic Calculus to be oﬀered in the fall of 1995. Tue., Thu., 2:30-3:45.

Statistics 607a, Stochastic Order Relations and Their Applications.

Mr. O. Kella The course deals with various kinds of stochastic orders. In particular we will start by studying stochastic, convex (concave), convex and increasing (concave and increasing), likelihood ratio and hazard rate orderings. We will also focus on majorization and stochastic majorization as well as consider stochastic orderings and various deﬁnitions of stochastic and increasing orderings for families of distributions and stochastic processes. After some theory we will investigate some applications to statistics, queueing and production.

Statistics 609a, Weak Convergence and Empirical Processes.

Mr. J. Chang. Stochastic processes as random elements of metric spaces. Weak convergence of probability measures on metric spaces. Almost sure representations, continuous mapping theorem, tightness. Donsker’s theorem and functional central limit theorems for dependent random variables. Uniform laws of large numbers, Vapnik-Cervonenkis classes and V-C dimension. Introduction to strong approximations. Applications chosen from statistics, econometrics, learning theory, recursive identiﬁcation methods. Prerequisite: Statistics 600.

Statistics 610a, Statistical Inference.

Mr. J. Chang. A systematic development of the mathematical theory of statistical inference covering methods of

estimation, hypothesis testing, and conﬁdence intervals. An introduction to statistical decision theory. Undergraduate probability at the level of Statistics 241 assumed. Tue., Thu., 10:30-11:45; begins Thursday, 1 Sepetember.

Statistics 612a, Linear Models.

(Also Statistics 312a.)

Mr. A. Barron. The geometry of least squares; distribution theory for normal errors; regression, analysis of variance, and designed experiments; numerical algorithms (with particular reference to S); alternatives to least squares. Generalized linear models. After Statistics 242 and Mathematics 222 or equivalents.

Tue., Thu., 2:30-3:45.

Statistics 618b, Asymptotics.

Mr. D. Pollard. A careful study of some standard asymptotic techniques in statistics and econometrics, and their modern reﬁnements. Classical likelihood theory and M-estimation. Empirical process methods. A gentle introduction to local asymptotic normality, with particular attention to concepts of eﬃciency. Applications to mixture models, binary choice models, simulation estimators, semiparametrics. Prerequisite: knowledge of probability at the level of Statistics 600b.

Statistics 624b, Optimization Methods for Statistics.

Mr. N. Hengartner Methods for solving optimization problems encountered in statistics: least squares, gradient and sub-gradient methods, constrained optimization, EM-algorithm, ACE, dualization, simulated annealing.

[Statistics 625a, Case Studies.]

[Statistics 626b, Practical Work.]

Statistics 627a, Statistical Consulting.

Mr. J. Hartigan. We study statistical problems encountered in scientiﬁc studies in various ﬁelds. There will usually be a presentation by the persons engaged in the studies, followed by a discussion of suitable statistical methods.

Statistics 625a, Statistical Case Studies.

Mr. N. Hengartner. Thorough analysis of complex data sets using S, with emphasis on the balance between graphical

techniques and formal inferential procedures. Census/PES data and data arising in geology will be investigated. Times to be arranged at organizational meeting.

Statistics 626b, Practical Work.

Staﬀ. Individual one-semester projects, with students working on studies outside the Department, under the guidance of a statistician.

Statistics 652a, Bayes Methods.

Mr. J. Hartigan. Topics include: probability models for statistical problems; ﬁnitely additive and non-unitary probabilities; decision theory; prior distributions; Bayes asymptotics; robust Bayes procedures; discrete priors; Markov chain Monte Carlo; recognition. After Statistics 242b or equivalent.

Statistics 661a, Data Analysis.

(Also Statistics 361a).

Mr. N. Hengartner. By analyzing data sets using the S statistical computing language, a selection of statistical topics are studied: linear and non-linear models, maximum likelihood, resampling methods, curve estimation, model selection, classiﬁcation and clustering. Weekly sessions will be held in the Social Sciences Statistical Laboratory. After Statistics 242b or equivalent.

Mon., Wed., Fri., 2:30-3:20; begins Thursday, 1 September.

[Statistics 664b, Introduction to Information Theory].

(Also Statistics 364b). Oﬀered alternate years.

Statistics 668b, Information Theory for Statistics.

Mr. A. Barron. The role of information theory in statistical inference. The minimum description length principle and its implications for parameter estimation, curve estimation, model selection, tests of multiple hypotheses, universal data compression, universal prediction, and the choice of priors for Bayesian inference. Also, characterization of optimal rates for statistical risk using relative entropy, mutual information, and Fano’s inequality. Applications to adaptive estimation of histograms, neural nets, and universal portfolio selection. Intended for students in Statistics, Engineering, Economics, Finance, Mathematics, and Computer Science. Prior completion of Statistics 364/664 (Introduction to Information Theory) is preferred.

Departmental Seminar

Important activity for all members of the department. Either at 24 Hillhouse Avenue or at EPH. See weekly seminar announcements. Monday 4:15