Yale Department of Statistics 1997-98 Course List

Yale University
Department of Statistics

Yale Statistics Courses

Course List for 1997-98

Primarily undergraduate courses

Director of Undergraduate Studies: Joseph Chang

Nicolas Hengartner (Acting Director/Fall)

Statistics 101-103, (66101,66103), Introduction to Statistics (FALL)
Cross-listing: Statistics 501a-503a

Instructor: Mr. A. Barron. TTh 1:00 pm - 2:15 pm
Each of these courses gives a basic introduction to statistics, requiring no mathematics beyond high school algebra. Topics include numerical and graphical summaries of data, probability, hypothesis testing, confidence intervals, and regression. Each course focuses on applications to a particular field of study and is taught jointly by two instructors, one specializing in statistics and the other in the relevant area of application. The Tuesday lecture, which introduces general concepts and methods of statistics, is attended by all students in Statistics 101-103 together. The course separates for Thursday lectures, which develop the concepts with examples and applications. Computers are used for data analysis. These courses are alternatives; they do not form a sequence and only one may be taken for credit. They do not count toward the natural sciences requirement.

Statistics 101aG - Biology 150aG (66101) Introduction to Statistics: Life Sciences.
Instructor: Mr. Andrew Barron, Mr. Junhyong Kim.
Statistical and probabilistic analysis of biological problems presented with a unified foundation in basic statistical theory. The problems are drawn from genetics, ecology, epidemiology, and bioinformatics.

Statistics 102aG - EP & E 203a - Political Science 425a (66102-01) Introduction to Statistics: Social Sciences.
Instructor: Mr. Andrew Barron, Mr. Martin Gilens.
Statistical analysis of social science problems, primarily drawn from political science and sociology, presented with a unified foundation in basic statistical theory.

Statistics 102aG - EP & E 203a - Political Science 425a (66102-02) Introduction to Statistics: Social Sciences.
Instructor: Mr. Andrew Barron, Mr. Donald Green.
Statistical analysis of social science problems, primarily drawn from political science and psychology, presented with a unified foundation in basic statistical theory.

Statistics 102aG - EP & E 203a - Political Science 425a (66102-03) Introduction to Statistics: Data Analysis.
Instructor: Mr. Andrew Barron, Mr. John Hartigan.
An introduction to probability and statistics with emphasis on analysis of data, presented with a unified foundation in basic statistical theory.

Statistics 103aG - F & ES 205aG (66103) Introduction to Statistics: Environmental Sciences. Instructor: Mr. Andrew Barron, Mr. Kenneth Carling.
An introduction to probability and statistics with emphasis on applications to forestry and environmental sciences, presented with a unified foundation in basic statistical theory.

Statistics 200La and 200Lb (66200), Statistical Computing Laboratory
Instructor: Mr. D. Pollard (fall) Mr. J. Hartigan (spring). Friday 2:30pm - 5pm
This lab offers an introduction to the S-plus statistical computing environment, including features such as customized graphics, language extensions, and interface with other languages. Is a co-requisite for Statistics 230a, Statistics 312a and Statistics 361a and is recommended for those taking Statistics 242b.
The first five weeks of the course will present a rapid introduction to the main features of Splus, which students from other Statistics courses are welcome to audit.
At Stat Lab, 140 Prospect.

Statistics 230a (66230), Introductory Data Analysis (FALL)
Cross-listing: Statistics 530a, PLSC 530b

Instructor: Mr. N. Hengartner. MW 2:30 pm - 3:45 pm
Survey of statistical methods: plots, transformations, regression, analysis of variance, clustering, principal components, contingency tables, and time series analysis. Techniques are demonstrated on the computer. Concurrent with Statistics 200L; after or concurrent with Statistics 101a.

Statistics 241a (66241), Probability Theory (FALL)
Cross-listing: Statistics/Mathematics 541a

Instructor: Mr. D. Pollard. MWF 9:30 am - 10:20 am
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.

Statistics 242b (66242), Theory of Statistics (SPRING)
Cross-listing: Statistics 542b, Mathematics 242b

Instructor: Mr. M. Wegkamp.
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; Statistics 200Lb recommended.
Time: Mon., Wed., Fri., 9:30-10:20

Statistics 251b (66251), Stochastic Processes (SPRING)
Cross-listing: Statistics 551b

Instructor: Mr. N. Hengartner.
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 241a or equivalent.

Statistics 312a (66312), Linear Models (FALL)
Cross-listing: Statistics 612a

Instructor: Mr. D. Pollard. 10:30 am - 11:20 am
The geometry of least squares; distribution theory for normal errors; regression, analysis of variance, and designed experiments; numerical algorithms (with particular reference to S-plus); alternatives to least squares. Generalized linear models. After Statistics 242b and Mathematics 222 or equivalents. Statistics 200Lb is a prerequisite.

Statistics 361b (66361), Data Analysis (SPRING)
Cross-listing: Statistics 661b

Instructor: Mr. J. Hartigan.
By analyzing data sets using the S-plus 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 242 or equivalent. Statistics 200L is a prerequisite.

Statistics 364b (66364), Information Theory (SPRING)
Cross-listing: Statistics 664b

Instructor: Mr. J. Chang.
Foundations of information theory in mathematical communications; statistical inference, statistical mechanics, probability, and algorithmic complexity. Quantities of information and their properties: entropy, conditional entropy, divergence, redunda ncy, mutual information, channel capacity. Basic theorems of data compression, data summarization, and channel coding. Applications in statistics and finance. After statistics Statistics 241.

Primarily graduate courses

Director of Graduate Studies: Andrew Barron

Statistics 600b (66600), Advanced Probability (SPRING)
Cross-listing: Statistics 330b

Instructor: Mr. A. Barron.
Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.

Statistics 603b (66603), Stochastic Calculus (SPRING)
Instructor: Mr. J. Chang.
Martingales in discrete and continuous time, Brownian Motion, Sample path properties, predictable processes, stochastic integrals with respect to Brownian motion and semimartingales, stochastic differential equations. Applications mostly to coutnin g processes and finance. Knowledge of measure-theoretic probability at the level of Statistics 600 is a prerequisite for the course, although some key concepts, such as conditioning, will be reviewed. After:
Statistics 600.

Statistics 610a (66610), Statistical Inference (FALL)
Instructor: Mr. M. Wegkamp.
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 241a assumed.

Statistics 625a (66625), Statistical Case Studies (FALL)
Instructor: Mr. J. Hartigan.
We will study large data sets on second hand smoke, reticulate evolution, bloc voting, NCAA Academic Thresholds, Connecticut Educational Standards - and other fun things.

Statistics 626b (66626), Practical Work (SPRING)
Instructor: Mr. J. Hartigan.
Individual one-semester projects, with students working on studies outside the Department, under the guidance of a statistician.
Time: Times to be arranged at organizational meeting.

Statistics 665a (66665), Function Estimation (FALL)
Instructor: Mr. N. Hengartner.
Nonparametric function estimation techniques are important tools for modern data analysis. In this course, we will study and compare methodologies, such as kernel based methods, regression splines, neural networks, hazard functions, conditional expec tations and conditional medians. Further topics covered include data driven bandwidth selection, adaptive estimation, local likelihoods, additive models and uniform confidence bands. I expect the students to have had introductory courses in probability an d statistics, at least at the Stat 241-242 level.
Time: Times to be arranged at organizational meeting.

Statistics 666b (66666), Resampling (SPRING)
Instructor: Mr. M. Wegkamp.
The "bootstrap" and "jackknife" are popular computer intensive methods in Statistics. Typically they improve upon more traditional methods for estimating the variability of statistical quantities. We shall be concerned with theoretical questions like: "When does the bootstrap work?" and "Why are they more accurate?" etc. Some keywords: consistency, second order correctness, bootstrapping in finite populations, density estimation, M-estimation, empirical processes, statistical functionals.

Statistics 670b (66670), Time Series (SPRING)
Instructor: Mr. A. Barron. Characterizing and extracting components of signals, methods of prediction, statitical models and inference in time series. Students are expected to find and analyze time series and to complete and present reports.
Time: Times to be arranged at organizational meeting

Statistics 685a (66685), Asymptotic Admissibility (FALL)
Instructor: Mr. J. Hartigan.
This course will develop a general method for evaluating estimation procedures. It will develop methods for doing Edgeworth expansions in many dimensions which will be applied to posterior distributions and to distributions of estimates. In this way, the asymptotic risks of Bayes estimates and other estimates will be computed. In particular it will be shown under which conditions maximum likelihood estimates are asymptotically Bayes and so asymptotically admissible.
Time: Times to be arranged at organizational meeting

Statistics 700, Departmental Seminar
Important activity for all members of the department. Either at 24 Hillhouse Avenue or at EPH. See weekly seminar announcements.
Time: Monday 4:15-

Revision: 11 Jun 1997 lmk