Yale Department of Statistics 1995-96 Course List

Yale University
Department of Statistics

Yale Statistics Courses

Courses for 1995-96

Primarily undergraduate courses

Director of Undergraduate Studies: Joseph Chang

Statistics 123a, Introduction to Statistical Methods and Probabilistic Reasoning
Cross-listing: Statistics 523a

Instructor: Mr. P. Everson.
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.
Time: Tue., Thu., 1:00-2:15; Lab session Monday afternoon; begins Thursday, September 7.

Statistics 200Lb, Statistical Computing Laboratory
Instructor: Mr. J. Hartigan.
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 230b, and is recommended for those taking Statistics 242b. It will be a prerequisite in future years for Statistics 312a and Statistics 361a.
[SYLLABUS] [Course material]
Time: Wednesday 2.30-5.00, Stat Lab, 140 Prospect

Statistics 230b, Introductory Data Analysis
Cross-listing: Statistics 530b, PLSC 530b

Instructor: 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. Concurrent with Statistics 200Lb; after or concurrent with Statistics 123a or Psychology 200a or b or equivalent.
Time: Tuesday 2:30-2:45 at 107 Dana; Thursday 2:30-3:45 at Stat Lab, 140 Prospect

Statistics 241a, Probability Theory
Cross-listing: Statistics/Mathematics 541a

Instructor: 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.
Time: Mon., Wed., Fr.,
9:30-10:20; begins Wednesday, September 6.

Statistics 242b, Theory of Statistics
Cross-listing: Statistics 542b, Mathematics 242b

Instructor: Mr. D. Pollard.
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.
[SYLLABUS] [Course material]
Time: Mon., Wed., Fri., 9:30-10:20 in room 207 WLH.

Statistics 251b, Stochastic Processes
Cross-listing: Statistics 551b

Instructor: 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 241a or equivalent.
Time: Mon., Wed., 2:30-3:45 in room 104 Mason Lab.

Statistics 312a, Linear Models
Cross-listing: Statistics 612a

Instructor: Mr. J. Hartigan.
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. (In future years, Statistics 200Lb will also be a prerequisite.)
Time: Tue., Thu., 2:30-3:45; begins Thursday, 7 September.

Statistics 361a, Data Analysis
Cross-listing: Statistics 661a

Instructor: Mr. N. Hengartner.
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 242b or equivalent. (In future years Statistics 200Lb will also be a prerequisite.)
Time: Mon., Wed., Fri., 2:30-3:20; begins Thursday, 7 September.

Statistics 364b, Introduction to Information Theory
Cross-listing: Statistics 664b

Instructor: Mr. A. Barron
Information theory foundations in mathematical communications, statistical inference, probability theory, statistical mechanics, and algorithmic complexity. Quantities of information and their properties: entropy, conditional entropy, divergence, redundancy, mutual information, channel capacity. Basic theorems of data compression, data summarization, and channel coding. Applications in statistics and finance. After Statistics 241a and Mathematics 301a.
Time: Thursday 10:30-12:00 in room 107 Dana House.

Primarily graduate courses

Director of Graduate Studies: John Hartigan (fall); Andrew Barron (spring)

Statistics 600b, Advanced Probability
Cross-listing: Statistics 330b

Instructor: Mr. J. Chang.
Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.
Time: Tue., Thu., 2:30-3:45 in room 113 WLH.

Statistics 603a, Stochastic Calculus
Instructor: Mr. D. Pollard.
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 counting processes and finance. Knowledge of measure-theoretic probability at the level of Statistics 600b is a prerequisite for the course, although some key concepts, such as conditioning, will be reviewed.
Time: Times to be arranged at organizational meeting

Statistics 610a, Statistical Inference
Instructor: Mr. D. Pollard.
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.
Time: Tue., Thu., 10:30-11:45; begins Thursday, 7 September.

Statistics 614b, Hierarchical Models
Instructor: Mr. P. Everson.
Hierarchical models make it possible to account properly for different levels and sources of variation in complex data sets and may be used to provide better inferences for individual units by borrowing strength of information from the ensemble. Emphasis will be on applications to real problems and on the implementation of methods in S-plus. After Statistics 612a.
Time: Wednesday 10:00-12:00 in room 107 Dana House.

Statistics 625a, Statistical Case Studies
Instructor: Mr. P. Everson.
Thorough analysis of complex data sets using S-plus, with emphasis on the balance between graphical techniques and formal inferential procedures. Problems arising in health policy will be investigated.
Time: Times to be arranged at organizational meeting

Statistics 626b, Practical Work
Instructor: Mr. J. Hartigan.
Individual one-semester projects, with students working on studies outside the Department, under the guidance of a statistician.

Statistics 651b, Counterexamples
Instructor: Mr. N. Hengartner.
Foundational issues of statistical inference and probability are explored through counter- examples. The course will be held seminar-like in that we will work through papers by Fisher, Basu, Berger, and others. Students are expect to have had some exposure to classical mathematical statistics. Topics covered will included the likelihood principle, notion of Statistical information, sufficiency, estimation in presence of nuisance parameters, pivot Statistics and fiducial inference, ancillary statistics, partial likelihoods, randomization.
Time: Thursday 10:30-12:30 in room 107 Dana House.

Statistics 668b, Computational Learning Theory and Statistics
Instructor: Mr. A. Barron
Valiant's model for computationally feasible inference problems. Determination of NP-hard problems and computationally feasible subproblems: satisfiability, set splitting, inference of multivariate Boolean functions, inference of multivariate polynomial functions, optimization of multi-unit neural networks. The roles of empirical process theory and measures of complexity. Intended for graduate students in Statistics, Computer Science, Mathematics, Electrical Engineering and Economics. After Statistics 241a or equivalent.
Time: Friday 10:30-12:30 in room 107 Dana House.

Statistics 687a, Stochastic Models of Evolution
Instructor: Mr. J. Chang.
Probabilistic and statistical study of evolution, with emphasis on population genetics and phylogeny reconstruction. Fluctuations of gene frequencies, genealogies and coalescent processes. Effects of selection, recombination, geography and variable population size. Methods of phylogeny reconstruction and their statistical properties. Markov models, parsimony, distance methods, maximum likelihood, site-to-site rate variation and dependence. Reliability of estimated trees and alternatives to tree-like phylogenies. Recommended background: Probability and Statistics at the level of Statistics 241a and Statistics 242b.

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-

Courses of interest in other departments

Political Science 505b, Statistical Graphics
Instructor: Mr. E. Tufte
Techniques for the visual display of quantitative information, including multivariate graphics. Examination of many examples of data graphics in science, social science and journalism. Development of empirical measures of graphical performance. Also the use of tables and words to convey statistical data.
Time: Tuesday, 3:30-5:20 at 124 Prospect Room 102

Revision: 20 July 1995