Department of Statistics

- Organizational Meeting for all Fall term courses whose times are not listed below: Tuesday, 5 September 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. Kennedy beforehand and submit their schedules.
- The Department has consolidated training in the use of the S-plus statistical computing environment into the course Statistics 200b. It is at present required only for Statistics 230b. At some stage in the future it will become a prerequisite for several other Statistics courses. S-plus can be used at several different levels: a high-powered calculator; a simple statistics package, for the fitting of regressions and the production of simple statistical summaries; a powerful language for statistical graphics; and as an environment for the production of new statistical tools.
- Courses whose numbers end with
**a**are taught in the fall; courses whose numbers end with**b**are taught in the spring.

Fall courses: 123/523, 241/541, 312/612, 361/661, 603, 610, 625, 687, 700

Spring courses: 200, 230/530, 242/542, 251/551, 364/364, 600/330, 614, 626, 651, 668, 700

**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.

[SYLLABUS]

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.

[SYLLABUS]

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.

[SYLLABUS]

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.

[SYLLABUS]

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.)

[SYLLABUS]

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.)

[SYLLABUS]

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.

**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.

[SYLLABUS]

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.

[SYLLABUS]

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.

[SYLLABUS]

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-

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