Course List for 2005-2006

course number instructor level time
Introduction to Statistics  101-106a Reuning-Scherer & Staff intro, no prereqs T,Th 1:00-2:15
Probability and Statistics for Scientists 238a Chang intro M,W,F 2:30-3:20
Probability Theory with Applications 241/541a Pollard
intro, with calculus M,W,F 9:30-10:20
Linear Models 312/612a Leeb
intermediate T,Th 9:00-10:15
Data Analysis 361/661a Hartigan
intermediate M, W 2:30-3:45
[Stochastic Calculus] 603a Pollard
[Foundations of Statistics]
605a Hartigan
Statistical Inference 610a Zhou intro grad T,Th 10:30-11:45
Statistical Case Studies 625a Emerson intermediate grad T,Th 2:30-3:45
Monte Carlo Methods

Bayes Theory

Internship in Statistical Research 695a Hartigan

Introductory Statistics
M,W,F 10:30 - 11:20
Introductory Data Analysis 230/530b Leeb
intro M,W  2:30-3:45
Theory of Statistics 242/542b Zhou intro, with calculus M,W,F 9:30-10:20
Stochastic Processes 251/551b Madiman
intermediate M,W 1:00-2:15
Advanced Probability 330/600b Pollard adv. undergrad/ 
intermediate grad
T,Th 2:30-3:45
Information Theory 364/664b Barron
intermediate T,Th 9:00-10:15
Data Mining and Machine Learning 365/665b Leeb
M,W 11:30-12:45
Applied Math Senior Seminar AM490b Barron
W 3:30 - 5:20
Markov Processes and Random Fields

T,Th 10:30-11:45
[Inequalities for Probability & Statistics]

Practical Work 626b Emerson adv. grad 1:00-2:00
Statistical Consulting 627b Emerson
T 2:30 - 3:45, F 1:00 - 4:00
Statistical Methods in Genetics and Bioinformatics 645b Chang
T, TH 10:30 - 11:20, F 2:00 - 2:50
Multivariate Methods for the Social Sciences
660b Reuning-Scherer
T, TH 1:00 - 2:15
[Probabilistic Networks, Algorithms, and Applications]

Information and Probability

Nonparametric Statistics


Primarily undergraduate courses

Director of Undergraduate Studies, 2005:  Professor Joseph Chang.

STAT 100b / STAT 500b, Introductory Statistics
Instructor: Mr. John Emerson
Time:  Mon, Wed, Fri 10:30 am - 11:20 am
An introduction to statistical reasoning.  Topics include numerical and graphical summaries of data, data acquisition and experimental design, probability, hypothesis testing, confidence intervals, correlation and regression.  Application of statistical concepts to data; analysis of real-world problems.

STAT 101a-106a / STAT 501a-506a, Introduction to Statistics
Instructor: Mr. Jonathan Reuning-Scherer and faculty from other departments.
Time: Tues, Thurs 1:00 pm - 2:15 pm

A basic introduction to statistics, including 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 101-106 together. The course separates for Thursday lectures (sections), 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. No prerequisites beyond high school algebra.

STAT 101a / E&EB 210aG / MCDB 215a, Introduction to Statistics: Life Sciences.
Instructor:  Mr. Jonathan Reuning-Scherer / Mr. Gunter Wagner
Statistical and probabilistic analysis of biological problems presented with a unified foundation in basic statistical theory. Problems are drawn from genetics, ecology, epidemiology, and bioinformatics.

STAT 102a / EP&E 203a / PLSC 425a, Introduction to Statistics: Political Science.
Instructor:  Mr. Jonathan Reuning-Scherer / Mr. Donald Green
Statistical analysis of politics and quantitative assessments of public policies. Problems presented with reference to a wide array of examples: public opinion, campaign finance, racially motivated crime, and health policy.

STAT 103a / SOCY 119a, Introduction to Statistics: Social Sciences.
Instructor:  Mr. Jonathan Reuning-Scherer
Descriptive and inferential statistics  applied to analysis of data from the social sciences. Introduction of concepts and skills for understanding and conducting quantitative research.

[STAT 104a / PSYC 201a, Introduction to Statistics: Psychology.  Not offered this semester.]

STAT 105a, Introduction to Statistics:  Medicine.
Instructor:  Mr. Jonathan Reuning-Scherer / Mr. David Salsburg
Statistical methods relied upon in medicine and medical research.  Practice in reading medical literature competently and critically, as well as practical experience performing statistical analysis of medical data.

STAT 106a, Introduction to Statistics: Data Analysis. 
Instructor: Mr. Andrew Barron
 Time: Tues, Thurs 2:30-3:20 An introduction to Probability and Statistics with emphasis on data analysis.

STAT 230b / STAT 530a / PLSC 530b, Introductory Data Analysis
Instructor: Mr. Hannes Leeb
Time: 2:30 - 3:45
Survey of statistical methods: plots, transformations, regression, analysis of variance, clustering, principal components, contingency tables, and time series analysis. Uses SPLUS and Web data sources. After or concurrent with Statistics 101-105.

STAT 238a / STAT 538a, Probability and Statistics for Scientists
Instructor: Mr. Joseph Chang
Time: Mon, Wed, Fri 2:30-3:20
Fundamental principles and techniques that help scientists think probabilistically, develop statistical models, and analyze data. Essentials of probability: conditional probability, random variables, distributions, law of large numbers, central limit theorem, Markov chains.  Statistical inference with emphasis on the Bayesian approach:  parameter estimation, likelihood, prior and posterior distributions, Bayesian inference using Markov chain Monte Carlo.  Introduction to regression and linear models.  Computers are used throughout for calculations, simulations, and analysis of data.  After MATH 118a or b or 120a or b.  Some acquaintance with matrix algebra and computing assumed.

STAT 241a / STAT 541a, Probability Theory with Applications
Instructor: Mr. David Pollard
Time: Mon, Wed, Fri 9:30 - 10:20
A first course in probability theory: probability spaces, random variables, expectations and probabilities, conditional probability, independence, some discrete and continuous distributions, central limit theorem, law of large numbers. After or concurrent with Mathematics 120a or b or equivalents.

STAT 242b / STAT 542b / Mathematics 242b, Theory of Statistics
Instructor: Mr. Harrison Zhou
Time: Mon, Wed, Fri 9:30 - 10:20
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.

STAT 251b / STAT 551b, Stochastic Processes
Instructor: Mr. Mokshay Madiman
Time: Mon, Wed 1 - 2:15
Introduction to the study of random processes, including Markov chains, Markov random fields, martingales, random walks, Brownian motion and diffusions. Tecniques 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.

STAT 312a / STAT 612a, Linear Models
  Instructor: Mr. Hannes Leeb
Time: Tues, Thurs 9:00-10:15
The geometry of least squares; distribution theory for normal errors; regression, analysis of variance, and designed experiments; numerical algorithms (with particular reference to Splus); alternatives to least squares. Generalized linear models. Linear algebra and some acquaintance with statistics assumed.

STAT 361a STAT 661a, Data Analysis
  Instructor: Mr. John Hartigan
Time: Mon, Wed 2:30 - 3:45
Through analysis of data sets using the Splus statistical computing language, study of a selection of statistical topics such as linear and nonlinear models, maximum likelihood, resampling methods, curve estimation, model selection, classification and clustering. After Statistics 242 and Mathematics 222b or 225a or b, or equivalents.

STAT 364b / STAT 664b, Information Theory
  Instructor:  Mr. Andrew Barron
Time:    Tue, Thu 9:00 - 10:15
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, redundancy, mutual information, channel capacity. Basic theorems of data compression, data summarization, and channel coding. Applications in statistics and finance. After Statistics 241.

STAT 365b / STAT 665b, Data Mining and Machine Learning
  Instructor:  Mr. Hannes Leeb
Time:    Mon, Wed 11:30 - 12:45
Techniques for data mining and machine learning are covered from both a statistical and a computational perspective, including support vector machines, bagging, boosting, neural networks, and other nonlinear and nonparametric regression methods.  The course will give the basic ideas and intuition behind these methods, a more formal understanding of how and why they work, and opportunities to experiment with machine learning algorithms and apply them to data. After STAT 242b.

AM490b, Applied Math Senior Seminar and Project
Instructor: Mr. Andrew Barron
Time:  Wed 2:30 - 3:20
Under the supervision of a member of the faculty, each student works on an independent project.  Students participate in seminar meetings at which they speak on the progress of their projects.  Some meetings are devoted to talks by visiting applied mathematicians.

Primarily graduate courses

Director of Graduate Studies:  Professor John Hartigan.

STAT 600b / 330b, Advanced Probability
  Instructor: Mr. David Pollard
Time:  Tues, Thurs 2:30 - 3:45
Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.

[STAT 603a, Stochastic Calculus]

[STAT 605a, Foundations of Statistics]

STAT  606b, Markov Proceesses and Random Fields
Instructor: David Pollard
Markov chains on general state spaces;diffusions;Markov random fields;Gibbs measures; percolations. After STAT 600.

[STAT 607b, Inequalities for Probability & Statistics]

STAT 610a, Statistical Inference 
Instructor: Mr. Harrison Zhou
Time:  Tues, Thurs 10:30-11:45 am
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.

STAT 625a, Statistical Case Studies
Instructor: Mr. John Emerson and Mr. John Hartigan.
Time: Tues, Thurs 2:30-3:45 pm
Statistical analysis of a variety of problems including the value of a baseball player, the fairness of real estate taxes, how to win the Tour de France, energy consumption in Yale buildings, and interactive questionnaires for course evaluations.  We will emphasize methods of choosing data, acquiring data, and assessing data quality.  Computations will use R.

STAT 626b, Practical Work 
Instructor: Mr. John Emerson
Time: contact instructor
Place:  contact instructor

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

 STAT 627b, Statistical Consulting
Instructor: Jay Emerson
Time: TBA
Statistical consulting and collaborative research projects often require statisticians to explore new topics outside their area of expertise. This course exposes students to real problems, requiring them to draw on their expertise in probability, statistics, and data analysis. Students complete the course with individual projects supervised jointly by faculty outside the department and by one of the instructors.

STAT 636a, Monte Carlo Methods.
Instructor: Joseph Chang.
Theory and practice of Monte Carlo methods, with emphasis on Markov chain Monte Carlo and statistical applications. Generation of random variables, importance sampling, Metropo­lis Hastings, Gibbs sampling, variable dimension methods and model selection, multilevel and population based methods, convergence diagnostics. Markov chains in general state spaces and rates of convergence. Applications in Bayesian inference, simulation, and optimization.

STAT 645b, Statistical Methods in Genetics and Bioinformatics
Instructor: Mr. Joseph Chang
Time: TBA
Stochastic modeling and statistical methods applied to problems such as mapping quantitative trait loci, analyzing gene expression data, sequence alignment, and reconstructing evolutionary trees. Statistical methods include maximu likelihood, Bayesian inference, Monte Carlo Markov chains, and some methods of classification and clustering. Models introduced include variance components, hidden Markov models, Bayesian networks, and coalescent. Recommended background: Stat 541, Stat 542. Prior knowledge of biology is not required.

STAT 653a, Bayes Theory
Instructor: Mr. John Hartigan
Time: TBA
Axioms and interpretations of probability. Construction of probablilty distributions. Optimality of Bayes procedures. Martingales. Asymptotics. Markov sampling. Robustness against violations in the assumed distributions. Choice among models.

STAT 660b, Multivariate Statistics for Social Sciences
Instructor:  Mr. Jonathan Reuning-Scherer
Time:; Tues, Thur 1:00 pm - 2:15 pm
A practical introduction to the analysis of multivariate data as applied to
examples from the social sciences. Topics to include multivariate analysis of variance (MANOVA),
principle components analysis, cluster analysis (hierarchical clustering, k-means), canonical correlation,
multidimensional scaling, factor analysis, discriminant analysis, and structural equations modeling.
Emphasis is placed on practical application of multivariate techniques to a variety of examples in the
social sciences. There are regular homework assignments and a final project. Regular use of some
statistical software package (students may choose among SAS, SPSS, and MINITAB). A complete
syllabus will be available on the classes server.

STAT 667b / ENAS 503, Probabilistic Networks, Algorithms, and Applications
Instructor:  Mr. Sekhar Tatikonda
Time:  Tues, Thurs 11:30 - 12:45
This course examines probabilistic and computational methods for the statistical modeling of complex data. The emphasis will be on the unifying framework provided by graphical models, a formalism that merges aspects of graph theory and probability theory.  Graphical models: Markov random fields, Bayesian networks, and factor graphs.  Algorithms: filtering, smoothing,
belief-propagation, sum-product, and junction tree.  Variational techniques: mean-field and convex relaxations.  Markov processes on graphs: MCMC, factored HMMs, and Glauber dynamics.  Some statistical physics techniques: cavity and replica methods.  Applications to error-correcting codes, computer vision, bio-informatics, and combinatorial optimization.

STAT 668a Information and Probability. Andrew Barron, Mokshay Madiman
TBA. Study of several key results in probability using ideas and methods from information theory. Topics include entropy and its relationship to Fisher information, the law of large numbers, central limit theorem (normal approximation), law of small numbers (Poisson approximation), large deviations, martingales, Markov chains, and information projection. The approach we take quantitifies the increase in entropy or more generally the drop in information distance from an approximating distribution. Interpretations from statistics, physics, and finance.

STAT 680b, Nonparametric Statistics. Harrison Zhou.
Introduction to nonparametric methods such as kernel estimation, Fourier basis estimation, wavelet estimation. Optimal minimax convergence rates and constants for function spaces, with connections to information theory. Adaptive estimators (e.g., adaptive shrinkage estima­tion). If time permits: high dimensional function estimation, functional data estimation, classification, or nonparametric asymptotic equivalence. Applications to real data. Some knowledge of statistical theory at the level of STAT 610a is assumed.

STAT 695a, Internship in Statistical Research (1 credit)
Instructor: Mr. John Hartigan
The Internship is designed to give students an opportunity to gain practical exposure to problems in the analysis of statistical data, as part of a research group within industries such as: medical and pharmaceutical research, financial, information technologies, telecommunications, public policy, and others.  The Internship experience often serves as a basis for the Ph.D. dissertation.  Students will work with the Director of Graduate Studies and other faculty advisors to select suitable placements.

Students will submit a one-page description of their Internship plans to the DGS by May 1st, which will be evaluated by the DGS and other faculty advisors by May 15th.  Upon completion of the Internship, students shall submit a written report of their work to the DGS, no later than October 1st.  The Internship will be graded on a Satisfactory/ Unsatisfactory basis, and will be based on the student's written report and an oral presentation.
This course is an elective requirement for the Ph.D. degree.

STAT 699, Research Seminar in Statistics
Instructor:  Mr. Sekhar Tatikonda / Mr. David Pollard
Time: Friday, 10:00 - 12:00

STAT 700, Departmental Seminar
Time: Monday 4:15 pm - 5:30 pm
Important activity for all members of the department. See weekly seminar announcements.

Course lists for prior years may be found here. Please note these older pages are not being updated, and as such, some of the links may no longer be working.

Revision: 22 July 2005