Statistics Department
Courselist for Fall 2006/Spring 2007

• Organizational Meeting for all SPRING term courses whose times are not listed below: 10:00am Friday 12 January at 24 Hillhouse Avenue, Room 107 .
• Those interested in attending one of the courses but unable to be present at this meeting should inform Amy Mulholland beforehand and submit their schedules.
• Courses whose numbers end with a are offered in the FALL;
  courses whose numbers end with b are offered in the SPRING;
  courses whose numbers end with ab are offered in both semesters.
• Courses whose first or only number is 600 or above (such as Stat 600b/330b or Stat 610a) are intended primarily for graduate students. If such a course does not have an undergraduate cross-listing, undergraduates need special permission to enroll.
• Schedule of times when 24 Hillhouse Room 107 is in use.
• Course lists for prior years: These pages are not being updated; some of the links may no longer be working.
• Director of Undergraduate Studies: Andrew Barron
• Director of Graduate Studies: Jay Emerson
• Typical 1st-year courses for Ph.D. and M.A. students.

Introductory Statistics (STAT 100b / STAT 500b)

Instructor: Jay Emerson
Time: Mon, Wed, Fri 10:30 - 11:20
Place: Mason 211 (tentative)
Webpage: http://www.stat.yale.edu/Courses/QR/stat100.html
Every day we are inundated with data. How do we recognize dishonest or even unintentionally distorted representations of quantitative information? How can we reconcile two medical studies with seemingly contradictory conclusions? How many observations do we need in order to make a sound decision? This course introduces statistical reasoning, emphasizing how Statistics can help us understand the world. Topics include numerical and graphical summaries of data, data acquisition and experimental design, probability, hypothesis testing, confidence intervals, correlation and regression. Students will learn to apply statistical concepts to data using Excel and reach conclusions about real-world problems.

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Introduction to Statistics (STAT 101a-106a/STAT 501a-506a)

Instructor: Jonathan Reuning-Scherer and staff
Time: Tues, Thurs 1:00 - 2:15
Place: OML 202 (tentative)
Webpage: http://www.stat.yale.edu/Courses/QR/stat101106.html
Statistics is the science and art of prediction and explanation. In most fields of study research relies on statistical analysis of data. Each of these courses, led by an expert from the field of study, introduces statistical reasoning and emphasizes how Statistics is applied to the particular discipline. Topics include numerical and graphical summaries of data, data acquisition and experimental design, probability, hypothesis testing, confidence intervals, correlation and regression. Students will learn to apply statistical concepts to data using Minitab and reach conclusions about real-world problems. 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 discipline particular to the course (Life Sciences for Stat 101, Political Science for Stat 102, and so on). The courses meet together for the first seven weeks and separately for the final six weeks. The first part of the course is taught by Jonathan Reuning-Scherer and covers fundamentals of probability and statistics. Periodic examples are provided by individual course instructors. The courses separate by area of specialty for the final six weeks.

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Introduction to Statistics: Life Sciences (STAT 101a/E&EB 210aG/MCDB 215a)

Instructor: Jonathan Reuning-Scherer and 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.

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Introduction to Statistics: Political Science (STAT 102a/EP&E 203a/PLSC 425a)

Instructor: Jonathan Reuning-Scherer and Alan Gerber
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.

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Introduction to Statistics: Social Sciences (STAT 103a/SOCY 119a)

Instructor: 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.

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[Introduction to Statistics: Psychology] (STAT 104a/PSYC 201a)

Time: not taught this year

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Introduction to Statistics: Medicine (STAT 105a)

Instructor: Jonathan Reuning-Scherer and 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.

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Introduction to Statistics: Data Analysis (STAT 106a)

Instructor: Jonathan Reuning-Scherer and Andrew Barron
An introduction to Probability and Statistics with emphasis on data analysis.

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Statistics as a Way of Knowing (STAT 129a/PSYC 129a)

Instructor: Nelson Donegan
Time: Tues, Thurs 11:30 - 12:45
Place: TBA
An introduction to basic concepts of statistics and probability that allow us to describe, evaluate, and understand aspects of the world and make informed choices. Exploration of relationships among statistical reasoning, cognitive psychology, and philosophical theories of knowledge.

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Introductory Data Analysis (STAT 230b/STAT 530a/PLSC 530b)

Instructor: Joseph Chang
Time: Mon, Wed 2:30 - 3:45
Place: TBA
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.

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Optimization and Convexity (AMTH 237a/AMTH 537a)

Instructor: Mokshay Madiman
Time: Mon, Wed 1:00 - 2:15
Place: TBA
Fundamental theory and algorithms of optimization, emphasizing convex optimization, with applications to a wide range of fields. The geometry of convex sets, basic convex analysis, optimality conditions, duality. Numerical algorithms: steepest descent, Newton's method, interior point methods. Applications from statistics, communications, control, signal processing, physics, and economics. Prerequisites: linear algebra and differential calculus.

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Probability and Statistics for Scientists (STAT 238a/STAT 538a)

Instructor: Joseph Chang
Time: Mon, Wed, Fri 2:30-3:20
Place: ML 104 (tentative)
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.

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Probability Theory with Applications (STAT 241a/STAT 541a/MATH 241a)

Instructor: Harrison Zhou
Time: Mon, Wed, Fri 9:30 - 10:20
Place: WLH 208 (tentative)
Webpage: http://www.stat.yale.edu/~hz68/241/
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.

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Theory of Statistics (STAT 242b/STAT 542b/MATH 242b)

Instructor: Harrison Zhou
Time: Mon, Wed, Fri 9:30 - 10:20
Place: BCT 102
Webpage: http://www.stat.yale.edu/~hz68/242/
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.

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Stochastic Processes (STAT 251b/STAT 551b)

Instructor: Andrew Barron
Time: Mon, Wed 1:00 - 2:15
Place: ML 104
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.

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Linear Models (STAT 312a/STAT 612a)

Instructor: Hannes Leeb
Time: Tues, Thurs 9:00-10:15
Place: 24 Hillhouse
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.

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Data analysis (STAT 361a/STAT661a)

Instructor: Lisha Chen and Jay Emerson
Time: Mon, Wed 2:30 - 3:45
Place: Statlab, 140 Prospect Street
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.

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Information theory (STAT364b/STAT664b)

Instructor: Sekhar Tatikonda
Time: Tues, Thurs 9:00 - 10:15
Place: 24 Hillhouse
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.

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Data Mining and Machine Learning (STAT365b/STAT665b)

Instructor: Lisha Chen
Time: Mon, Wed 11:30 - 12:45
Place: 24 Hillhouse
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.

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Applied Math Senior Seminar and Project (AM490b)

Instructor: Andrew Barron
Time: Mon 6:00-7:50
Place: 24 Hillhouse
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.

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Advanced Probability (STAT 600b/STAT 330b)

Instructor: David Pollard
Time: Tues, Thurs 2:30 - 3:45
Place: WLH 113
Webpage: http://www.stat.yale.edu/~pollard/600.spring07
Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.

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Probability Coupling (STAT 602b)

Instructor: David Pollard
Time: Tues, Thurs 10:30 - 11:45
Place: 24 Hillhouse
Webpage: http://www.stat.yale.edu/~pollard/602.spring07
Some of the most striking advances in probability theory have involved coupling: the representation of distributional relationships by means of deterministic properties of specially created joint distributions. The course explores the method through applications such as quantile coupling; almost sure representations for convergence in distribution; problems of mass transportation; Strassen's theorem and stochastic ordering; Wasserstein distances; rapidly mixing Markov chains; interacting systems of particles; the Hungarian (KMT) strong approximations; Poisson approximation; distances between statistical models (Blackwell/Le Cam theory). Acquaintance with measure theoretic probability would be an advantage, but all topics are made accessible to students with a knowledge of probability at the level of STAT 541a.

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Stochastic Calculus (STAT 603a)

Instructor: -
Time: not taught this year

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Markov Processes and Random Fields (STAT 606b)

Instructor: -
Time: not taught this year
Place: 24 Hillhouse
Webpage: http://www.stat.yale.edu/~pollard/stat606
Markov chains on general state spaces; diffusions; Markov random fields; Gibbs measures; percolation. After STAT 600.

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Inequalities for Probability and Statistics (STAT 607b)

Instructor: -
Time: not taught this year
Place: 24 Hillhouse

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Statistical Inference (STAT 610a)

Instructor: Hannes Leeb
Time: Tues, Thurs 10:30-11:45
Place: 24 Hillhouse
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.

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Statistical Decision Theory (STAT 619b)

Instructor: Harrison Zhou and Andrew Barron
Time: Tues, Thurs 4:00 - 5:15
Place: 24 Hillhouse
Webpage: http://www.stat.yale.edu/~hz68/619/
Shrinkage estimation and its connection to minimaxity, admissibility, Bayes, empirical Bayes, and hierarchical Bayes. Shrinkage captures essential nonlinearity necessary to outperform standard linear estimators in Gaussian regression models and random effects models. Relationship to model selection and to sparsity in the estimation of functions by selection from large dictionaries of candidate terms. Nonparametric estimation. Tests of statistical hypotheses. Multiple comparisons. Some knowledge of statistical theory at the level of STAT 610a is assumed.

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Statistical Case Studies (STAT 625a)

Instructor: Jay Emerson and Lisha Chen
Time: Mon, Wed 10:30 - 11:45
Place: 24 Hillhouse, basement computer lab
Webpage: http://www.stat.yale.edu/~jay/625.html
Statistical analysis of a variety of problems which, in past years, have included: 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. Graduate, professional, and undergraduate students from any department are welcome, but must seek permission (discussing their background in statistics and goals for the semester) at or before the first class meeting. At least one prior course in statistics is required, but the most important prerequisite is a willingness to get your hands dirty working with real data sets. This will entail a certain amount of "programming," which we believe can be best taught by example, trial and error.

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Practical Work (STAT 626b)

Instructor: Jay Emerson
Time: TBA
Place: 24 Hillhouse
Individual one-semester projects, with students working on studies outside the Department, under the guidance of a statistician. This course is a one-credit elective requirement for the Ph.D. degree.

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Statistical Consulting (STAT 627ab)

Instructor: Jay Emerson
Time: Friday 2:30 - 4:30
Place: 24 Hillhouse Room 107
Webpage: http://www.stat.yale.edu/~jay/627.html
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. The course meets once a week all year, and students receive one half-credit each semester.

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Monte Carlo Methods (STAT 636a)

Instructor: -
Time: not taught this year
Place: -
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.

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Statistical Methods in Genetics and Bioinformatics (STAT 645b)

Instructor: Hongyu Zhao
Time: Tues, Thurs 1:00-2:30
Place: LEPH Rm. 106
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.

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Bayes Theory (STAT 653a)

Instructor: -
Time: not taught this year
Place: 24 Hillhouse
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.

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Topics in Bayesian Inference and Data Analysis (STAT 654a)

Instructor: Joseph Chang
Time: Wed, Fri 9:00 - 10:15
Place: 24 Hillhouse
Topics in the theory and practice of Bayesian statistical inference, ranging from a review of fundamentals to questions of current research interest. Motivation for the Bayesian approach. Bayesian computation, Monte Carlo methods, asymptotics. Model checking and comparison. A selection of examples and issues in modeling and data analysis. Discussion of advantages and difficulties of the Bayesian approach. After STAT 551 and STAT 610.

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Multivariate Statistics for Social Sciences (STAT 660b)

Instructor: Jonathan Reuning-Scherer
Time: Tues, Thurs 1:00 - 2:15
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.

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Probabilistic Networks, Algorithms, and Applications. (STAT 667a)

Instructor: Sekhar Tatikonda
Time: Tues, Thurs 1:00 - 2:15
Place: AKW 500
This course examines probabilistic and computational methods for the statistical modeling of complex data. The emphasis is 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, bioinformatics, and combinatorial optimization.

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Information and Probability (STAT 668a)

Instructor: -
Time: not taught this year
Place: 24 Hillhouse, basement
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.

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Information and Statistics (STAT 669a)

Instructor: Andrew Barron and Mokshay Madiman
Time: Tues, Thurs 4:00 - 5:15
Place: 24 Hillhouse
Study of the pivotal role that information theory plays in illuminating modern statistics. Topics include the equivalence of data compression and statistical modeling (from the Shannon, universal coding, and Kolmogorov viewpoints), and its relationship to the minimum description length principle; aspects of hypothesis testing (fixed and sequential tests, error exponents, multiple testing); clean risk bounds for complex estimation scenarios based on an index of resolvability; and the arbitrary sequence approach to online learning with applications to prediction, data compression, and portfolio selection. Additional topics if time permits.

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Analysis of Spatial and Time Series Data (STAT 674a)

Instructor: -
Time: not taught this year
Place: 24 Hillhouse

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Nonparametric Statistics (STAT 680b)

Instructor: -
Time: not taught this year
Place: 24 Hillhouse
Webpage: http://www.stat.yale.edu/~hz68/680
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.

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Independent Study (STAT 690ab)

Instructor: Staff
Time: -
Place: -
By arrangement with faculty. Approval of director of graduate studies required.

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Internship in Statistical Research (STAT 695ab)

Instructor: Jay Emerson
Time: -
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, but is distinct from the required Stat 626b. 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.

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Research Seminar in Statistics (STAT 699ab)

Instructor: Sekhar Tatikonda and David Pollard
Time: Wed 11:30 - 1:30
Place: 24 Hillhouse basement
Continuation of the dissertation seminar: message passing algorithms, random graphs, the objective method. Not for credit.

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Departmental Seminar (STAT 700ab)

Instructor: -
Time: Monday 4:15 - 5:30
Place: 24 Hillhouse Avenue, room 107
Webpage: http://www.stat.yale.edu/seminars.html
Important activity for all members of the department. See webpage for weekly seminar announcements.

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