Statistics

Faculty of the Department of Statistics

Donald B. Rubin, Professor of Statistics (Chair)
Arthur P. Dempster, Professor of Theoretical Statistics (on leave spring term)
S.C. Samuel Kou, Assistant Professor of Statistics
Jun S. Liu, Professor of Statistics
Fabrizia Mealli, Visiting Associate Professor of Statistics
Xiao-Li Meng, Professor of Statistics (Director of Graduate Studies)
Mayumi Morimoto, Lecturer on Statistics
Carl N. Morris, Professor of Statistics (on leave 2001-02)
David van Dyk, Associate Professor of Statistics (Head Tutor)
Steve C. Wang, Lecturer on Statistics (Head Tutor)
Wing H. Wong, Professor of Statistics (FAS) and Professor of Computational Biology (Public Health)

Other Faculty Offering Instruction in the Department of Statistics

Frederick Mosteller, Professor of Mathematical Statistics, (Emeritus), (FAS), Roger Irving Lee Professor of Mathematical Statistics (Public Health) (Emeritus)
Bernard Rosner, Professor of Medicine (Medical School)
Alan Zaslavsky, Associate Professor of Statistics (Medical School)

In 2001–2002, the Statistics Department offers four courses at the introductory level (below Statistics 110). Statistics 100 and 101 are essentially equivalent in terms of their quantitative requirements, but differ in the amount of emphasis placed on different techniques and applications. Statistics 100 emphasizes regression, including multiple regression, which is essential in economics and related fields. Statistics 101 emphasizes analysis of variance, which is widely used in experimentally oriented subjects such as psychology and biology. Statistics 104 combines the content of Statistics 100 and 101, and moves somewhat faster than these courses, assuming a stronger quantitative orientation. Statistics 102 is comparable to Statistics 104 in its technical level, but is specifically oriented toward biomedical applications and techniques.

Generally, Statistics 104 and 101 will be accepted as fulfilling any requirement or prerequisite which is fulfilled by Statistics 100. Consult the Statistics Department or your tutorial office for more information about which courses satisfy your concentration requirements, and for guidance on selecting a course. More detailed information can be accessed through the network at the Statistics Department home page at www.harvard.edu/~stats/.

Primarily for Undergraduates

*Statistics 91r. Supervised Reading and Research
Catalog Number: 6641
David van Dyk and members of the Department
Half course (fall term; repeated spring term). Hours to be arranged.
Note: Normally may not be taken more than twice; may be counted for concentration in Statistics if taken for graded credit; may be taken in either term; for further information consult with head tutor.

*Statistics 99hf. Tutorial — Senior Year
Catalog Number: 4381
David van Dyk and members of the Department
Half course (throughout the year). Hours to be arranged.
The systematic application of statistical ideas to a problem area.
Note: In exceptional circumstances, may be taken alternatively as a half course in the spring term only.

For Undergraduates and Graduates

Statistics 100. Introduction to Quantitative Methods
Catalog Number: 3808
Fabrizia Mealli (University of Florence) (fall term), Fabrizia Mealli (fall term) and Steve C. Wang (spring term)
Half course (fall term; repeated spring term). M., W., F., at 11, and a section meeting to be arranged. EXAM GROUP: 4
Introduces the key ideas underlying statistical and quantitative reasoning, including fundamentals of probability. Topics may include elements of sample surveys, experimental design and observational studies, descriptive and summary statistics for both measured and counted variables, and statistical inference including estimation and tests of hypotheses as applied to one- and two-sample problems, regression with one or more predictors, correlation, and analysis of variance. Emphasizes simple and multiple regression and applications in nonexperimental fields including, but not limited to, economics.
Note: Only one of the following courses may be taken for credit: Statistics 100, 101, 104.

Statistics 101. Introduction to Quantitative Methods
Catalog Number: 5128
Steve C. Wang
Half course (fall term). M., W., F., at 11, and a section meeting to be arranged. EXAM GROUP: 4
Covers the same topics as Statistics 100. Emphasizes the analysis of variance, applied in experimental fields such as psychology and other behavioral sciences.
Note: Only one of the following courses may be taken for credit: Statistics 100, 101, 104.

Statistics 102. Fundamentals of Biostatistics
Catalog Number: 0266
Bernard Rosner (Medical School)
Half course (spring term). M., W., F., at 11, and section meeting to be arranged. EXAM GROUP: 4
An introduction to statistical methods used in biological and medical research. Elementary probability theory, basic concepts of statistical inference, sampling theory, regression and correlation methods, analysis of variance, study design. Emphasis on applications to medical problems.
Note: Primarily for undergraduates with medical or biological interests.

Statistics 104. Introduction to Quantitative Methods
Catalog Number: 4582
David van Dyk
Half course (fall term). M., W., F., at 11, and a section time to be arranged. EXAM GROUP: 4
Covers the same topics as 100 and 101 combined, at a slightly higher level. Applications will be drawn from fields such as economics, behavioral and health sciences, policy analysis, and law.
Note: Only one of the following courses may be taken for credit: Statistics 100, 101, 104.

Statistics 110. Introduction to Probability
Catalog Number: 0147
Wing H. Wong
Half course (fall term). Tu., Th., 11:30–1, and a section meeting to be arranged. EXAM GROUP: 13, 14
A first course in probability pointed toward applications, for students with some calculus. Models include the normal, binomial, exponential, Poisson and gamma distributions. Topics include expectation, independence, conditioning, generating functions, joint distribution and density functions, and limit laws.
Prerequisite: Mathematics 21a or equivalent.

Statistics 111. Introduction to Theoretical Statistics
Catalog Number: 1836
Xiao-Li Meng
Half course (spring term). M., W., F., at 12, and a section meeting to be arranged. EXAM GROUP: 5
Basic concepts of statistical inference from frequentist and Bayesian perspectives. Topics include maximum likelihood methods, confidence and Bayesian interval estimation, hypothesis testing, least squares methods, and analysis of variance.
Prerequisite: Statistics 110 and basic linear algebra.

Statistics 139. Regression Analysis
Catalog Number: 1450
Steve C. Wang
Half course (fall term). Tu., Th., 10–11:30, and a section meeting to be arranged. EXAM GROUP: 12, 13
An introduction to data analysis using multiple regression. Topics may include model building and diagnostics, graphical checks of assumptions, transformations, multivariate graphics and visualization, exploratory data analysis, tests of significance and confidence intervals, and logistic regression. The course will emphasize analysis and investigation of real datasets using computer software.
Prerequisite: Statistics 100 or equivalent.

Statistics 140. Design of Experiments
Catalog Number: 7112
Mayumi Morimoto
Half course (spring term). W., F., 3:30–5. EXAM GROUP: 8, 9
Statistical designs for the estimation of the effects of treatments in randomizedexperiments. Topics include brief review of some basic structural inferenceprocedures, analysis of variance, randomized and Latin square designs, factorialdesigns, nested factorial designs, confounding in blocks, and fractional replications.
Prerequisite: Statistics 100 and 139, or equivalent.

[Statistics 149. Generalized Linear Models]
Catalog Number: 6617
Steve C. Wang
Half course (spring term). Hours to be arranged.
An introduction to the application and theory of generalized linear models. Emphasis is on understanding models and applying them to data. Topics include likelihood theory, exponential families, model specification, model checking and diagnostics, logistic and ordinal regression, log-linear models, quasi-likelihood, generalized estimating equations, and generalized linear mixed models. Applications are drawn from a variety of fields, including medicine, biology, and the social sciences.
Note: Expected to be given in 2002–03.
Prerequisite: Statistics 111 or equivalent and Statistics 139 or equivalent.

Statistics 160. Survey Methods
Catalog Number: 2993
Xiao-Li Meng
Half course (spring term). M., F., 2–3:30. EXAM GROUP: 7, 8
An introductory course to the methodology of sample surveys. Topics cover both design issues (e.g., multi-stagesampling) and analysis methods (e.g., regression estimation). Emphasis will be given to statistical insights and practical feasibility. The common problem of nonresponse in sample surveys will also be addressed.
Prerequisite: Statistics 111 or 139, or permission of instructor.

Statistics 171. Introduction to Stochastic Processes
Catalog Number: 4180
Jun Liu
Half course (spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
An introductory course in stochastic processes. Topics include Markov chains, branching processes, Poisson processes, birth and death processes, renewal theory, queuing theory, Brownian motion, and Martingales.
Prerequisite: Statistics 110 or equivalent.

[Statistics 185. Statistical Decision and Forecasting]
Catalog Number: 6788
David van Dyk
Half course (spring term). Hours to be arranged.
The development of a Bayesian approach to the related problems of decision and forecasting. Decision topics will include utility, loss, decision rules, risk, admissibility of decision rules, and decision theoretic aspects of sequential analysis. Forecasting will be developed through the dynamic linear model and include topics such as sequential analysis and smoothing; models for polynomial trends, seasonal trends, and adjustment for covariates; and forecast intervention, monitoring, and error analysis. Theory and computational methods will be developed with a strong emphasis on applications to a variety of data sets.
Note: Expected to be given in 2002–03.
Prerequisite: Statistics 110 or 139 or equivalent.

Primarily for Graduates

Statistics 210. Probability Theory and Statistical Inference I
Catalog Number: 2487
Jun S. Liu
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Random variables, their distributions and densities. Families and exponential families of distributions. Expectation. Independence, product spaces, and joint distributions. Types of convergence. Limit theorems (weak and strong laws, central limit problem). Conditional probability and expectation, multivariate Normal distribution, particular examples of conjugate, marginal, and conditional distributions. Inequalities, approximations, and stochastic simulation. Sampling distributions, likelihood function, sufficiency, and information.
Prerequisite: A course in probability and statistics at least at the level of Statistics 110, 111.

Statistics 211. Probability Theory and Statistical Inference II
Catalog Number: 1946
S.C. Samuel Kou
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Introduction to statistical inference. Frequency, Bayesian, and decision-theoretic approaches. Likelihood, sufficiency, multivariate Normal distribution, and exponential families. Testing hypotheses and estimation. Maximum likelihood estimation, likelihood ratio tests, linear models, models for frequency data, large and moderate sample approximations, including the delta method.
Prerequisite: Advanced calculus, Statistics 210, or equivalent.

Statistics 214. Causal Inference in Statistics and the Social and Biomedical Sciences
Catalog Number: 4042
Donald B. Rubin and Fabrizia Mealli (University of Florence)
Half course (fall term). Th., 2:30–5. EXAM GROUP: 16, 17, 18
Approaches to causal inference. Covers randomized experiments with and without noncompliance, observational studies with and without ignorable treatment assignment, instrumental variables and sensitivity analysis. A number of applications from economics, medicine, education, etc., are discussed.

Statistics 215 (formerly Statistics 315a and 315b). Fundamentals of Computational Biology
Catalog Number: 3304
Jun S. Liu and Wing H. Wong
Half course (spring term). F., 1–3:30, Th., 2–4:30. EXAM GROUP: 6, 7, 8, 16, 17, 18
Covers developments in bioinformatics/computational biology in the past 30 years, with emphasis on topics of recent interest. Topics include the basics of statistical estimation, BLAST methods and theory, cDNA sequence analysis, clustering and classification methods, data resources, hidden Markov models, Gibbs sampler, microarray analysis, gene regulatory motif discoveries, phylogenetic inference, protein structures, comparative genomics.
Note: Course will have weekly meetings in both Cambridge and at the School of Public Health with identical content.

Statistics 220 (formerly Statistics 220r). Bayesian Data Analysis
Catalog Number: 6270
David van Dyk
Half course (fall term). M., W., F., at 10. EXAM GROUP: 3
Begins with basic Bayesian models, whose answers often appear similar to classical answers, followed by more complicated hierarchical and mixture models with nonstandard solutions. Includes methods for monitoring adequacy of models and examining sensitivity of conclusions to change in models. Throughout, emphasis on drawing inferences via computer simulation rather than mathematical analysis.
Prerequisite: Statistics 110 and 111.

Statistics 221. Statistical Computing Methods
Catalog Number: 5959
S.C. Samuel Kou
Half course (spring term). Tu., F., 2–3:30. EXAM GROUP: 7, 8, 16, 17
A study of computing methods commonly used in statistics. Topics include generation of random numbers, Monte Carlo methods, optimization methods, numerical integration, and advanced Bayesian computational tools such as the Gibbs sampler, Metropolis Hastings, the method of auxiliary variables, marginal and conditional data augmentation, slice sampling, exact sampling, and reversible jump MCMC. Computer programming exercises apply the methods discussed in class.
Prerequisite: Linear algebra, Statistics 111, and knowledge of a computer programming language. Statistics 220 is recommended.

[Statistics 232 (formerly Statistics 332). Incomplete Multivariate Data]
Catalog Number: 4196
Half course (fall term). Hours to be arranged.
Methods for handling incomplete data sets with general patterns of missing data, emphasizing likelihood-based and Bayesian approaches. Focus is on the application and theory of iterative maximization methods, iterative simulation methods, and multiple imputation. Includes coverage of some multivariate tools and theory relevant to missing data problems. Real examples are drawn from a variety of fields, including health sciences, history of science, and government.
Note: Expected to be given in 2002–03.
Prerequisite: A course in probability (Statistics 110-level), a course in theoretical statistics (Statistics 111-level), and knowledge of regression and linear algebra (Statistics 139-level).

[Statistics 239. Advanced Regression Analysis]
Catalog Number: 7423
Half course (fall term). Hours to be arranged.
Besides the applications done jointly with Statistics 139, students meet separately to develop the theory (multivariate normal, maximum likelihood, likelihood ratio tests, Gauss-Markov, etc.) of linear models. Students do some of the homework assignments from Statistics 139, but also other assignments that differ and are more advanced. Grading is separate from Statistics 139.
Note: Expected to be given in 2002–03.
Prerequisite: Probability and statistics at the level of Statistics 110 and 111.

Graduate Courses of Reading and Research

*Statistics 301. Special Reading and Research
Catalog Number: 4474
Arthur P. Dempster 2345 (on leave spring term), Jun S. Liu 3760, S. C. Samuel Kou 4054, Xiao-Li Meng 4023, Carl N. Morris 2178 (on leave 2001-02), Frederick Mosteller 2235, Bernard Rosner (Medical School) 4018, Donald B. Rubin 7966, Steve C. Wang 2581, Wing H. Wong 3759, Alan Zaslavsky (Medical School) 1927, and David van Dyk 2669

*Statistics 302. Direction of Doctoral Dissertations
Catalog Number: 3382
Arthur P. Dempster 2345 (on leave spring term), S. C. Samuel Kou 4054, Jun S. Liu 3760, Xiao-Li Meng 4023, Carl N. Morris 2178 (on leave 2001-02), Bernard Rosner (Medical School) 4018, Donald B. Rubin 7966, Wing H. Wong 3759, Alan Zaslavsky (Medical School) 1927, and David van Dyk 2669

*Statistics 310hfr. Astrophysics Seminar
Catalog Number: 9367
David van Dyk 2669
Half course (throughout the year). Tu., 2–4. EXAM GROUP: 16, 17

[Statistics 311. Recent Advances in Markov Chain Monte Carlo Technology]
Catalog Number: 0826
David van Dyk 2669
Half course (fall term). Hours to be arranged.
Starting with a review of such standard techniques as Data Augmentation, the Gibbs sampler, and Metropolis Hastings, the course will focus on recent research papers on such topics as adaptive rejection sampling, the method of auxiliary variables, simulated tempering, the collapsed Gibbs sampler, marginal and conditional data augmentation, the nested EM algorithm, slice sampling, exact sampling, simulated sintering, reversible jump MCMC, regeneration, and sequential MC methods.
Note: Expected to be given in 2002–03.
Prerequisite: Statistics 220 or equivalent.

*Statistics 312r (formerly Statistics 312hfr). Advanced Topics in Statistical Computing
Catalog Number: 7775
Xiao-Li Meng 4023 4023
Half course (fall term). M., 2–4. EXAM GROUP: 7, 8

*Statistics 314r (formerly Statistics 314hfr). Seminar: Non-Parametric Methods
Catalog Number: 5052
S.C. Samuel Kou 4054 4054
Half course (fall term). Hours to be arranged. EXAM GROUP: 7, 8

*Statistics 316. Research Seminar: Statistics of Complex Systems
Catalog Number: 4442
Arthur P. Dempster 2345 (on leave spring term) 2345
Half course (fall term). Hours to be arranged. EXAM GROUP: 9
Statistical modeling and analysis appied to complex systems, including climate and ecological systems and complex memory systems used in visual recognition.

[*Statistics 317. Statistical Inference on Probablistic Reasoning: Research Seminar]
Catalog Number: 1478
Arthur P. Dempster 2345 (on leave spring term)
Half course (spring term). Hours to be arranged.
Study of systems for evidence-based probabilistic reasoning, such as Fisherian, Bayesian, and Dempster-Shafer inference, with applications to inferential analyses, including prediction, risk asessment, and decision analysis.
Note: Expected to be given in 2002–03.

[*Statistics 349r. Analysis of Psychological Data: Issues and Examples]
Catalog Number: 4528
Donald B. Rubin 7966
Half course (fall term; repeated spring term). Hours to be arranged.
Consulting projects on statistical problems arising in psychological and related research areas. Participants expected to contribute actively to one or more projects.
Note: Expected to be given in 2002–03.

*Statistics 392hfr (formerly Statistics 292r). Topics in Statistics
Catalog Number: 0925
Donald B. Rubin 7966 7966
Half course (throughout the year). W., 2–3:30. EXAM GROUP: 7, 8
A range of currently active projects. All involve real applications and require mathematical statistical development. Applications include education, census, political science, biomedical research. Techniques include design of experiments, Bayesian modelling, multiple imputation.