Statistics
Statistics
Statistical modeling and analysis, including the collection and interpretation of data, form an essential part of the scientific method in diverse fields, including social, biological, and physical sciences. Statistical theory is primarily based on the mathematical theory of probability, and covers a wide range of topics, from highly abstract areas to topics directly relevant for applications. Research in statistics covers many issues, some closely tied to theoretical principles of statistical inference, and others more concerned with developing and extending techniques for descriptive and exploratory analysis of data. The theory and practice of designing the efficient collection of data through experiments, surveys, and observational studies constitute important areas of statistics. Since computers play a major and often crucial role in statistical research through simulation techniques, and in statistical applications through the analysis of data, statistical computation is another major subfield.
Statisticians are frequently concerned with modeling complex phenomena, especially by developing and applying appropriate probability models to empirical data, and often these efforts are intimately connected to policy-relevant decision-making in business and government. We seek to train statisticians who will contribute to theory, develop innovative and useful statistical models and methods, and conduct serious applied statistical scientific investigations. Individual statisticians will vary in their emphasis, but the field includes all of these aspects.
Statisticians with advanced training are in substantial demand for positions in academic teaching and research, in research laboratories and organizations, in government agencies, and in business. As society, science, and the technology of data handling grow in complexity, the need for highly qualified statisticians is expected to grow steadily.
The Department of Statistics offers courses of study leading to both the PhD and master’s degrees. The department encourages applications from students with strong mathematical backgrounds who plan to concentrate on theoretical statistics, students with training in substantive fields whose primary interest is in applied statistics, and students whose backgrounds and interests lie between these two extremes. In addition to formal course work and dissertation research, students are encouraged to work closely with faculty and to attend seminars concerning current problems in empirical research and thereby to gain experience with interdisciplinary statistical research and consulting. All PhD candidates are expected to engage in some teaching during their period of training.
Preparation in Mathematics, Statistics, and Computation
The minimum mathematical preparation for admission to graduate study in statistics is linear algebra and advanced calculus. Ideally, each student’s preparation should include at least one term each of mathematical probability and mathematical statistics. Additional study in statistics and related mathematical areas, such as analysis and measure theory, is helpful. In the initial stages of graduate study, students should give high priority to acquiring the mathematical level required to satisfy their objectives. Before registering for their fall term classes, all entering students will be required to take a diagnostic test in mathematics. Performance on this test will assist the department in determining whether students need additional mathematics preparation.
Successful applicants demonstrate that they understand what the discipline of statistics entails, and show evidence of involvement in applications or a strong theoretical interest. They are able to articulate a strong motivation for studying statistics.
As statistics is so intimately connected with computation, computation is an important part of almost all courses and research projects in the department. Ideally, students should have programming experience in, or exposure to, some high-level computer language, such as SAS, S+, Fortran, and C.
Doctor of Philosophy (PhD)
The formal residence requirement for the PhD is 16 half-courses devoted to advanced study. Other formal requirements are the passing of a qualifying exam, the completion of a qualifying paper, the fulfillment of the cognate requirement, and the completion of a PhD dissertation. Details are provided below.
Program of Study. Students should plan their course program with three objectives in view: (i) acquiring basic knowledge in preparation for the qualifying examination; (ii) investigating a range of advanced topics; and (iii) exploring in some depth a field outside of statistics. To satisfy (i) and (ii), students will normally take a minimum of nine half-year courses offered by the Department of Statistics, including at least four on advanced topics.
Cognate Requirement. To satisfy (iii), students are required to demonstrate competence at communication (in lieu of a formal language requirement) in a selected cognate field. The most important criterion is an investment in the language, methods, and use of statistics in the cognate field. Examples of cognate fields are mathematics, computer science, or in some field of application of statistics such as astrophysics, biostatistics, business, computational biology, economics, education, engineering science, environmental science, sociology, psychology, public health, or public policy Students satisfy the cognate requirement with two half-courses at an appropriate level in the chosen field/s.
Courses that ordinarily would not give students the intended cognate experience, such as courses in mathematics and applied mathematics will require the approval of the Director of Graduate Study. For example, students with strong mathematical aptitudes and preparation who wish to pursue this direction may select a cognate in mathematics in preparation for research in mathematical statistics, and satisfy this requirement with two half-courses in mathematics; an analogous plan may be appropriate for students with a strong interest in computer science.
Details of programs should be established in consultation with the faculty advisors. During the second year of study, students should submit their prospective programs for approval by the department. Students will be expected to complete all work with distinction.
Qualifying Examination. The student must pass a written qualifying examination in statistics, which is given once each year. The examination is normally taken by students in their second year. It is given at the end of the spring term, with two parts, the first on theoretical statistics including probability and mathematical statistics, and the second on applied statistics including statistical design and data analysis.
Research Presentations. At the end of each term, all students who have passed the qualifying exam present to department faculty and to fellow students brief summaries of their research in progress.
Qualifying Paper. The objective of the qualifying paper is to provide the student with an opportunity to explore a serious topic in statistics and to express the findings coherently in a written document. Although the work need not be original, it should demonstrate understanding of the topic, knowledge of the tools of research, and clarity of exposition. The effort involved is expected to require no more than the equivalent of one term at one-third time. This paper should be submitted and accepted by the department as early as possible, and preferably during the year following the qualifying exam. Delays in submission require permission of the department.
Dissertation. Each student is expected to exercise initiative in seeking out both a dissertation topic and a faculty advisor who will take primary responsibility for supervising the student’s work. The PhD dissertation is expected to be a research contribution of high quality adding to our knowledge of either the theory or practice of statistics. A PhD dissertation in statistics may also consist primarily of an innovative analysis of a specific, complex body of data in some substantive field. Generally, the material in a PhD dissertation should be publishable in a refereed journal.
Two copies of the completed dissertation must be submitted for consideration in the department office at least two weeks prior to a department colloquium on the substance of the dissertation. The faculty will consider the submitted dissertation and make recommendations, which generally lead to revisions. Next, the faculty, with the explicit advice of three faculty readers nominated by the department, vote on the completed dissertation as submitted in finished form, which must conform to the requirements described in The Form of the PhD Dissertation, available in the Registrar’s office. The approved final dissertation can be submitted to the Registrar. The time from the colloquium to the final vote is ordinarily about one month.
Recent dissertation topics have included:
“Contributions to Law and Empirical Methods” (D. James Greiner)
“Decoding Mammalian Gene Regulatory Programs through Efficient Microarray, ChIPchip, and Sequence Analysis” (Hongkai Ji)
“Effective Modeling and Scientific Computation with Applications to Health Study, Astronomy, and Queuing Network” (Jingchen Liu)
“Integrating Related Data Sets to Improve Inference in Computational Biology” (Xiaodan Fan)
“Methods of Approximate Inference: Applications to Stochastic Differential Equations, Video Microscopy, and Network Data” (Benjamin P. Olding)
“Assessing Thought Disordered Behavior Using Finite Mixture Models and Comparing Approximations for Logistic Regression” (Charity Johanna Morgan)
“Nonparametric Studies of Doubly Stochastic Poisson Processes, Binomial Data, and High Dimension, Low Sample Size Data” (Tingting Zhang)
“Decoding Gene Expression Regulation through Motif Discovery and Classification” (Yuan Yuan)
“Bayesian Inference of Interactions in Biological Problems” (Jing Maria Zhang)
“Bayesian Two-Glasso for the Study of Financial Contagion” (Alan Lenarcic)
“Statistical Methods for Detecting Expression Quantitative Trait Loci (eQTL)” (Wei Zhang)
“Profile HMMs for DNA Sequence Families: the Conditional Baum-Welch and Dynamic Model-Surgery Algorithms” (Paul Edlefsen)
“Estimation of Overflow Probabilities for Models with Heavy Tails and Complex Dependencies” (Chenxin Li)
“Hierarchical Models for Relational Data: An Example from Political Science” (Andrew C. Thomas)
“Statistics, Science and Statistical Science: Modeling, Inference and Computation with Applications to the Physical Sciences” (Paul Baines)
“Three Applications of Statistics to Medical Research” (Yves Chretien)
“Statistical Missing Data and Computation Problems: Theories and Applications in Astophysics, Finance and Economics” (Zhan Li)
“Efficient Monte-Carlo Methods and Asymptotic Analysis for Stochastic Systems” (Kwai Hung Henry Lam)
“Two Tales of Frequentist Properties of Bayesianly Motivated Methods: Multiple Imputation and Shrinkage Estimation” (Xianchao Xie)
“Rerandomization to Improve Covariate Balance in Randomized Experiments” (Kari Lock)
“Efficient Monte Carlo Methods for Sampling and Inference: Networks, Brains and Proteins”(Kevin C. Bartz)
“Topics and Applications in Missing Data and Causality” (Roee Gutman)
Limitation of Time to Degree. The department policy is that, except in unusual circumstances, students cannot register for the PhD program or be paid research assistant or teaching assistant salaries after their sixth year. A student who has completed the sixth year in the department and satisfied all requirements except the PhD dissertation may take a leave of absence, and the department will ordinarily consider a dissertation submitted before or during the ninth year. After the ninth year, the student is required to petition the faculty to have a dissertation considered, and will ordinarily be required to retake and pass the qualifying exam.
Master of Arts (AM)
The Department of Statistics welcomes applicants for the terminal AM degree. Typical AM candidates are PhD candidates in another field at Harvard for whom a statistics minor is appropriate, well-prepared undergraduates eligible for the AB/AM program, and candidates with appropriate mathematics backgrounds (linear algebra and multivariate calculus) who can demonstrate motivation for pursuing a terminal AM degree. As the Department of Statistics cannot provide tuition fellowships for terminal AM candidates, candidates seeking only the AM degree must be financially self-supporting. Teaching fellowships may be available for partial financial support.
The AM degree requires the satisfactory completion of eight half-courses approved by the department, normally requiring two terms of residence and study at Harvard. The courses must include at least six letter-graded half-courses at the level of Statistics 110 and above taken within the Department of Statistics. The actual course of study will vary according to the student’s interest and preparation and will be determined in consultation with the student’s advisor. Statistics 110 or 210 and Statistics 111 or 211 or equivalent are required. AM students must earn a B average in Statistics courses and no more than one C in all courses. Terminal AM students can take at most one 300-level course, which ordinarily cannot be used to meet the minimum requirement for letter-graded statistics courses.
The remaining two half-courses may include courses in related areas (such as economics, psychology, and biostatistics) that develop statistical methodology and are judged to be at an equivalent level to Statistics 110 or above. They may also include upper-level mathematics courses, computer science courses, or, in some cases, other courses that broaden the student’s ability to apply statistical methods. The department maintains a list of approved related courses. Generally, the department encourages a coherent theme connecting the related courses.
Admissions and Financial Aid
Students are admitted for the fall term only; applications must be received by December 14 for admission in the following fall. Applications received after December 14 cannot be guaranteed consideration. For more detailed information and forms, write to: Admissions Office, Harvard Graduate School of Arts and Sciences, Holyoke Center 350, 1350 Massachusetts Avenue, Cambridge, MA 02138. We encourage online submission of the application. See the website. GRE General scores are required, and subject scores, particularly in mathematics, are recommended. GREs should be taken by October so that examination score reports arrive in time for admission decisions. For financial aid, the appropriate financial aid application should be completed.
The statistics department usually provides adequate financial support, which includes tuition, health fees, and living expenses, to PhD students in good standing. In the first year of graduate study, this support typically involves a grant-in-aid to cover tuition, fees, and living expenses. In the second year, support is typically a grant-in-aid to cover tuition and fees, and teaching/research fellowships to cover living expenses. In the third through sixth years, when tuition is considerably reduced, the department usually can provide a teaching and research fellowship sufficient to cover tuition and living expenses. The department cannot provide financial aid beyond the sixth year.
Teaching and research fellowships are normally limited to 40 percent of full-time in the first two years and to 60 percent of full-time in the third through sixth years.
The statistics department is able to support a very limited number of qualified applicants each year. Applicants are therefore expected to apply for all non-Harvard and competitive Harvard scholarships for which they are eligible. For example, US citizens should investigate fellowships offered by the National Science Foundation and many other public and private sources.
Students with an interest in biostatistics should explore the PhD program in biostatistics at the School of Public Health. For more information, write to Department of Biostatistics, HSPH, 677 Huntington Avenue, Boston, MA 02115, or see http://www.hsph.harvard.edu/departments/biostatistics/.