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 the AM 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.
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. Preferably, students should have programming experience relevant for statistical computation and simulation.
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, 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.
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 January of their second year. The exam has two parts, the first on statistical metholology including probability and mathematical statistics, and the second on applied statistics including statistical design and data analysis.
To get students started early in thinking about their research, all first-year students are required to take the year-long Statistics 366: Introduction to Research.
Students in their third year and above are required to present each semester in the Statistics 300: Research in Statistics course. The presentations, made to department faculty and students, are brief summaries of the student’s research and progress on qualifying papers or dissertation.
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-- 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. In the fall term of the G3 year (after passing the qualifying exams) students must notify the department of their dissertation advisors. This would include their primary advisor plus any additional faculty who will advise or collaborate on the dissertation. 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.
One copy of the completed dissertation must be submitted for consideration in the department office at least four weeks prior to the oral dissertation defense. 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 through the Registrar’s office. The time from the defense to the final vote is ordinarily about two weeks.
Recent dissertation topics have included:
- "Advances in the Normal-Normal Hierarchical Model" (Joseph Kelly)
- "Dilemmas in Design: From Neyman and Fisher to 3D Printing" (Arman Sabbaghi)
- "Complications in Causal Inference: Incorporating Information Observed after Treatment is assigned" (David Watson)
- "Distributed and Multiphase Inference in Theory and Practice: Principles, Modeling, and Computation for High-Throughput Science" (Alexander Blocker)
- "Partition Models for Variable Selection and Interaction Detection" (Bo Jiang)
- "Sensitivity Analyses in Empirical Studies Plagued with Missing Data" (Viktoriia Liublinska)
- "Advances in Empirical Bayes Modeling and Bayesian Computation" (Nathan Stein)
- "Statistical Learning of Some Complex Systems: From Dynamic Systems to Market Microstructure" (Xiao Tong)
- "Three Essays of Applied Bayesian Modeling: Financial Return Contagion, Benchmarking Small Area Estimates, and Time-Varying Dependence" (Andrew Vesper)
- "Statistical Computation for Problems in Dynamic Systems and Protein Folding" (Samuel Wong)
- "Methods in Hypothesis Testing, Markov Chain Monte Carlo and Neuroimaging Data Analysis" (Xiaojin Xu)
- "Stochastic Modeling and Bayesian Inference with Applications in Biophysics" (Chao Du)
- "Three Essays on Credit Risk Models and Their Bayesian Estimation" (Tae Yeon Kwon)
- "Statistical Missing Data and Computation Problems: Theories and Applications in Astrophysics, Finance and Economics" (Zhan Li)
- "Topics and Applications in Synthetic Data" (Bronwyn Loong)
- "The Method of Batch Inference for Multivariate Diffusions" (Martin Lysy)
- "Respondent-Driven Sampling and Homophily in Network Data" (Sergiy Nesterko)
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 awards terminal AM degrees, as well as AM degrees to students who are continuing in the PhD program. The department will consider for the AM degree PhD candidates in other fields 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 taken within the Department of Statistics and approved by the student’s department advisor, at the level of Statistics 110 and above, with at least one course at the 200-299 level. 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 and 111 are required; Statistics 210a may be substituted for 110. With the prior approval of the advisor and the Director of Graduate Studies, one 300-level (SAT/UNSAT graded) course may be allowed to count toward the degree as one of the non-200-level courses. The eight statistics courses must include at least three courses at the interface of theory and application. Examples of such courses are Statistics 115, 121, 131/231, 139, 140, 149, 160/260, 183, 186, 220, 221, 225, 230, 232r, 240, 244 and 245. AM students must earn a B average in Statistics courses and no more than one C in all courses.
Admissions and Financial Aid
Students are admitted for the fall term only; applications must be received by December 1, 2014, for admission for the 2015-16 academic year. We require online submission of the application. Please visit the GSAS Admissions website for more information about the application process and a link to the application. GRE General scores are required. Subject scores, particularly in mathematics, are recommended but not required. GREs should be taken by October so that examination score reports arrive in time for admission decisions. 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, third, and fourth years, support is typically a grant-in-aid to cover tuition and fees, and teaching/research fellowships to cover living expenses. In the fifth and 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 Harvard T.H. Chan School of Public Health. For more information, see the Biostatistics Department website.