Ph.D. Program

Admissions

All applications should be submitted directly to the Yale Graduate School Office of Admissions:
Application requirements and guidelines
Apply online (preferred method)

Course of Study

The Department offers a broad training program comprised of the main areas of statisical theory (with emphasis on foundations, Bayes theory, decision theory, nonparametric statistics), probability theory (stochastic processes, asymptotics, weak convergence), information theory, econometrics, classification, statistical computing, and graphical methods.

With this background, graduates of the program have found excellent positions in universities, industry, and government. Recent graduates have accepted appointments at the Duke University, University of California at Santa Barbara, The City University of New York, Yale University, Bristol-Meyers Squibb, RAND, Federal Reserve Board, New York University, Trinity University, Iowa State University, Merck, and Tulane University.

There is no foreign language requirement. Normally during the first two years, fourteen term courses in this and other departments are taken to prepare students for research and practice of statistics. These include courses devoted to case studies and practical work, for which students prepare a written report and give an oral presentation.

Qualifying Examination

Course work prepares students for a Ph.D. qualifying examination, which is usually taken after three semesters of study. The qualifying examination consists of three parts: a written report on an analysis of a data set, a written paper on theoretical statistics, and an oral examination. A provision exists for one reexamination of one or more parts of the qualifying exam in the event that a student does not pass the first time. All parts of the qualifying examination must be competed before beginning the third year.

Dissertation research in collaboration with one member of the faculty is begun during the third year. A prospectus for the dissertation should be submitted no later than the first week of March in the third year. The prospectus must be accepted by the department before the end of the third year. Upon successful completion of the qualifying examination and the prospectus (as well as meeting the Graduate School Honors requirements), the student is admitted to candidacy. Most students complete the dissertation in the fifth year. Please see our Alumni page (link) for a sampling of recent Dissertation topics.

M.A. Program

M.A. (en route to the Ph.D.): This degree may be awarded upon completion of eight term courses and two terms of residence.

The undergraduate Applied Mathematics major requires a concentration in a particular area of applied mathematics. One of the available concentrations is Statistics.

Statistics is the science and art of prediction and explanation. The mathematical foundation of statistics lies in the theory of probability, which is applied to problems of making inferences and decisions under uncertainty. Practical statistical analysis also uses a variety of computational techniques, methods of visualizing and exploring data, methods of seeking and establishing structure and trends in data, together with a mode of questioning and reasoning that quantifies uncertainty.

The Statistics program at Yale is a blend of the mathematical theory of probability and statistical inference, the philosophy of inference under uncertainty, computational techniques, the practice of data analysis, and statistical analysis applied to economics, biology, medicine, engineering, and other substantive areas. Statistical methods are widely used in the sciences, medicine, business, industry, and government, and graduates can find employment in these areas or continue on to graduate school. The Statistics concentration requires a minimum of four Statistics courses numbered 230 or greater in addition to Statistics 241: Introduction to Probability, and Statistics 242: Theory of Statistics, which are required of every Applied Mathematics major.

These courses may be chosen from:
Statistics 230: Introductory Data Analysis
Statistics 251: Stochastic Processes
Statistics 312: Linear Models
Statistics 330: Advanced Probability
Statistics 361: Data Analysis
Statistics 364: Information Theory

In addition, each year several graduate courses are offered on a variety of topics, many of which are accessible to undergraduates; these are also appropriate electives for fulfilling the Statistics requirement. Each year will have a different mix of courses. For example, recent offerings have included courses on stochastic calculus (with applications to finance), computational learning theory, and stochastic models of evolution.

Full information about this year's courses is available on our Courses page.