Prof. Carlstein

Formula for Success

A member of the faculty since 1984, Ed Carlstein's education includes: B.Sc. (1979), Cornell University; M.A. (1980), M.Phil. (1983), Ph.D. (1984), Yale University.

In the classroom:

Ed Carlstein teaches Mathematical Decision Sciences students in his statistics courses. He urges students to learn concepts and methods that will help them successfully attack problems, rather than just memorizing formulas.

"They should take from these courses ways of thinking that they can use in their major, in their daily lives, and throughout their careers."

Students respond to his teaching, as evidenced by his receiving the university's prestigious Tanner Award for Excellence in Undergraduate Teaching.

In his own words, Carlstein's researches:

• Methods of nonparametric statistical inference, that is, methods that do not require the user to know what particular distribution or model produced the data at hand. Such methods are needed when the statistician lacks prior knowledge of the underlying data-generating process, or when the statistician wants a robust corroborator for results from a parametric analysis of data.
  
  
• Nonparametric estimation of change-points and boundaries, and of sampling distributions (via resampling). A change-point is the time at which observations in a sequence cease to arise from the "old" distribution and begin to arise from a "new" distribution; nonparametric estimation of change-points is important in quality control and in epidemiology. When observations are on a grid, as in image-analysis or geological data, a boundary may partition the observations into homogeneous groups; this boundary can be estimated nonparametrically using methods analogous to the change-point estimators. To make statistical inferences, one needs information about the statistic's sampling distribution. Although in many situations the sampling distribution is approximately normal, there are many other cases where the sampling distribution cannot be derived theoretically, and may be quite non-normal, for example if the statistic is extremely complicated or if the observations are not independent. Resampling methods, such as the jackknife and the bootstrap, allow the statistician to nonparametrically estimate sampling distributions in these difficult situations, essentially by re-using the observed data.

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