B.A.(1960), M.A. (1964), Ph.D. (1966), University of Minnesota.
UNC-Chapel Hill (1968- )
Stanford University (1966-1968)
Estimating distortion in a binary symmetric channel consistently, IEEE Transactions on Information Theory, 37 (1991), 1466-1470.
On a problem of ammunition rationing (with L. Shepp and Y-C Yao), Advances in Applied Probabability, 23 (1991), 624-641.
On Steinhaus’ resolution of the St. Petersburg paradox (with S. Csörgö), Probability and Mathematical Statistics, 14, (1993), 157-172.
Simons’ interests are in statistical inference and applied probability. Recently, he and some graduate students worked on a sequential statistical model for conducting clinical trials with the expressed purpose of increasing the number of patients who receive the best treatment during and after the testing phase of the trials. Another area of interest is a collection of inferential questions asssociated with “binary symmetric channels,” a topic in a semiparametric context with relevance to coding and imaging. These projects include a challenging mixture of mathematics and numerical computations.
A project of mostly theoretical interest, has been an effort to unify some old work of J. L. Doob’s, concerned with the preservation of iid random variables under a sequence of stopping times, and some recent work by Ignatov, of a very different sort, concerned with the distributions of record values. A current project is the writing of a monograph with Sándor Csörgö on the “St. Petersburg Paradox,” a fascinating problem that engaged the interest of almost every leading thinker of mathematical note in the eighteenth century, and which, according to economist and Nobel laureate Paul Samuelson, “enjoys an honored corner in the memory bank of the cultured and analytic mind.” Beyond its concern with the historical side of the subject, the monograph will attempt to resolve the paradox through the inclusion of recent unpublished probabilistic research, some of which is still in progress.