# SSC Gold Medalist 2024

The Gold Medal is awarded to a person who has made outstanding contributions to statistics or probability, either to mathematical developments or in applied work. The award is normally awarded to someone still active in research. The recipient should be Canadian or a permanent resident of Canada, and must have made high quality research contributions to the statistical sciences in Canada. A recipient of the Gold Medal must be a member of the SSC.

The Gold Medal is awarded to Priscilla E. (Cindy) Greenwood.

Cindy Greenwood is Professor Emerita in the Department of Mathematics at the University of British Columbia. As one of the supporting letters for the nomination writes: “Cindy’s career has been an impressive demonstration of mathematical power, sustained intellectual energy, enduring love of certain main themes, and at the same time an immense openness to new ideas and new areas.”

The following account of her career intentionally pays tribute to her wide circle of collaborators over the years.

Cindy Greenwood (C.G.) received her Ph.D. in Mathematics in 1963 from the University of Wisconsin, with a thesis on a new method of prediction to replace the Wiener-Hopf method when the data are confined to a compact interval. Her early teaching was at the historically black North Carolina College in Durham. In 1966 she joined the Department of Mathematics at the University of British Columbia. A theme of her research in the 1970s was sample path properties of stochastic processes, such as stochastic splitting at the maximum, variations of Lévy processes, and dual pairs of stopping times for random walk. A C.G. invention was the Martintote, a random sequence for which the conditional asymptotic process distribution with respect to the past remains the same along the sequence of stopping times, as the Martingale does with the (conditional) expected value. A paper showing that random stopping (usually) preserves regular variation underscored the point. Major co-authors in the 1970s were Jim Pitman, Elja Arjas, Jeff Teugels, Moshe Shaked.

In the early 1980s Ed Perkins joined the Mathematics Department at UBC with his love of non-standard methods, which C.G. had used in earlier work with Reuben Hersh of the University of New Mexico. Together they studied Brownian local time on square root boundaries, using non-standard arguments but publishing in standard language. Also in the early 1980's, C.G. spent three summers plus a half year at the Steklov Mathematical Institute in Moscow. She wrote papers and a monograph with A.N. Shiryaev, a monograph with I. Evstigneev, and a book with M. Nikulin. She published with A. Novikov on boundary crossing of Lévy processes. Later, with I. Ibragimov she wrote on the Bahadur concept of efficiency. She lectured in Russian at several universities in the then Soviet Union. In 1983 C.G. visited Brighton and with Charles Goldie investigated set indexed processes, which led to later work on random fields. G. Hooghiemstra of Delft visited Vancouver and with C.G. authored papers solving the domain of attraction problem for a family of operators interpolating between sup and sum. Ron Doney of Manchester spent 1980-81 in Vancouver and with C.G. studied what happens when ladder times and heights belong to a joint domain of attraction.

In 1987 C.G. received an NSF visiting professorship at Johns Hopkins University where Andrew Barbour was visiting, resulting in joint work on Stein's method for Poisson approximation of random fields. A fruitful collaboration lasting decades began with Wolfgang Wefelmeyer, who was also visiting Hopkins in 1987, primarily on asymptotic efficiency (in the sense of LeCam) of stochastic process estimators in many contexts.

C.G.'s last year of leave from UBC before retirement was in 1996-7. Half of it was spent at the Weierstrass Institute in Berlin working with M. Nussbaum on LeCam's formulation of asymptotic equivalence of statistical experiments. Significant additional co-authors in the 1990's were postdoc Jiaming Sun on Gibbs measure and the Ising model, and Dan Haydon on synchronization using various models of predator and prey.

In the mid 1990's UBC's Peter Wall Institute for Interdisciplinary Studies offered $500K for a 3-year study. C.G. won the first competition and led a study on "crisis points", inspired by work with Wefelmeyer on inference for models containing critical points. The study, involving UBC professors in 5 departments, produced many joint works and influenced several students and post-docs towards interdisciplinary work. A long collaboration began between C.G. and Lawrence Ward, Psychology, UBC, first on the 1/f phenomenon, 1/f being the form of the spectral density of many processes found in nature (see their Scholarpedia article on 1/f noise) and then stochastic modelling in neuroscience, joint work that is still continuing.

Following retirement from UBC, C.G. spent 10 years as a visiting professor at Arizona State University where the Department of Mathematics and Statistics is strong in dynamical systems, and then at UNC and SAMSI in North Carolina. Inspired, she started work in stochastic dynamics in neuroscience and broadly in mathematical biology, which continues, principal co-authors being Lawrence Ward, Peter Rowat (UCSD), and Luis Gordillo (Utah State U). Since 2000 many papers in these topics have appeared, with these authors and also with Peter Lansky of Prague and with Rachel Kuske, UBC (now Georgia Tech), Peter Baxendale, USC, and others named above. Since 2011 C.G. has been enjoying a rich mathematical life in emeritus status at UBC.

C.G. has received earlier awards and honours. She is a Fellow of the Institute of Mathematical Statistics (1985), and was awarded the Krieger-Nelson Prize of the Canadian Mathematical Society in 2002. In 2008-2009 a Festschrift in the form of a special volume of Stochastics was put together in her honour. The lead article is a thoughtful summary of her contributions to that point by I. V. Evstegneev and N. Bingham, entitled “*Priscilla Greenwood: Queen of Probability*”. She was made a Member of the Order of Canada in 2020 “for contributions to the fields of statistics and mathematics, and for her pioneering work in probability theory”.

Now, at 86, C.G. continues to be active in research, a devoted supporter of the SSC, of the IMS, and of all young scholars, and grateful for many inspiring colleagues.

## The citation for the award reads:

*“To Priscilla E. (Cindy) Greenwood, for fundamental and highly original contributions to the theory of stochastic processes and to statistical inference for complex stochastic models; and for insightful illumination of stochastic mechanisms in neuroscience and other scientific disciplines.”*