Date: 2025-03-28

Time: 15:30-16:30 (Montreal time)

Location: In person, Burnside 1104

https://mcgill.zoom.us/j/85849766730

Meeting ID: 858 4976 6730

Passcode: None

Abstract:

I will provide a personalized account of a sequence of problems, that I have worked on over the years, beginning with string counts in Bernoulli sequences and transiting to multivariate discrete models. As a starting point, we consider independent Bernoulli trials with varying success probabilities 1/k for the kth trial, the sum of the products of two consecutive occurrences,  and  the problem of establishing that the sum is distributed Poisson with mean equal to 1.  We will explain how this finding connects to cycles in random permutations, records for continuous random variables, the Hoppe-Polya urn, and the classical Montmort matching problem.

Extensions to other success probabilities will be discussed and we present a multivariate version with Bernoulli arrays having multinomial independently distributed rows, where the object of the study is the joint distribution of column totals.  For a certain configuration of the underlying parameters,  a multivariate Poisson mixture with Dirichlet mixing arises and relates to multivariate discrete models with common margins, as well as to a sum and shares model developed with Chris Jones, to a multivariate splitting model by Peyhardi et al. (2021), and to a tree Polya splitting model by Valiquette et al. (2025).

Speaker

Éric Marchand has been a professor in the Department of mathematics of the Université de Sherbrooke since 2004. Prior to that, he was a Faculty member at the University of New Brunswick and completed his PhD. work at the Université de Montréal in 1990. He has served as Department chair from 2004 to 2010, 2020 to 2023, and since last September, and as Director of the Statistics Laboratory of the CRM from 2015-2019. Among other responsibilities, he served on the NSERC selection committee for Mathematics and Statistics, and he was a member of the Board of Governors at the Université de Sherbrooke. His research interests include Bayesian statistics, multivariate analysis, predictive analysis, statistical inference with parametric restrictions, as well discrete probability models.