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UID:20250720T073828EDT-1405tJaS2T@132.216.98.100
DTSTAMP:20250720T113828Z
DESCRIPTION: \n\nTitle: From the distribution of string counts in Bernoulli
  sequences to multivariate discrete models.\n\nAbstract:\n\nI 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 t
 ransiting to multivariate discrete models. As a starting point\, we consid
 er 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.\n\nExtensions to 
 other success probabilities will be discussed and we present a multivariat
 e version with Bernoulli arrays having multinomial independently distribut
 ed rows\, where the object of the study is the joint distribution of colum
 n totals.  For a certain configuration of the underlying parameters\,  a m
 ultivariate Poisson mixture with Dirichlet mixing arises and relates to mu
 ltivariate discrete models with common margins\, as well as to a sum and s
 hares model developed with Chris Jones\, to a multivariate splitting model
  by Peyhardi et al. (2021)\, and to a tree Polya splitting model by Valiqu
 ette et al. (2025).\n\nSpeaker\n\nÉric Marchand has been a professor in th
 e Department of mathematics of the Université de Sherbrooke since 2004. Pr
 ior to that\, he was a Faculty member at the University of New Brunswick a
 nd completed his PhD. work at the Université de Montréal in 1990. He has s
 erved as Department chair from 2004 to 2010\, 2020 to 2023\, and since las
 t September\, and as Director of the Statistics Laboratory of the CRM from
  2015-2019. Among other responsibilities\, he served on the NSERC selectio
 n committee for Mathematics and Statistics\, and he was a member of the Bo
 ard of Governors at the Université de Sherbrooke. His research interests i
 nclude Bayesian statistics\, multivariate analysis\, predictive analysis\,
  statistical inference with parametric restrictions\, as well discrete pro
 bability models.\n\nhttps://mcgill.zoom.us/j/85849766730\n\nMeeting ID: 85
 8 4976 6730\n\nPasscode: None\n\n \n
DTSTART:20250328T193000Z
DTEND:20250328T203000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Éric Marchand (Université de Sherbrooke)
URL:/mathstat/channels/event/eric-marchand-universite-
 de-sherbrooke-364437
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