Διάλεξη από τον Καθηγητή Wilfrid Kendall

Την Τετάρτη 15 Μαΐου 2024 στις 19:00 στην αίθουσα Α31 θα πραγματοποιηθεί διάλεξη απο τον Καθηγητή Wilfrid Kendall.

Ο Καθηγητής Kendall εκτός από το δικό του σπουδαίο έργο, έχει συνδέσει το όνομά του με την ιστορία της Στατιστικής αφού είναι γιος του επίσης διάσημου πιθανοθεωρητικού και στατιστικού David George Kendall (Oxford, Cambridge, Royal Society).

Title: MARKOV CHAIN MONTE CARLO AND PERFECT SIMULATION

Abstract: Dating back as far as the classic Metropolis et al. (1953) paper, approximate samples have been drawn by engineers, mathematicians, physicists and statisticians from probability densities with unknown normalizing constants, by considering long-time runs of Markov chains designed to have the desired probability density as equilibrium. In all but the most trivial instances, a major question is: how long should one run the Markov chain in order for it to be approximately in equilibrium? Propp and Wilson (1996) made a major breakthrough by showing that (in favourable cases) one can achieve an exact draw from equilibrium by (a) running the chain for a random not a deterministic length of time, and (b) running it from the far past till now rather than from now till the far future, and (c) using ingenious coupling. This idea is variously called Coupling from the Past (CFTP), Exact Simulation or Perfect Simulation; wide-ranging reviews can be found in Kendall (2005) and Huber (2015).
In this talk I will review CFTP and some of its developments. I shall describe how CFTP works in a simple case, discuss the very visual example of “dead leaves” from stochastic geometry, review the work of Connor and myself (2015) on perfect simulation for multiserver queues, and describe some work in progress by Connor and myself on the application of perfect simulation to some inference problems for the S-I-R epidemic.

Keywords: Coupling from the Past (CFTP); Dead Leaves; Epidemics; Exact Simulation; Markov Chain Monte Carlo; Multiserver Queues; Perfect Simulation.

Acknowledgments: The author acknowledges support of UK EPSRC grant EP/R022100.

Short Bio:
Wilfrid Kendall (WSK) is an emeritus professor at the Department of Statistics of the University of Warwick.
He studied mathematics at the University of Oxford for his BA, MSc and DPhil (1972-1978). His first job was to lecture in statistics at the University of Hull (1978-1984). He then moved to the University of Strathclyde in Glasgow (Scotland, 1984-1988) where he was first lecturer and then senior lecturer at the Department of Mathematics. In 1988 he moved to Warwick Statistics Department as lecturer, then reader, then professor, and has stayed there happily ever after.
WSK has served as Department Chair at Warwick (1999-2002), as Scientific Secretary (1996-2000) and President (2013-2015) of the Bernoulli Society, and as founding co-director of APTS (the UK body for training Statistics PhD students, 2007-2017). He has worked mostly in probability theory, with particular interests in: random processes, stochastic geometry, stochastic calculus, computer algebra in statistics and probability, and perfect simulation. He continues to be profoundly fascinated by the beauty, usefulness and immense social importance of probability and statistics.