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SUMMARY:Exact simulation of coupled Wright-Fisher diffusions
DTSTART;VALUE=DATE-TIME:20210611T161500
DTEND;VALUE=DATE-TIME:20210611T173000
UID:2ff9e0e070b3512ed46f93bf08e3aaeda4492d3bca5f82e652f0b3f0
CATEGORIES:Conferences - Seminars
DESCRIPTION:Celia Garcia Pareja\, EPFL CSQI\nSampling paths of a diffusion
process remains a challenging problem. The major bottleneck is that its
finite dimensional distributions are seldom available in closed form\, and
one often needs resorting to time-discretized numerical approximations.
Exact rejection algorithms of diffusion processes have therefore become in
creasingly popular in recent years. In this setting\, exact refers to the
fact that samples can be drawn from the true distributions without appro
ximation errors\, up to computer precision.\n\nIn this talk I introduce an
exact rejection algorithm for simulating paths of the coupled Wright-Fis
her diffusion\, which models the coevolution of interacting networks of ge
nes\, such as those encountered in studies of antibiotic resistance. Our
work presents the first extension of exact rejection algorithms to the
multivariate case for diffusion processes with non-unit coefficient. Can
didate proposals in our rejection scheme are independent multivariate neut
ral Wright Fisher diffusions\, whose transition density is only known in
infinite series form but can be sampled exactly by means of a modificatio
n of the alternating series method. Our algorithm provides samples of the
diffusion’s paths at a finite (random) number of time points\, the so-
called skeletons\, and the remaining of the paths can be recovered withou
t further reference to the target distribution by sampling from neutral m
ultivariate Wright-Fisher bridges\, for which an exact sampling strategy i
s also developed. Results on the algorithm’s complexity and its perform
ance in a simulation study will also be discussed. To put this work in con
text\, I will start presenting the type of population genetics’ problems
that motivate the coupled Wright-Fisher model\, as well as giving a bri
ef introduction to exact rejection algorithms and how they compare to tim
e-discretized approximations such as the Euler-Maruyama scheme.\n\nThis i
s a joint MATHICSE-STATS seminar
LOCATION:https://epfl.zoom.us/j/63839454745
STATUS:CONFIRMED
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