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CATEGORIES:Statistics
SUMMARY:Exact simulation of the Wright-Fisher diffusion -
Paul Jenkins (Warwick)
DTSTART;TZID=Europe/London:20151127T160000
DTEND;TZID=Europe/London:20151127T170000
UID:TALK60703AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60703
DESCRIPTION:The Wright-Fisher family of diffusion processes is
a class of evolutionary models widely used in pop
ulation genetics\, with applications also in finan
ce and Bayesian statistics. Simulation and inferen
ce from these diffusions is therefore of widesprea
d interest. However\, simulating a Wright-Fisher d
iffusion is difficult because there is no known cl
osed-form formula for its transition function. In
this talk I show how it is possible to simulate ex
actly from the scalar Wright-Fisher diffusion with
general drift\, extending ideas based on retrospe
ctive simulation. The key idea is to exploit an ei
genfunction expansion representation of the transi
tion function. This approach also yields methods f
or exact simulation from several processes related
to the Wright-Fisher diffusion: (i) its moment du
al\, the ancestral process of an infinite-leaf Kin
gman coalescent tree\; (ii) its infinite-dimension
al counterpart\, the Fleming-Viot process\; and (i
ii) its bridges. This is joint work with Dario Spa
no.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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