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SUMMARY:Exact simulation of the Wright-Fisher diffusion - Paul Jenkins (Wa
 rwick)
DTSTART:20151127T160000Z
DTEND:20151127T170000Z
UID:TALK60703@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:The Wright-Fisher family of diffusion processes is a class of 
 evolutionary models widely used in population genetics\, with applications
  also in finance and Bayesian statistics. Simulation and inference from th
 ese diffusions is therefore of widespread interest. However\, simulating a
  Wright-Fisher diffusion is difficult because there is no known closed-for
 m formula for its transition function. In this talk I show how it is possi
 ble to simulate exactly from the scalar Wright-Fisher diffusion with gener
 al drift\, extending ideas based on retrospective simulation. The key idea
  is to exploit an eigenfunction expansion representation of the transition
  function. This approach also yields methods for exact simulation from sev
 eral processes related to the Wright-Fisher diffusion: (i) its moment dual
 \, the ancestral process of an infinite-leaf Kingman coalescent tree\; (ii
 ) its infinite-dimensional counterpart\, the Fleming-Viot process\; and (i
 ii) its bridges. This is joint work with Dario Spano.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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