School of Mathematical Sciences

Tempered simplex sampler menu

Tempered simplex sampler

Speaker: 
Eleni Bakra
MRC Biostatistics Unit, Cambridge
Date/Time: 
Thu, 18/03/2010 - 16:30
Room: 
M203
Seminar series: 

Usual Markov chain Monte Carlo (MCMC) methods use a single Markov chain to sample
from the distribution of interest. If the target distribution is described by isolated
modes then it may be difficult for these methods to jump between the modes and for this
reason, the mixing is slow. Usually different starting positions are used to find out
isolated modes but this is not always feasible especially when the modes are difficult
to find or there is a big number of them. In this talk, I avoid these problems by
introducing a new population MCMC sampler, the tempered simplex sampler. The tempered
simplex sampler uses a tempering ladder to promote mixing while a population of Markov
chains is regarded under each temperature. The sampler proceeds by first updating the
Markov chains under each temperature using ideas from the Nelder-Mead simplex method
and then, by exchanging different populations of Markov chains under different
temperatures. The performance of the tempered simplex sampler is outlined on several
examples.