Markov chain Monte Carlo without likelihoods.
Many stochastic simulation approaches for generating observations from a posterior distribution depend on knowing a likelihood function. However, for many complex probability models, such likelihoods are either impossible or computationally prohibitive to obtain. Here we present a Markov chain Monte Carlo method for generating observations from a posterior distribution without the use of likelihoods. It can also be used in frequentist applications, in particular for maximum-likelihood estimation. The approach is illustrated by an example of ancestral inference in population genetics. A number of open problems are highlighted in the discussion.
Marjoram
Paul
P
Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA 90089, USA.
Molitor
John
J
Plagnol
Vincent
V
Tavare
Simon
S
D000465:Algorithms; D005075:Biological Evolution; D003198:Computer Simulation; D004247:DNA / Q000235:genetics; D004272:DNA, Mitochondrial / Q000235:genetics; D005828:Genetics, Population; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D013269:Stochastic Processes
D004272:DNA, Mitochondrial; D004247:DNA