|Title||Markov chain Monte Carlo without likelihoods.|
|Publication Type||Journal Article|
|Year of Publication||2003|
|Authors||Marjoram, P, Molitor, J, Plagnol, V, Tavare, S|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|Date Published||2003 Dec 23|
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.