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I am using the PYMC toolbox in python in order to carry out a model selection problem using MCMC. What I would like to have for each model is the marginal log-likelihood (i.e. model evidence).

The question: After I've run my sampler on the model, like

mc = MCMC(myModel)

does the following command return the marginal log-likelihood?

myModel.logp

Thanks very much in advance!

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  • $\begingroup$ So, it is clear now that the answer to the above is a definite no: lop does not return the marginal log-likelihood. However, I am skeptical as to whether it does really return the log-posterior for the current sample. $\endgroup$ – ngiann Jan 15 '15 at 8:22
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No, this returns the log-posterior for the current values of the model parameters. You need to integrate this value over all model parameters to calculate the evidence. Here is a start on a way, and here is a possibly missing) blog on a different way.

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    $\begingroup$ The first link seems to describe the harmonic mean estimator, which has poor convergence, see radfordneal.wordpress.com/2008/08/17/… $\endgroup$ – Juho Kokkala Jan 13 '15 at 18:33
  • $\begingroup$ Thanks for the answers. The negative answer above is already useful. Though I cannot imagine what a "log-posterior for the current values" means. I know that this is also mentioned in the documentation. I am experienced in Bayesian statistics but have never used MCMC, I try to use variational methods instead when possible. $\endgroup$ – ngiann Jan 14 '15 at 14:25
  • $\begingroup$ So the myModel.logp function returns an approximation to the true log(p(theta|data)) for the last sample theta saved in myModel? $\endgroup$ – ngiann Jan 14 '15 at 19:33
  • $\begingroup$ that is my understanding $\endgroup$ – Abraham D Flaxman Jan 15 '15 at 20:05
  • $\begingroup$ Thanks for your answer Abraham. In danger of breaking etiquette and asking a separate question: how can I calculate the average over all samples and not just the last sample? (I will edit my question above accordingly later.) $\endgroup$ – ngiann Jan 21 '15 at 15:47

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