Include Deviance Information Criterion in Modeling subpackage

[dhuppenkothen]

Since we allow the user to do MCMC, I think it would be useful to have an implementation of the Deviance Information Criterion (DIC), since it's more robust for model comparison than likelihood ratio tests, AIC, BIC and the like, but not quite as computationally expensive as the full marginal likelihood.

See here for details: https://arxiv.org/pdf/astro-ph/0701113.pdf https://arxiv.org/pdf/0803.4089.pdf

[Billaud]

Can you tell me where i can start(i read the references)

[dhuppenkothen]

@Billaud Thanks for your interest in this. After looking at this again, I realized that I may have gotten the references confused. This here is much clearer about how to do this: http://www.sph.umn.edu/faculty1/wp-content/uploads/2012/11/rr98-009.pdf

Essentially, this procedure has three steps:

1. Compute an MCMC sample for a model (this is already implemented in ParameterEstimation
2. Compute the deviance for all MCMC samples (there's an expression for the deviance I think in OptimizationResults or so)
3. Compute the mean of all deviances
4. Compute the means for all parameters from the MCMC sample (i.e. compute the mean of each column)
5. Compute the deviance using the means of all parameters
6. Take 2* the result of step 3 (the mean of all deviances) - the result of step 5 (the deviance of the mean parameters)

I hope this makes some sense. Feel free to post here or in slack if you have questions!

[Billaud]

Can you check this it is a first attempt.

test.txt