MCMC sampler

[maxbiostat]

If we have any hope for the hierarchical prior to be applicable in the real-world, we will need to devise a sampler that can incorporate the alphas and sample the model at the same time.

Currently we have working implementations in Stan, but that is just because the pooled prior happens to have a closed-form solution. The sampler has to be able to sample from the pooled prior even when it does not have a closed-form solution [which is the vast majority of interesting cases].

This article contains some useful information on a potential clog in this engine, the IMIS algorithm, that could be used to construct the pooled prior [or posterior, thanks to external Bayesianity].

[maxbiostat]

A good test case would be the example in #14

[fccoelho]

@maxbiostat
if you can put more informaton about the model is this issue or point to it in the manuscript . I can try to implement a sampler using the NUTS sampler in PyMC3

[maxbiostat]

See #14 and the link within for the structure of the model. Coincidently I also used Stan to do the parameter estimation for that model, because the differential equation happens to have an analytic solution. Take a look and tell me what you think. I plan on start writing the dynamic model section of the manuscript soon.