Computed log pointwise predictive density

[pkroenert]

Hi there,
I would like to compute the WAIC information criterion for a fitted Bayesian model.

However, in doing so one has to evaluate the computed log pointwise predictive density, as defined in Eq.(3) in:
https://arxiv.org/pdf/1507.04544.pdf

Specifically I don't know how to compute the term:

p(y_i, \theta^s),

which should be the likelihood with the sampled parameter values from the posterior.

How do I compute that with the returned chains from a NUTS() sampling?

Thanks for your help!!!

[devmotion]

Hi!

So it seems you want to compute the elementwise log-likelihoods? In that case probably you should use elementwise_loglikelihoods which @torfjelde just added to DynamicPPL. He also added an example to the ArviZ docs that shows how this function can be used to compute LOO.

[pkroenert]

Thank you very much @devmotion for this fast response and for the links!
I will check these out and leave a reply once I see if this works.

[torfjelde]

Following the above example you can also just use ArviZ.waic directly instead of implementing your own, if you'd like 👍

Also, @devmotion I believe I misremembered when I said I thought "elementwise likelihood` was being used in the literature; I was thinking of "pointwise likelihood" 😕

[devmotion]

Also, @devmotion I believe I misremembered when I said I thought "elementwise likelihood` was being used in the literature; I was thinking of "pointwise likelihood" confused

We can just rename it to pointwise_loglikelihoods and deprecate elementwise_loglikelihoods 🙂

[torfjelde]

We can just rename it to pointwise_loglikelihoods and deprecate elementwise_loglikelihoods

Honestly, that sounds like a good idea to me 👍

[torfjelde]

This can be closed, right?

[pkroenert]

Yes, thanks again!