Likelihood for calculating WAIC in arviz package

Interfaces CmdStan
1

As it follows the question on github https://github.com/arviz-devs/arviz/issues/668, may I ask @ahartikainen a very quick question: if my likelihood is censored, then I do not need to include the censored part in the likelihood, am I correct?

For example, I have

    for (k in 1:N) 
        target += lognormal_lpdf(t[k] | param1, param2) + lognormal_lccdf(E_R[k] | param1, param2);

then for arviz I would only write:

    for (k in 1:N)
         log_likelihood[k] = lognormal_lpdf(t[k] | param1, param2);

Thank you in advance for your time!

2

I think you should use the censored likelihood.

But @avehtari or @jonah have more information than I do.

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3

Thank you for your quick reply - really appreciated!

Roughly speaking, it means that I need to repeat the same likelihood as I write in my model block.

4

Yes, by matching what you have in the model block, you are computing the actual individual terms which were added to target. As the truncation part depends on k you need to include that, too.

1 Like
5

Thanks! That makes sense and solves my initial confusion

1 Like
6

It is nice that if something wrong in one of the model, WAIC comparison become unreliable. For example, it can become negative. In this case, calculation of WAIC could be a double check for some unfortunate typos.

Thank you two again!