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LucileTerminassian / causal_prospective_merge

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Computing EIG ratio #1

Closed Jakefawkes closed 8 months ago

Jakefawkes commented 8 months ago

There is an issue in computing the ratio in a way that is stable for EIG. Currently we are trying to do:

step 3 : taking the expectation of [log(density(numerator))]

step 4 : taking the expectation of [log(density(denominator))]

Step 3 is fine but step 4 seems to be running into issues as density(denominator) itself is an average of likelihoods. Computing likelihoods directly is numerically unstable, often ending up in inf values so instead we would like to use log likelihoods as we do in the denominator. However we need log (avg over some likelihoods) so not clear how to do.

Probably best to work directly with the ratio as:
expectation of [log(density(numerator)/density(denominator))] but can't q figure it out.

Jakefawkes commented 8 months ago

Fixed due to stan post: https://mc-stan.org/docs/2_23/stan-users-guide/evaluating-posterior-predictive-section.html