R2D2 prior and Gaussian Processes

[jroon]

@avehtari

Do you still get them if you run more iterations?

There is just not much information in the data about some parameters, which leads to challenging posterior shape.

I’ve run up to 10,000 iterations with no only small increased in emfi values. I’ve also trie don larger datasets and problem still happens.

@avehtari

You could include the linear model (Intcpt + Xc*beta) to the GP covariance matrix (using dot product and constant covariance functions) to remove one identifiability issue and reduce the number of unknown parameters.

Ok sounds good I’m really willing to try this, but I don’t quite follow what you mean I’m afraid :/ (Edit: to be clear I understand the motivation to avoid calculating F, but I don’t understand how it should be coded)

@avehtari

After having everything in the GP covariance matrix, you could integrate out also F (the new one including everything) using the new laplace_marginal_bernoulli_logit_lpmf() function.

Yes I’ve been looking forward to try this out!

[jroon]

@avehtari

After having everything in the GP covariance matrix, you could integrate out also F (the new one including everything) using the new laplace_marginal_bernoulli_logit_lpmf() function.

So I tested this in one model and getting an error:

This seems incorrect to me - surely it should accept a vector of reals like the non-laplace version?

@avehtari

You could include the linear model (Intcpt + Xc*beta) to the GP covariance matrix (using dot product and constant covariance functions) to remove one identifiability issue and reduce the number of unknown parameters.

I’m still lost on this having thought about it all weekend. Any further details on what you intended would be much appreciated :)

[avehtari]

@jroon

So I tested this in one model and getting an error:

Sorry for recommending this before testing it myself. The documentation has some errors and I’ve also found a couple bugs, so I can’t recommend it before I get it working myself. It is also possible that the function signatures are not yet as flexible as for other functions.

[jroon]

No worries at all - I know it’s only at release candidate stage, I half expected a problem to happen! What’s given me more stress is the moving the linear model to the GP covariance matrix topic, since it may hopefully unlock my final issue with the model but I dont’ know what to do!