rgdata-hbm-tau.ipynb - Hierarchical A

[daw538]

Attempts to reintroduce A as a hierarchical parameter so far have caused the convergence on the final star in the test sample to drift away from 1. I don't particularly want to remove this star: one because it's not exactly that unusual in terms of the data; secondly if the model can be made to deal with it then it should be more robust when applied to the larger data set.

Below are the relevant lines from the Stan script showing where the hierarchical element is implemented.

 // Transformed Parameters
    A[i] = A_std[i] * A_sig + (AA * (dnu[i])^(-AB));

 // Hierarchical Parameters
    A_std ~ normal(0, 1);
    A_sig ~ normal(0, 0.5);
    AA ~ normal(0.06, 0.02);
    AB ~ normal(0.88, 0.05);

I remember you mentioned using the Student-t distribution, which I've found in Stan as X~student_t(a,b,nu) however I'm not sure which of the above I should be substituting for? I tried A_std however that resulted in initialisation failure so probably wasn't the reasonable route to take.

Given the starting values appear to be as good as they can be, are there any other tweaks that would improve the convergence on the last star?

[grd349]

'A_std ~ normal(0, 1);'

Wants to become:

'A_std ~ students_t(nu, 0, 1)'

where nu should be something like 3 to 10. nu = 30 should be virtually indistinguishable from $\mathcal{N}(0, 1)$.

[daw538]

Thanks, looks like I had been putting the nu in the wrong position.

However, having tried a number of options for the value of ν, I can't seem to get the convergence down enough (see current version of file). Anything else that could be changed?

[grd349]

Was this 'working' before with a Gaussian distribution?

On Wed, 20 Feb 2019 at 13:54 daw538 notifications@github.com wrote:

Thanks, looks like I had been putting the nu in the wrong position.

However, having tried a number of options for the value of ν, I can't seem to get the convergence down enough (see current version of file). Anything else that could be changed?

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[daw538]

Was this 'working' before with a Gaussian distribution?

No, not whilst A is a hierarchical parameter at least, which I mentioned was causing the convergence to fail on the sixth star in the opening post.

When A is not hierarchical all is good and convergence is successful - this is what you saw in the meeting on Monday. I've uploaded that version (you'll find it with the suffix '(converged)') so you can see the difference with the version that does have A as a hierarchical parameter.