Model Comparison: How to constrain a model to positive mu-differences?

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Thank you so much for the code example. This is great info. I don’t know if that is even anywhere in the documentation. Using the graphviz plot I see what’s going on. I imagine it now as mapping the observed data to the mus. I scoured the internet in an effort to find any explanation for how to use it, to not occupy too much more of your time, but I didn’t find a single example using the indexing method. So I am once again kindly asking for your help.

I found a well illustrated primer on different shape types. And a blog post which explains that shapes in PyMC3 are, unfortunately, one hot mess. It also states:

distribution_shape == batch_shape + event_shape
[observed] data should have a shape that looks like sample_shape + distribution_shape .

If I understood correctly, for a model where I estimate 6 parameters (e.g. \sigma for n_blocks(3)*n_projections(2)) for each user by drawing from independent univariate distributions (same distribution family), my sample shape is n_trials (per block), batch shape is n_users*n_blocks*n_projections, and event shape = ().

I have the data in long format like you suggested:

user block  direction    projection   
0    1      parallel     7.129121
0    1      parallel     3.414878
0    1      parallel     -6.330880
0    1      parallel     0.428940
0    1      parallel     -3.650233
...  ...    ...          ...
1    3      orthogonal   -2.223337
1    3      orthogonal   -1.275683
1    3      orthogonal   -0.796934
1    3      orthogonal   2.221719
1    3      orthogonal   -5.626795

I could unstack the ‘direction’ if that was of any use, as these are guaranteed to be the same length for each individual block.
I tried different shape settings and I don’t know which one is correct. For example,

with pm.Model() as model3:
    sigma = pm.HalfNormal('sigma', 5., shape=12)  # 2 users * 6 parameters. batch shape?
    obs = pm.Normal('obs', 0.0, sigma[samples['user']], shape=12, observed=samples['projection'])

But it’s hard to identify which parameter (sigma 0-11) belongs to which user/block/direction coordinate.
Whatever else I tried with the indexing and shape argument, I always got this error:

RecursionError: maximum recursion depth exceeded in comparison

If I manage to use it as intended I may write something about how to vectorize a model properly without missing data using your indexing method to ease the struggle for other beginners.

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