Use unit normal as default init_dist in GaussianRandomWalk and AR

[ricardoV94]

Closes #5744

[codecov]

Codecov Report

Merging #5779 (c6e58ed) into main (862bd05) will decrease coverage by 0.00%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main    #5779      +/-   ##
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- Coverage   89.27%   89.27%   -0.01%     
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  Files          74       74              
  Lines       13813    13809       -4     
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- Hits        12332    12328       -4     
  Misses       1481     1481              

Impacted Files	Coverage Δ
pymc/distributions/timeseries.py	77.55% <100.00%> (ø)
pymc/sampling.py	88.34% <0.00%> (-0.06%)	⬇️

[ricardoV94]

Should we issue a warning that the default behavior changed from being a Flat in V3 to being a unit Normal?

Edit: Added it to the release notes at least

[twiecki]

Didn't we default to Flat? I think that makes most sense. Or at least a Normal with high SD.

[ricardoV94]

@twiecki The problem with flat is that you can't do prior and posterior predictive with it.

You couldn't do this before with AR ofc.

The GRW did not respect the init dist and just assumed the initial point was zero, regardless of what the distribution was. That was just broken behavior imo.

We can make the default Flat, but users will perhaps be upset when their model can't be used for posterior predictive after sampling. I don't have a strong preference.

[twiecki]

That's a good point. How about a SD of 10? I know it's arbitrary, but not more arbitrary than 1. And maybe add a note that it's important for the user to test.

[twiecki]

Hm, but why can't we do posterior predictive with Flat? We still get a non-flat posterior for the initial dist?

[ricardoV94]

Hm, but why can't we do posterior predictive with Flat? We still get a non-flat posterior for the initial dist?

If the GRW is the likelihood, posterior predictive will try to resample it using forward sampling, which it can't because of the Flat. If it's a variable that is in the trace then it won't be an issue as it won't be resampled.

[ricardoV94]

We can also just remove the default behavior and force users to always specify the init_dist. That's probably the best if there is no sane default.