Updated DEMetropolis warnings

[michaelosthege]

• removed general warning (DEMetropolis: Remove warning #3718)
• added warning when too few chains are set (DEMetropolis: Warn on too small population #3719)
• test for the warning

[codecov]

Codecov Report

Merging #3721 into master will decrease coverage by 0.01%.
The diff coverage is 93.33%.

@@            Coverage Diff             @@
##           master    #3721      +/-   ##
==========================================
- Coverage   89.94%   89.93%   -0.02%     
==========================================
  Files         134      134              
  Lines       20413    20422       +9     
==========================================
+ Hits        18361    18366       +5     
- Misses       2052     2056       +4

Impacted Files	Coverage Δ
pymc3/step_methods/metropolis.py	86.79% <ø> (-1.03%)	⬇️
pymc3/step_methods/arraystep.py	93.61% <0%> (-0.71%)	⬇️
pymc3/tests/test_step.py	100% <100%> (ø)	⬆️
pymc3/sampling.py	83% <100%> (+0.11%)	⬆️

[junpenglao]

We also already have warning for number of chains here: https://github.com/pymc-devs/pymc3/blob/1c30a6f487afaeef73464a98320e35961b11873f/pymc3/step_methods/arraystep.py#L214-L216

[aloctavodia]

We also already have warning for number of chains here:

https://github.com/pymc-devs/pymc3/blob/1c30a6f487afaeef73464a98320e35961b11873f/pymc3/step_methods/arraystep.py#L214-L216

Probably this warning should be removed in favour of the new one, because the later is more informative. Other than that this LGTM

[michaelosthege]

We also already have warning for number of chains here:
https://github.com/pymc-devs/pymc3/blob/1c30a6f487afaeef73464a98320e35961b11873f/pymc3/step_methods/arraystep.py#L214-L216

Probably this warning should be removed in favour of the new one, because the later is more informative. Other than that this LGTM

No that's not possible: With less than 2 other chains, DEMetropolis can not work (ValueError, because no chains to sample a vector from), but with 2 < n_chains <= n_dims it does work, but it's really not recommended (UserWarning)

What happens if N ≤ d? Because N points lie in an N − 1
dimensional space, all proposals (2) will lie in this reduced
space when e = 0. Therefore convergence of DE-MC would
rely on e, which would take a long time if its variance is small.

(from ter Braak (2006))

[aloctavodia]

We also already have warning for number of chains here:
https://github.com/pymc-devs/pymc3/blob/1c30a6f487afaeef73464a98320e35961b11873f/pymc3/step_methods/arraystep.py#L214-L216

Probably this warning should be removed in favour of the new one, because the later is more informative. Other than that this LGTM

No that's not possible: With less than 2 other chains, DEMetropolis can not work (ValueError, because no chains to sample a vector from), but with 2 < n_chains <= n_dims it does work, but it's really not recommended (UserWarning)

What happens if N ≤ d? Because N points lie in an N − 1
dimensional space, all proposals (2) will lie in this reduced
space when e = 0. Therefore convergence of DE-MC would
rely on e, which would take a long time if its variance is small.

(from ter Braak (2006))

You are right! What about making the error message more explicit?

[michaelosthege]

We also already have warning for number of chains here:
https://github.com/pymc-devs/pymc3/blob/1c30a6f487afaeef73464a98320e35961b11873f/pymc3/step_methods/arraystep.py#L214-L216

Probably this warning should be removed in favour of the new one, because the later is more informative. Other than that this LGTM

No that's not possible: With less than 2 other chains, DEMetropolis can not work (ValueError, because no chains to sample a vector from), but with 2 < n_chains <= n_dims it does work, but it's really not recommended (UserWarning)

What happens if N ≤ d? Because N points lie in an N − 1
dimensional space, all proposals (2) will lie in this reduced
space when e = 0. Therefore convergence of DE-MC would
rely on e, which would take a long time if its variance is small.

(from ter Braak (2006))

You are right! What about making the error message more explicit?

Actually, it was possible to raise even earlier in the call tree.
I still kept the original check even though it should never trigger as long as pm.sample is used.

Also tried to write more informative messages. Is it what you had in mind?

[aloctavodia]

LGTM!