pyro-ppl / numpyro / 39423603539

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fix(distributions): correct InverseWishart off-diagonal variance (#2369)

`InverseWishart.variance` used `(Psi_ij^2 + Psi_ii Psi_jj) / ((nu-p-1)^2 (nu-p-3))`
for every entry. That is only correct on the diagonal; the exact elementwise
variance is

    ((nu-p+1) Psi_ij^2 + (nu-p-1) Psi_ii Psi_jj) / ((nu-p) (nu-p-1)^2 (nu-p-3)).

Replace the Monte-Carlo variance test (rtol 0.10-0.15 at nu >= 15, which hid
the ~6% error there) with an exact comparison against
`scipy.stats.invwishart.var()` for a non-diagonal 3x3 scale, plus a check of
the nu > p + 3 existence threshold.

Fixes #2368.

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