MvStudentT distribution random method producing anomalous values

[bsmith89]

Description of your problem

Please provide a minimal, self-contained, and reproducible example.

import pymc3 as pm
import numpy as np

np.random.seed(1)

y_dist = (
    pm.MvStudentT.dist(mu=np.array([0, 0]),
                       cov=np.array([[1, 0.5],
                                     [0.5, 1]]),
                       nu=1000)
)
y = y_dist.random(size=100)

print(np.cov(y.T))
# Produces
# [[0.00070349 0.00033094]
#  [0.00033094 0.00086568]]
# for me.

This is clearly far from the expected covariance estimate and reflects
that the data are all close to 0, e.g.

[[-0.0354673  -0.05517701]
 [ 0.03031922 -0.00241219]
 [ 0.01348659 -0.06386095]
 [-0.03874406 -0.06483306]
 [-0.00504599 -0.01334566]
 [-0.00685522 -0.06665865]
 [ 0.01513208  0.00279986]
 [-0.01452284 -0.05150485]
 [ 0.0196839  -0.0096905 ]
 [-0.00998187  0.00775652]
...
]

And get progressively smaller with increasing values of nu.

Versions and main components

• How did you install PyMC3: pip and conda
• PyMC3 Version: 3.8 (development install at commit e47b98a)
• Theano Version: 1.0.4 (conda build key: py37hfd86e86_0)
• Python Version: 3.7.6 (conda build key: h0371630_2)
• Operating system:

$ hostnamectl
Operating System: RHEL
CPE OS Name: cpe:/o:redhat:enterprise_linux:7.8:GA:server
Kernel: Linux 3.10.0-1127.10.1.el7.x86_64
Architecture: x86-64

[twiecki]

Yeah, something is up with that distribution. Also when using it in the model it gives completely nonsensical results. @aseyboldt at one point checked the math and didn't find any problems so not sure what's going on there.