Slice sampler does not converge in simple MvNormal prior model

[ricardoV94]

This example is taken from the step_tests here:

pymc/pymc/tests/test_step.py

Line 89 in 4d2f3a8

def test_step_continuous(self):

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

import pymc as pm
import numpy as np

mu = np.array([-0.1, 0.5, 1.1])
p = np.array([[2.0, 0, 0], [0.05, 0.1, 0], [1.0, -0.05, 5.5]])
tau = np.dot(p, p.T)

with pm.Model() as model:
    pm.MvNormal( "x",  mu, tau=tau,)

expected_mean = mu
expected_std = np.diag(np.linalg.inv(tau)) ** 0.5

with model:
    trace = pm.sample(
        tune=10_000,
        draws=10_000,
        chains=1,
        step=pm.Slice(),
        return_inferencedata=False,
    )

# Very bad, the second mean seems to be consistently biased
print(expected_mean, trace["x"].mean(axis=0))
# [-0.1  0.5  1.1] [-0.14368236  1.76355742  1.11952911]

# Quite good
print(expected_std, trace["x"].std(axis=0)) 
# [ 0.56672996 10.00041321  0.18181818] [0.56335647 9.88682831 0.18468393]

This was also the case in V3: https://colab.research.google.com/drive/1Pw7a-1J-bnb4dPsPvxwuWH6TdFENYb5m?usp=sharing

[ricardoV94]

Well, Metropolis is even worse?

changing to step=pm.Metropolis(), I sometimes get stuff like:

# Very bad, the second mean seems to be consistently biased
print(expected_mean, trace["x"].mean(axis=0))
# [-0.1  0.5  1.1] [  0.29549842 -14.04723709   1.09591073]

# Also poor
print(expected_std, trace["x"].std(axis=0)) 
# [ 0.56672996 10.00041321  0.18181818] [0.53156382 4.79229857 0.18407155]

Edit: Metropolis can cope if we pass an appropriate S to it for the covariance of the proposal

[twiecki]

What do the traces look like?

[ricardoV94]

Slice sampler:

Metropolis sampler:

NUTS:

[ricardoV94]

I understand the default Metropolis has one single proposal distribution (?), but the Slice should propose values independently per dimension, so I don't understand why is it still biased.

Maybe it's not too biased, it's just the crazy standard deviation of the second component?

Edit: Yeah, maybe the test was just too damn strict

[ricardoV94]

I think I found a bug in the Slice sampler. It is no longer biased after fixing it