different results when using multiprocessing Pool() (sometimes)

General information:

• emcee version: 2.2.1
• platform: Windows
• installation method (pip/conda/source/other?): pip

Problem description:
I was doing some sanity checks with the line.py example and run into different results whether or not I used multiprocessing Pool() when initializing EnsembleSampler (or PTSampler for that matter). Under other circumstances the results are in fact the same.

Minimal example:

These are the modification to line.py I made:

from multiprocessing import Pool
### same code
# widen the parameter ranges
def lnprior(theta):
    m, b, lnf = theta
    if -50.0 < m < 50 and -50.0 < b < 50 and -50.0 < lnf < 50:
        return 0.0
    return -np.inf
### same code
# less optimal initial positions and sample more times
pos = [result["x"] + 5*np.random.randn(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(x, y, yerr), pool = None) # or pool = Pool()
sampler.run_mcmc(pos, 1500, rstate0=np.random.get_state())

A rough example based on the code above.

Start with the line.py example and reproduce the comparison between pool=None and multiprocessing Pool() on Windows using the reported emcee 2.2.1 setup. Read the EnsembleSampler and PTSampler initialization and run_mcmc paths, focusing on how the pool and rstate0 are handled. Done means the discrepancy is consistently reproduced and its cause is identified or the seeded runs produce equivalent results.