Understanding the parameters of pymc3 package

Question

In python's pymc3 package, a typical model building works as follows (imported from https://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC3.ipynb -

import pymc3 as pm
import theano.tensor as T

with pm.Model() as model:
   ... ... ...
   obs = pm.Bernoulli("obs", p, observed=occurrences)

    step = pm.Metropolis()
    trace = pm.sample(18000, step=step)
    burned_trace = trace[1000:]

However I have come across additional parameters for pm.sample that can be supplied to like chains=1, tune=1000, and draws=1000. In the above documentation there is no mention of these 3 parameters.

Can anyone please help me to understand these 3parameters like what purpose they solve, how their values influence accuracy of the converge of posterior distribution etc.

Any pointer will be highly appreciated.

Answer 1

1. tune: Markov Chain Monte Carlo samplers are based on the concept of Markov Chains. Markov Chains start from a random distribution and slowly converge to the distribution of your model (called stationary distribution). So, if you want to sample "real" (unbiased) samples from your model, you will need to "tune" (let it converge) the chain. So, by setting tune=1000, you are saying pymc3 to let the chain converge to the distribution of your model for 1000 iteration. Once 1000 iterations are complete, start drawing from the distribution. This takes us to our next parameter draws.

2. draws: This parameter says pymc3 how many samples you want to draw from your model's distribution (markov chain) once the tuning step is complete. So, by setting draws=1000, you are saying pymc3 to draw 1000 samples. Now, sometimes, the markov chain doesn't converge and your get biased samples. How to test if your chain has converged or not? This takes us to our last parameter chains.

3. chains: This parameter is used to say how many "chains" we want to sample. i. e: the number of markov chains to run. You can run more than one markov chain to see if the chain converged to its stationary distribution (which is your model's distribution) and if not how much divergent is it?? This is useful as, if one of the chain didn't converge, you can use alternate chains that you sampled. It is normally recommended to keep this parameter greater than 1 otherwise it makes it impossible to run some convergence checks.

Other Readings

1. Markov chains on Wikipedia
2. Markov Chain Monte Carlo on Wikipedia