Pymc3 sampling processes

Questions
1

Simple question for you:

In a sampling process, where no inference is being done, is pymc3 simply taking one sample from each distribution 500 times for a draws=500 process?

In other words is:

    with pm.Model() as model:
        a = pm.Normal('a')
        b = pm.Normal('b')
        c = pm.Deterministic('c', a+b)
        pm.sample(draws=500)

equivalent to

a = np.random.normal(size=500)
b = np.random.normal(size=500)
c=[]
for i in a:
    c.append(random.sample(list(a),1)+random.sample(list(a),1)
2

Other than the fact that PyMC3 use MCMC to draw samples when pm.sample is called, the model code will roughly equivalent to

a = np.random.normal(size=500)
b = np.random.normal(size=500)
c = a + b  # <= deterministic
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3

awesome, thank you for getting back to me.
Follow-up question:
If i do such a simple sampling process with pymc3, my complete runtime including compilation is about 10 seconds, while with the np/scipy case it is done in 0.5 seconds. Is there a way to speed up pymc3 for easy cases like these? Is pymc3 not the right tool for such easy naive monte carlo processes?

4

Usually, for simple forward simulation, you should use pm.sample_prior_predictive instead.

5

thank you once again for getting back to me.

I tried the pm.sample_prior_predictive as well, but i did not see a significant increase in computation-time.

So in order to understand the computational advantages with pymc3 over numpy, i implemented the Metropolis-sampling described in https://twiecki.io/blog/2015/11/10/mcmc-sampling/
and compared that to the same model set up in pymc3.

For small number of draws, I saw that the numpy-way was significantly faster, while as for bigger number of draws/samples pymc3 outperformed numpy, as expected.

Can i by this conclude that for my simple “forward simulation”, pymc3 is too much of a powerful tool for a job simple enough for numpy to handle, and that pymc3 is slower for such jobs?

6

Depending on what you want to do - the nice thing of using a full PPL is you can write the forward sampling and reverse inference just once, instead of writing the forward simulation and then later on write the model again.

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