Expand sampler-stats.ipynb example

[junpenglao]

include model diagnose similar to case study example in Stan

[twiecki]

@junpenglao This is great, thanks for the port. I think it would be better to have it as a separate NB though which links to the stats one.

[junpenglao]

@twiecki No problem;-)

[fonnesbeck]

Thanks for this. Could you add some descriptive annotation to the notebook in markdown blocks? All of our notebook examples should be self-explanatory so that the user knows how to interpret the inputs and outputs of the model. This one in particular will be unfamiliar to many, so descriptive text will be helpful.

See some of the other notebooks for examples.

[twiecki]

Depending on the license of the STAN docs we can also copy&paste the text.

[twiecki]

CC-BY 4.0 license, so should be good.

[fonnesbeck]

Also, please add axis labels to all plots.

[junpenglao]

@fonnesbeck Sure.
BTW, is doing step = pm.NUTS(k=.85) the same as setting the adapt_delta=0.85 in Stan?
In a way, it is quite interesting that in PyMC3, the pathological samples from the trace is not necessary at the funnel (unlike Stan), and the sampler is generally doing a better job exploring the high curvature area even for a poorly parameterized model (at least in this example). I am not sure if this generalised to other models, but it might also mean that diagnosing biased inference is more difficult in PyMC3.

[fonnesbeck]

No, adapt_delta in pystan corresponds to target_accept in PyMC3.

adapt_kappa corresponds to k.

[fonnesbeck]

Looks good from here

[twiecki]

@junpenglao Looks great. Can you fix the pep8 issues in the model:

with pm.Model() as Centered_eight:
    mu = pm.Normal('mu',mu=0,sd=5)
    tau = pm.HalfCauchy('tau',beta=5)
    theta = pm.Normal('theta',mu=mu,sd=tau,shape = J)
    obs = pm.Normal('obs',mu=theta,sd=sigma,observed = y)

(spaces after , and no spaces around kwargs).

You can also link to my blog post on the same issue: http://twiecki.github.io/blog/2017/02/08/bayesian-hierchical-non-centered/

Good question regarding the divergences not being close to the funnel. @aseyboldt any ideas?

[twiecki]

Also, lets explicitly ask @betanalpha if he's fine with us porting his blog post.

[junpenglao]

Thanks for the patient answers I am complete newbie :-)
@twiecki Fixing the styling now. I already cited your post but will now make it more apparent.
Also, I am sending @betanalpha an email now.

[betanalpha]

The code in the case study is BSD (3 clause), the text is CC BY-NC 4.0.

[twiecki]

@junpenglao Did you change docs/source/notebooks/sampler-stats.ipynb? If not, should not show up in the diff.

[twiecki]

@junpenglao Also need to add this to docs/source/examples.rst, probably under how-to.

[fonnesbeck]

Just a picky thing: maybe use a Markdown quote block (>) for the direct quotes from Betancourt's paper/blog post. It will look better, and be more visually apparent that it is a quote.

[junpenglao]

@junpenglao Did you change docs/source/notebooks/sampler-stats.ipynb? If not, should not show up in the diff.

I did not - but ipynb picked up the change when I ran the notebook.

@junpenglao Also need to add this to docs/source/examples.rst, probably under how-to.

Cool.

Just a picky thing: maybe use a Markdown quote block (>) for the direct quotes from Betancourt's paper/blog post. It will look better, and be more visually apparent that it is a quote.

Done.

[twiecki]

Thanks for the great contribution @junpenglao.