Suggested example to illustrate HMC vs Gibbs

[Robert Grant]

Sorry if this has been discussed before, I couldn't see anything in the forum. To present advantages of StataStan to Stata users, who have some built-in Gibbs/M-H functionality, is there an example people would particularly suggest? I want to keep it a realistic prospect for most users, with reasonable numbers of observations and parameters, but maybe some unpleasantly correlated parameters? Something like the example in the NUTS paper.

[Michael Betancourt]

Our go to is usually a hierarchical model — the 8 schools

model is great because it’s relatively small but still really

hard to fit with Random Walk Metropolis and Gibbs.

On Aug 10, 2015, at 4:03 AM, Robert Grant <email.r...@gmail.com> wrote:

Sorry if this has been discussed before, I couldn't see anything in the forum. To present advantages of StataStan to Stata users, who have some built-in Gibbs/M-H functionality, is there an example people would particularly suggest? I want to keep it a realistic prospect for most users, with reasonable numbers of observations and parameters, but maybe some unpleasantly correlated parameters? Something like the example in the NUTS paper.

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[Jonah]

8 schools is good, but make sure to use the non-centered parameterization or even the Stan results will be iffy (although still better than RWM and Gibbs).

On Monday, August 10, 2015 at 1:45:07 PM UTC-4, Michael Betancourt wrote:

Our go to is usually a hierarchical model — the 8 schools

model is great because it’s relatively small but still really

hard to fit with Random Walk Metropolis and Gibbs.

On Aug 10, 2015, at 4:03 AM, Robert Grant wrote:

Sorry if this has been discussed before, I couldn't see anything in the forum. To present advantages of StataStan to Stata users, who have some built-in Gibbs/M-H functionality, is there an example people would particularly suggest? I want to keep it a realistic prospect for most users, with reasonable numbers of observations and parameters, but maybe some unpleasantly correlated parameters? Something like the example in the NUTS paper.

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[Ben Goodrich]

On Monday, August 10, 2015 at 7:03:55 AM UTC-4, Robert Grant wrote:

Sorry if this has been discussed before, I couldn't see anything in the forum. To present advantages of StataStan to Stata users, who have some built-in Gibbs/M-H functionality, is there an example people would particularly suggest? I want to keep it a realistic prospect for most users, with reasonable numbers of observations and parameters, but maybe some unpleasantly correlated parameters? Something like the example in the NUTS paper.

The eight schools example is good for illustrating sampling pathologies, but it is sort of weird substantively and depending on how you do it, you may find that the group-level variance is near zero.

I just do a flat probit model. Gibbs with data-augmentation will perform well and Stan will perform almost equally well. One-parameter-at-a-time Gibbs or M-H will perform worse than Stan. Then, you can do an ordinal probit model where Gibbs with data-augmentation will perform worse than Stan because of the cutpoints update.

Ben

[Michael Betancourt]

One thing to keep in mind is that there are two motivations:

1) Stan is faster than everyone else.

2) Stan gets the right answer when everyone else doesn't.

Different models are compatible with the two motivations.

My own interests lie in the latter, hence hierarchical model

examples.

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[Andrew Gelman]

Hi, Robert regarding StataStan in particular, Bob Carpenter and Daniel Furr did some simulations comparing StataStan to Stata’s built-in Bayes, and StataStan wins by orders of magnitude.  The examples are item response models and hierarchical models, they’re the sort of applications that people want to use Bayes for.

I’m ccing Bob and Daniel and Sophia who should be able to send you the details.

Andrew