difference in n_eff of population mean depending on model specification

[cjungerius]

difference in n_eff of population mean depending on model specification

[rmcelreath]

Michael Betancourt has a long post about this: https://betanalpha.github.io/assets/case_studies/hierarchical_modeling.html

I didn't review it this morning, but if I remember right, you get an inverted funnel problem when the likelihood is strong and use non-centered.

[rmcelreath]

Hi Chris. This is a major topic in my book and course, the centered vs non-centered parameterizations of multilevel priors. In the book, see Chapter 13. In most recent lectures, lecture 13. Here's a linked set to the beginning of the relevant section:

https://www.youtube.com/watch?v=sgqMkZeslxA&list=PLDcUM9US4XdPz-KxHM4XHt7uUVGWWVSus&index=13&t=2432s

Lecture 14 has more content on the topic, including some technical aspects with multivariate priors.

[cjungerius]

Thank you! These are exactly the bits of your lecture series I watched last night which led to my edit - which has taught me a valuable lesson about not taking shortcuts 😅. Because of various factors, including brms using non-centered parameterization as the default, I assumed it was strictly better than the alternative. I understand now that my type of data (many trials, approximately equal trial numbers for each condition for each participant) might be an example of a case where it is not.

Out of curiosity, is there any intuition for why the non-centered parameterization does worse in such data dominant cases? I mean to say: I understand the opposite, where unnesting allows for more efficient exploration of e.g. Neal's funnel-type posteriors, but how can the unnesting of parameters make the posterior harder for the MCMC chains to explore? Is it because the chains spend a lot of time in low-probability areas when the exploration of e.g. a_bar is made independent from the lower level parameters?

I clearly have some more reading to do, so I shall return to the relevant chapters of your book. Thanks again!