Contradiction or misunderstanding

[Tran]

Hi all,

In page 325 of the Manual (latest version 2.14.0) I see something that sound contradictory.

A hierarchical model such as the above will suffer from the same kind of inefficiencies as Neal’s funnel, because the values of beta, mu_beta and sigma_beta are highly correlated in the posterior. The extremity of the correlation depends on the
amount of data, with Neal’s funnel being the extreme with no data. In these cases, the non-centered parameterization, discussed in the next section, is preferable; when there is a lot of data, the centered parameterization is more efficient. See Betancourt and Girolami (2013) for more information on the effects of centering in hierarchical
models fit with Hamiltonian Monte Carlo.

Non-Centered Parameterization

When there is a lot of data, such a hierarchical model can be made much more efficient
by shifting the data’s correlation with the parameters to the hyperparameters. Similar
to the funnel example, this will be much more efficient in terms of effective sample
size when there is not much data

Thus if I understand correctly then in both cases (no data or a lot of data) non-centered parameterization is preferable. Therefore the first statement is contradictory with the second one.

Or do I misunderstand something?

Kind regards,

Tran.

[Michael Betancourt]

Sorry, the second paragraph should say “when there is _not_ a lot of data”.

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[Michael Betancourt]

See http://mc-stan.org/documentation/case-studies/divergences_and_bias.html for further discussion.