Extract percentile values?

[Mahdi Akbarzadeh]

Hi all;

Suppose that we run a hypothetical simple model and the as you know the estimation output is as follow:

------------------------------------------------

> fit

Inference for Stan model: model.

1 chains, each with iter=10; warmup=5; thin=1; 

post-warmup draws per chain=5, total post-warmup draws=5.

      mean se_mean   sd  2.5%   25%   50%   75% 97.5% n_eff Rhat

mu   -0.06    0.08 0.17 -0.27 -0.12 -0.12  0.11  0.12     5 0.76

lp__ -6.85    0.06 0.13 -7.00 -6.96 -6.87 -6.72 -6.72     5 0.76

-----------------------------------------------

How to extract the percentile value (for example 0.12) and save it to a vector for further work on it. 

Note that I want to replicate the model and save the values to a vector.

Best Regards

Mahdi

[Ben Goodrich]

 
The print() method does not return anything, so I think your best bet would be

sapply(as.data.frame(fit), FUN = quantile, probs = 0.25)

Ben

[Mahdi Akbarzadeh]

Thank you Ben.

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Sincerely,

Mahdi Akbarzadeh,

PhD Candidate in Biostatistics;

School of Public Health,

Department of Biostatistics and Epidemiology,

 

 

 

[Michael Betancourt]

Note that these yield MCMC _estimates_ of the posterior quantiles,

not exact values.  In particular, quantiles below 5% and above 95%

are notoriously hard to estimate and the estimators will be really

noisy.

[Mahdi Akbarzadeh]

These values are percentiles of the parameter posterior distribution. I use them as HPD intervals (0.025 and 0.0975).

[Michael Betancourt]

No, they are empirical percentiles estimated from the MCMC

draws.  In particular, the 2.5% and 97.5% estimates are very

very noisy and we do not recommend using then to estimate

a HPD interval.  A 5%-95% interval is relatively robust but a

10%-90% is even better while still giving you a good idea of

the posterior concentration.

[Tamas Papp]

There is a related (dormant?) issue about accessors which I opened a
while ago: https://github.com/stan-dev/rstan/issues/116

[Mahdi Akbarzadeh]

Then what is the confidence coefficient for that? (5%-95%)?

Can you introduce a reference for the statement? 

[Michael Betancourt]

Unfortunately there is little literature on the estimation of quantiles

from samples, but you see some of the issues in Andy’s paper,

http://www.stat.columbia.edu/~gelman/research/published/HPD_STCO.pdf.

The biggest challenge with these quantile estimators is that it’s

hard to assign confidence intervals because they’re not quite

expectations and hence don’t quite fall into MCMC central

limit theorems.  But if you don’t believe me then simulate it

yourself — start with IID gaussian draws and see how many

samples it takes to accurate pin down the extreme quantiles.

[Bob Carpenter]

I think you guys may be talking past each other.

I think Mahdi's asking for how you assign confidence
to a parameter estimate, not how you calculate confidence
intervals for MCMC estimators of quantiles (though I
am interested in hearing more about the answer to that
question given that they're not expectations).

Mahdi --- those posterior intervals are Bayesian and any text
on Bayes should explain what's going on. They are not
highest posterior density intervals, just central ones. And
by all means do what Michael suggests in terms of pinning down
extreme quantiles. We should have that in a tutorial somewhere.

- Bob

[Andrew Gelman]

If you really want to compute 95% interval from simulations more efficiently, we do have this:
http://www.stat.columbia.edu/~gelman/research/published/spin.pdf
But it seems so complicated that we haven't put it into Stan.
A

[Krzysztof Sakrejda]

On Thursday, May 26, 2016 at 10:37:36 AM UTC-4, Michael Betancourt wrote:

limit theorems.  But if you don’t believe me then simulate it

yourself — start with IID gaussian draws and see how many

samples it takes to accurate pin down the extreme quantiles.

Or don't do it yourself but take a look at a very basic script here: 

https://github.com/sakrejda/stan-workshop/blob/master/odsc-10-quantile-estimation.R

K

 

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[Mahdi Akbarzadeh]

Hi all,

Thanks for your generous helps.I got useful information from messages you receive.

Krzysztof; I used the script for quantiles. thanks.

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