R_hat, effective sample size, ... are OK but divergent transitions

[Tran]

Hi,

I have a concern. Suppose that in a case R_hat, effective sample size, MC errors, pen tests for the trace plots (that I often check when working with OpenBUGS and JAGS) are OK but we have a number of divergent transitions.

Does this mean in general that the model still have something wrong? And in this case are the parameter estimates reliable?

Would you have any idea?

Tran.

[Michael Betancourt]

http://mc-stan.org/documentation/case-studies/divergences_and_bias.html

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[Trung Dung Tran]

Hi Michael,

Thanks a lot!

Maybe I miss something, but from where you take the true value 0.7657852 'abline(h=0.7657852, col="grey", lty="dashed", lwd=3)' to compare with the sampled values of log(tau)?

And how do we know to choose tau instead of mu or theta[] to show non-convergence or bias? I ask this because in case a model has a lot of parameters then we should start inspecting from one of them.

Thank you for your time,

Tran.

On 31 March 2017 at 14:38, Michael Betancourt <betan...@gmail.com> wrote:

http://mc-stan.org/documentation/case-studies/divergences_and_bias.html

On Mar 31, 2017, at 5:39 AM, Tran <trungd...@gmail.com> wrote:

Hi,

I have a concern. Suppose that in a case R_hat, effective sample size, MC errors, pen tests for the trace plots (that I often check when working with OpenBUGS and JAGS) are OK but we have a number of divergent transitions.

Does this mean in general that the model still have something wrong? And in this case are the parameter estimates reliable?

Would you have any idea?

Tran.

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[Trung Dung Tran]

In addition, in practice when estimating the parameters, we do not have true values to compare.

Tran.

[Michael Betancourt]

The true value is shown to demonstrate that the diagnostics

indeed identify biased inferences.  It will indeed not be available

in a real analysis.

Also in a real analysis you will not know which trace plot might

exhibit pathological behavior.  You have to use the structure of

the specific model to motivate where to look.  But the point is

that divergences will identify problems for you so you don’t

have to go looking at all of the trace plots one by one.

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[Trung Dung Tran]

Thank you so much, Michael! A thing that I do not understand is that in your article you talk about step size and in case of divergent transitions we might decrease it.

However the suggestion in rstan after showing divergence is increasing adapt_delta. I am wondering why we do not directly work with step size?

Tran.

[Michael Betancourt]

Because step size is determined via an adaptation algorithm.

adapt_delta controls the behavior of that algorithm.

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