Understanding / preventing chains with very high log probability?

[David Manheim]

Hi all,

It's me again! I'm running my model, and sometimes get (few) chains that go very slowly, then converge to have very high log probabilities (hundreds,) as compared to all the other chains with log probabilities in the negative hundreds.

(This is again a model with an embedded differential equation. I have it running much better now that I've eliminated a large source of colinearity.)

1) What does this imply? Is that chain converging to a bad place, or it is (as I suspect) not really converging?

2) How should I prevent this? I'd prefer not to specify the initialization, but that may prevent it from converging to strange places. Alternatively, I can lengthen warmup, or alter parameters?

3) Can I exclude the chain? (No, I'm sure.) Can I consider the median instead of the mean value of the posterior? (Implicitly excluding it, since I have many other chains?)

Thanks,

David

[Bob Carpenter]

> On Jan 8, 2016, at 3:19 PM, David Manheim <davidm...@gmail.com> wrote:
>
> Hi all,
>
> It's me again! I'm running my model, and sometimes get (few) chains that go very slowly, then converge to have very high log probabilities (hundreds,) as compared to all the other chains with log probabilities in the negative hundreds.
>
> (This is again a model with an embedded differential equation. I have it running much better now that I've eliminated a large source of colinearity.)
>
> 1) What does this imply? Is that chain converging to a bad place, or it is (as I suspect) not really converging?

Run multiple chains and evaluate R-hat and use our effective
sample size calculations.

But yes, it almost certainly implies that the model's not
converging because the variable lp has nowhere near the same
posterior mean in two chains.

> 2) How should I prevent this? I'd prefer not to specify the initialization, but that may prevent it from converging to strange places. Alternatively, I can lengthen warmup, or alter parameters?

Reparameterization can often help.

> 3) Can I exclude the chain? (No, I'm sure.) Can I consider the median instead of the mean value of the posterior? (Implicitly excluding it, since I have many other chains?)

Not safely. You can look at posterior medians (in theory,
the posterior median is the estimate minimizing expected
absolute error whereas the posterior mean minimizes expected
squared error [i.e., Euclidean distance]).

- Bob