Importance weight PDF shape about dynesty HOT 4 CLOSED

Hi,

I can't comment on the question of the convergence, since you don't show anything that would suggest the lack of convergence, but the importance weight graph looks fine to me. The fact that it has multiple peaks is perfectly fine.

It is easy to make the importance weight graph of "any" shape even if you consider posteriors shaped like Gaussian mixtures of the form

$f_1 N(x|0,\sigma_1) + f_2 N(x|0,\sigma_2)$

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Thank you for your comments! I'm sorry, the corner plot was in the attached .ipynb file.
While I understand that the importance weight can exhibit a multimodal distribution when the posterior distribution is multimodal, I have another point that concerns me.
I believe that the importance weight is the product of the likelihood and the decrease in volume. However, at the first peak of the importance weight, the likelihood is extremely low. In fact, I have looked at the observational and model images around this moment, and they were not modeled well at all. Compared to the run plot in the dynesty paper or example codes, the run plot I obtained has a high importance weight at a very early stage of sampling (where -ln X is close to 0). I am concerned about this. Do you think there might be a problem related to this?

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Thank you for your comments! I'm sorry, the corner plot was in the attached .ipynb file.

TBH I do not see anything suspicious in the corner plot

While I understand that the importance weight can exhibit a multimodal distribution when the posterior distribution is multimodal,

The posterior distribution does not need to be multimodal to show mutlimodality in the importance weigths. My example had only one one mode.

I have another point that concerns me. I believe that the importance weight is the product of the likelihood and the decrease in volume. However, at the first peak of the importance weight, the likelihood is extremely low. In fact, I have looked at the observational and model images around this moment, and they were not modeled well at all.

This seems to be a feature of your likelihood+prior. I.e. significant volume of your posterior seems to be there (at low logl values) . Whether that's how it should be, or you have incorrectly specified either the prior, or the likelihood I don't know. But those are the possibilities IMO.

Compared to the run plot in the dynesty paper or example codes, the run plot I obtained has a high importance weight at a very early stage of sampling (where -ln X is close to 0). I am concerned about this. Do you think there might be a problem related to this? !

Again on it's own the importance weight can show anything, it really depends on how the function log-likelihood vs prior volume above the logl value. For a typical Gaussian posterior, you only get one peak, for something very different you don't.

So personally I would check if your likelihood function is defined correctly.

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Thank you for the detailed advice! I will check my code again.

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