Hi all, I did a simulation to test a model’s performance. In the simulation, I predetermined the “true” value for all parameters and simulated the data collection process with observation errors being imposed. I then used the simulated data to fit the model to estimate the parameters and compared t…

[image] llx: The divergency will disappear if we increase the data quantity (e.g., observe the state once every year instead of once every two years) If you can get rid of divergences with better data, then by all means use the better data and feel good about the model! But that does not mea…

In general, the way divergent transitions can lead to really bad inference is if the true parameter values sit in (or “behind”) the region where the divergences start cropping up. For example, if you have a funnel geometry, then the way for your inference to be badly wrong is if the true parameter …

[image] llx: I then used the simulated data to fit the model to estimate the parameters and compared the estimates with the predetermined “true” values. The accuracy and precision of the parameter estimates were acceptable (pretty close to the “true” values). This is a good practice, but supe…

Just clarifying my own understanding: It can also be the case that the true values get sampled, but the sampler doesn’t explore the neighborhood of the true values in a manner that generates samples that reflects properly propagated uncertainty. So, your posterior distributions may have their modes …

Not quite. Posterior distributions will not in general have their modes at the true values. If the modes were on the true values, then we wouldn’t need all this uncertainty stuff. In general, if the true value were guaranteed to reside within the region that is well explored, it would be desirable…

Thanks. This is super clear. In my case, the range of the parameter concerned in the real-world is known. And the simulation samples the “true” value for the parameters from the known range and repeats the process to ensure the ergodicity. Does it imply (not guarantee) that the true value in real-wo…

the range of the parameter concerned in the real-world is known Then you should encode this knowledge via the prior. If this suppresses all divergences, then you’re fine. If you’re still seeing divergences, that means that the nasty geometry overlaps regions where your prior and data collective…

Just wanted to expand upon @jsocolar ’s answer a bit. In Bayesian inference we aim to construct a posterior distribution that quantifies how compatible each model configuration is with both the observed data and whatever domain expertise we encoded in the prior model. The hope is that this compatib…

Thank you for your explanation, @betanalpha . If a simulation finds that the estimates with divergences are close enough to the “true” value, does it mean that the “exclusion of some compatible model configurations” mentioned might be less important to the estimates of the particular parameter? The p…

Are outputs with divergent transitions not at all useful?

General

llx January 27, 2023, 1:57pm 9

Thanks. Yes. I do use prior to reflect the realistic range of the parameter. However, the divergences are still present.

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Are outputs with divergent transitions not at all useful?

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