Bayesian Model Selection?

[Millet21]

Hi everyone,
Does the sbi package provide a way to select between competing models? If not, do you think that it could be possible to use the "learnt harmonic mean estimator" (https://astro-informatics.github.io/harmonic/index.html) with a trained posterior from the sbi package?
Thanks in advance

[janfb]

Hi @Millet21

very good question. It is not directly implemented in sbi, but there are ways to do it. Recently, we implemented a CategoricalMADE discrete density estimator that enables you to learn a discrete posterior. You could train it with a training data set consisting of simulated data from different competing models, modeled by a categorical variable with categories, say 1, 2, N.

This has been done before, see e.g., here: https://github.com/janfb/mcabc/tree/master/mcabc/model, and with more detail here: https://2019.ccneuro.org/proceedings/0000578.pdf

For the harmonic mean estimator, I have not looked at it in detail, but once you have performed NPE or NLE using the sbi package, you effectively have access to the posterior.log_prob, or the likelihood.log_prob, which might just be what you need for this estimator.

Does this help?

Best,
Jan

[Millet21]

Yes, I will investigate how to use it in my case
thank you!
Mathis