Normalization of simulations and parameters

[htjb]

I'm trying to use the SNLE implementation to generate a joint likelihood function (analytically intractable) for two correlated observations from two different experiments that I can then sample over with Nested Sampling to get a joint evidence.

My call to the sbi package looks something like

posterior = infer(simulation, prior, method="SNLE", num_simulations=10000)

and I am aware that this is a non-normalised posterior but my prior is uniform so I can just do $\log L(D_1, D_2|\theta) = \log P(\theta|D_1, D_2) - \log \pi(\theta)$ to get back to the joint likelihood.

My question is whether the data and parameters are normalised by default with the SNLE method? and can I turn this off?

This is not immediately clear in the documentation and has an impact on the recovered $\log L$ and corresponding evidence from the NS run. I am aware that normalisation is advisable when training flows but I can implement this myself.

I think if the data and parameters are normalised i.e. $D \rightarrow \tilde{D}$ and $\theta \rightarrow \tilde{\theta}$ then the recovered posterior from posterior.log_prob(samples) is $\log P(\tilde{\theta}| \tilde{D_1}, \tilde{D_2}) = \log L(\tilde{D_1}, \tilde{D_2}|\tilde{\theta}) + \log \pi(\tilde{\theta})$ which when rearranged for $L$ and sampled over with NS gives me $\tilde{Z} = P(\tilde{D_1}, \tilde{D_2})$ when I want $Z = P(D_1, D_2)$.

This should be fixable via some jacobian transformation $\log L(D_1, D_2|\theta) = \log L(\tilde{D_1}, \tilde{D_2}|\tilde{\theta}) + \log det(|\frac{\delta \tilde{D}}{\delta \tilde{\theta}}|)$ or something similar. If the data and parameters are normalised is this jacobian accessible? Note that this isn't the usual normalising flow jacobian but an additional correction.

Thanks for the help!

[janfb]

In this case (and in most other cases :) ) we would recommend using the flexible interface, here' s a tutorial: https://github.com/sbi-dev/sbi/blob/main/tutorials/02_flexible_interface.ipynb.

And then you can specify your custom density estimator as described here

https://github.com/sbi-dev/sbi/blob/main/tutorials/04_density_estimators.ipynb

to turn off normalization, e.g., in likelihood_nn set z_score_x="none".

[htjb]

Ahh I see okay thanks for the help! I will have a play with the flexible interface and see if I can grab the jacobian I need.