 # How to compute the uncertainty from the guide (epistemic uncertainty of BNN)?

Hi all,

I am new to probabilistic programming and Bayesian inference, so I apologize in case that question is trivial or lacks clarity. I searched the forum for similar questions but couldn’t find an answer.

Let us consider a problem where we want to sample from `P(Y|X,D)` where `X` is the input, `D` is the training dataset, and `Y` is the expected output. Also, let us assume that we are using a Bayesian Neural Network (BNN) as the model, and a guide whose weights I will refer to as `theta` here. After inference with `SVI`, my understanding is that `Predictive(model, guide, num_samples,...)` will approximate the following integral by averaging `num_samples` samples of `theta`: .

Now, if I’m not mistaken, the variance of `P(theta|D)` can be considered as the epistemic uncertainty, and the aleatoric uncertainty is encoded in the distribution `P(Y|X,theta)`.

However, `Predictive` returns samples from `P(Y|X,D)`, and approximating the variance of those predictions (e.g. via sample variance) means that I lose the ability to distinguish between epistemic and aleatoric uncertainty.

Is there any way to recover he uncertainty from `P(theta|D)`, which (I think) is the uncertainty of the guide? Thank you very much for your help.

Edit: After playing around, it seems that `pyro.param` can be used for retrieving what I’m looking for. For example, if the guide is `AutoNormal`, then `pyro.param("AutoDiagonalNormal.scale")` seems to provide what I need. However I am unsure, so confirmation of this still would be very much appreciated.