Hi all, I’m reading Uncertainty Quantified Deep Bayesian Model Discovery · Overview of Julia's SciML. to play around with Bayesian NODEs. I noticed the loss function which actually gets passed to AdvancedHMC’s samplers is l(θ) = -sum(abs2, ode_data .- predict_neuralode(θ)) - sum(θ .* θ), where the “likelihood” part is proportional to a Gaussian likelihood model with a fixed standard deviation.
My question is this one, say I want to use Normal from Distributions.jl and simultaneously fit the standard deviation parameter during fitting/sampling; are there examples of such use? Are there any pitfalls I should be cautious of? (e.g. different scale of parameters, etc)