@chartl Thanks this helps alot!
(5) I think I get what you are saying here. Just to confirm if I understand this correctly, the existence of a scalar function g(a,b) implies that a and b are not uniquely identifiable but still identifiable as a function correct? This means that I have to create a new parameter which is a function g(a,b) and sample from that?
(4) Okay, so I have to probably just change all my Theano dependencies to Aesara. Thats nice!
(3) By optimisation of likelihood I assume you mean optimising my black box vehicle dynamics model. Although I could potentially make that run even faster, my end goal is to use a more complicated (and extremely well optimised) model as a black box. This model will still be slower than the current model I am using. Is there any other place I can optimise to make my sampling faster?
(2) I see. That makes sense.
(1) I think I understand what you are getting at. One question I have is why cant I use KDE to approximate Q_{post}[\theta]?