Tempered posterior in Blackjax

[Davidmolin4]

Hi everyone,

I would like to know if it is possible to implement the "log tempered posterior" which is defined as follows:

$logp(\theta | x, y)^{\frac{1}{T}} = \frac{1}{T} \left( logp(y|\theta, x) + logp(\theta) \right) + C(T),$

with $T>0$ and $C(T)$ a normalization constant.

I don't know if it is necessary to find the constant $C(T)$ otherwise it is straightforward.

[rlouf]

Hi,

Would you mind giving me more background: a paper, an example, etc. so I can better answer your question ?

[rlouf]

You can't simply rescale because changing the functional form of your potential changes the equations of motion! If you simply rescale, the Langevin dynamics that is used to draw samples does not target your original distribution anymore but something else, hence the results you see.

It's a good exercise for me too, so I'll take a look at the theory again and come back to you with an explanation, and hopefully a solution.

[Davidmolin4]

Ok! Thank you for your support

[rlouf]

You can follow the progress on #396 where we're adding support for temperature != 1 in SgLD and SgHMC.

[Davidmolin4]

Thanks for the information :)

[rlouf]

You can now use a temperature != 1 with both SGLD and SGHMC with blackjax-nightly.

[rlouf]

You can now use a temperature != 1 with both SGLD and SGHMC with blackjax-nightly.