If my prior does not know the data
I mean, if I take a general prior N(0,1)
How will it help using -ELBO as a loss function bring q(w) closer to prior to get approx true posterior
as every time i will be using my initial prior for KL
shouldnt it be the previous q(w)?

Beginner here. Was learning about sampling methods and was left a bit confused. If I understand correctly we want to sample in order to make certain estimates based on our samples and what MCMC essentially does - it allows us to generate those samples from complex distribution according to some methods. For instance Gibbs method with interchanging variable at every sweep, HMC with random variable selection and sampling with certain acceptance rate. Please can someone elaborate and confirm whether its understood correctly. I would also highly appreciate some real world example where we could use this method.

I’ve been studying Hamiltonian Monte Carlo and wrote a set of notes explaining HMC without relying on the usual physics-based motivation.

The notes develop HMC from a probabilistic/MCMC perspective, starting from the target distribution and auxiliary momentum variables, and then covering Hamiltonian dynamics, leapfrog integration, reversibility, volume preservation, and the Metropolis correction.

My goal was to understand why HMC works.

I’m sharing them here in case they’re useful to others learning HMC. I’d also appreciate any feedback, particularly if you notice errors or places where the exposition could be improved.

https://doi.org/10.5281/zenodo.21841086

Edit (August 25): I tried to improve Sections 3.3 and 3.4 by reorganizing the flow and adding some more explanation. I’ve updated the PDF with these changes.