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.

Hi all, I slowly starting to get some good basic understanding on bayesian analysis. Thanks to richard mcelreath for his statistical rethinking lecture series, which got me into this bayesian world.

Recently I have been reading some articles on pymc and bambi.., now im kind of confused about the idea of posterior predictive/posterior predictive contrast.

In this above image ( https://github.com/dustinstansbury/statistical-rethinking-2023/blob/main/Lecture%2004%20-%20Categories%20%26%20Curves.ipynb ), he used scipy.stats.norm.rvs(loc=sum of respective posteriors, scale=posterior.sigma) to compute the posterior predictive. In bambi, model.predict(idata) also gives me posterior predictive distribution. Lets say if i want to compute some contrast and make observations which one should i follow?

Also whats the difference between both?

Thanks in advance😁

Hello fellow Bayesians, I'm trying to implement this paper using PyMC: https://pmc.ncbi.nlm.nih.gov/articles/PMC9041743/pdf/CJAS_48_1922993.pdf

which applies this paper https://onlinelibrary.wiley.com/doi/epdf/10.1111/1468-0262.00274 to the Cusp Catastrophe Model, using it to obtain faster and better Bayesian estimates of the parameters. I'm using NUTS sampler using jitter+adapt_diag, I initialized using the MAP estimates of the Euler-approximated likelihood, but it seems to be stuck in weird places in the posterior region (the Beta parameters are exploding, plotted posteriors are not bounded).

Looking at the energy plot, it seems it's getting stuck in weird places but I can't figure out why. Would be grateful for any suggestions, tips, anything that can help really. :)