Bayesian

Basic Procedure of Bayesian Statistics

1. Model setup: state the parameters of interest θ that we are interested in finding the value of.
2. Prior distribution: Assign a prior probability distribution to parameters θ, which represent our degree of belief with respect to θ.
3. Posterior distribution: Update our degree of belief with respect to θ, based on data. The new degree of belief is called our posterior probability distribution of θ.

An observed result changes our degrees of belief in parameter values by changing a prior distribution into a posterior distribution.

https://www.stat.auckland.ac.nz/~brewer/stats331.pdf https://vasishth.github.io/bayescogsci/book/sec-analytical.html

You can sample from the posterior if you have the joint. That’s what metropolis Hastings is really. The top line of Bayes gives you the joint.

https://stats.stackexchange.com/questions/307882/why-is-it-necessary-to-sample-from-the-posterior-distribution-if-we-already-know