The technologies I’m suggesting are just implementations of Bayes, which is what you’re trying to do. There’s some theory as to *how* they do inference (special versions of MCMC basically), but this is an “implementation detail” to a degree. Here’s some references to get you started, though they’re mostly Stan-centered http://mc-stan.org/users/documentation/external.html . If you want a better overall picture of the theory I really like this https://ben-lambert.com/a-students-guide-to-bayesian-statistics/ book, takes you from basics all the way to Stan usage
The technologies I’m suggesting are just implementations of Bayes, which is what you’re trying to do. There’s some theory as to *how* they do inference (special versions of MCMC basically), but this is an “implementation detail” to a degree. Here’s some references to get you started, though they’re mostly Stan-centered http://mc-stan.org/users/documentation/external.html . If you want a better overall picture of the theory I really like this https://ben-lambert.com/a-students-guide-to-bayesian-statistics/ book, takes you from basics all the way to Stan usage