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This is an alternative to the frequentist approach of machine learning. Bayesian incorporates human intuition and training a model does not require a lot of data. This is an incredible method and is often overlooked by more popular machine learning methods that require lots of data.
Fun fact: If you have an 'infinite' amount of data, then your Bayesian Results will approach that of Ordinary Least Squares.
Github for code:
https://github.com/SpencerPao/Data_Science/tree/main/Bayesian%20Regression
Full Conditionals
https://bragqut.files.wordpress.com/2018/04/deriving-the-full-conditionals.pdf
Additional Stan Model output explanations
https://m-clark.github.io/easy-bayes/rstanarm-glm.html
0:00 - What is Bayesian Regression?
1:30 - Why should you use Bayesian Regression?
2:35 - Bayesian Regression Equation
3:32 - Theory behind Gibbs Sampler (MCMC)
4:05 - Understanding and preparing data for Bayesian Analysis
7:02 - Designing Gibbs Sampler (MCMC)
12:10 - Accuracy, Burn-in, Convergence, Confidence Intervals, Predictions
17:23 - rstanarm library