# Bayes intuitions

Bayesian inference is just a convenient name for conditional probabilities according to probability theory. In other words, Bayesian statistics is mathematically grounded and based on three mathematical axioms (in addition to the axioms of math itself) from which all Bayesian statistics can be derived and proved.

# Purpose: intuitive understanding of gibbs samplers

Being mathematically coherent, Bayesian statistics is actually really easy to understand. You just have to learn a few basic ideas and use logic to understand the rest. This is less the case with classical statistics where the lack of coherence make you prone to misinterpret p-values (which is not the probability of the model being true), confidence intervals (which isn’t the interval that the parameter lies in with 95 % probability) etc. Bayesian stats quantifies these things directly.

This page is about getting these fundamental intuitions right and in doing that, making it easier to understand what BUGS, JAGS and other Gibbs samplers do.