Understanding The Naive Bayes Classifier

Let's step back first and frame our classification problem in Bayesian terms -- where we have a set of prior beliefs and update our beliefs as we observe and collect evidence. In statistics, everything revolves around hypotheses. We make a hypothesis (an informed guess) about how the world works, and then we go about collecting evidence to test that hypothesis (if you would like to know the details, I wrote a post about hypothesis testing here). Classification models can be framed as a hypothesis as well. Let's first write out the objective and variables of our classification problem: OK, so that's classification -- now let's examine classification through a Bayesian lens.