What Naive Bayes Is and Is Not - Naive Bayes from Counts

The finale keeps the exact count table visible while naming the modeling boundary. The arithmetic is exact; the independence assumption and any broader performance claim stay outside the computation.

highlighted = computed this step

What is exact

The priors, likelihoods, scores, and posteriors are exact rational values from the shown integer counts.

\text{counts}\rightarrow\text{ratios}\rightarrow\text{products}\rightarrow\text{posteriors}

What is assumed

The independence statement is a modeling assumption, not a transcendental boundary. The smoothing policy here is none, so zero likelihoods are rejected.

\text{smoothing}=\text{none}

Summary

The priors, likelihoods, products, and posteriors are exact rational values from the shown counts. The independence assumption is a stated modeling choice; this pins counting mechanics, not a claim about accuracy, calibration, or generalization.

\text{exact counting mechanics only}