Naive Bayes Classifier

At x=1.0, the spam curve gives density 0.228 vs ham's 0.038. The observation is closer to spam's mean (2), so P(x|spam) > P(x|ham). These likelihoods feed into Bayes' rule in the next step.

With a 40% prior on spam and observing x=1.0, the posterior favours spam at 80.2%. Drag the x slider towards the spam mean (2) to increase P(x|spam), or towards the ham mean (-1) to increase P(x|ham).

High correlation violates the naive assumption significantly — yet NB often still works surprisingly well because it only needs the right class ranking, not calibrated probabilities.

Both features combined favour spam (94.0%). The naive assumption lets us simply multiply P(x₁|spam) × P(x₂|spam) instead of modelling joint distributions. Try moving x₂ towards ham's mean (-0.5) to see the features disagree.

With equal priors, the decision boundary depends only on the likelihoods — it sits where P(A|x) = P(B|x).

The combined word likelihoods favour spam (99.5%). The strongest spam signal is "prize" with a spam/ham ratio of 25.0. Try lowering spam-indicative words or raising ham-indicative ones to flip the verdict.