Bayes' Theorem
Probability is about what you expect. Bayes' theorem is about what you learn. Language: Python Apply Bayes' theorem to compute posterior probabilities from priors, likelihoods, and evidence. Build a Naive Bayes text classifier from scratch with Laplace smoothing and log-space computation. Compare MLE and MAP estimation and explain how MAP corresponds to L2 regularization. Implement sequential Bayesian updating using Beta-Binomial conjugate priors for A/B testing. A medical test is 99% accurate. You test positive. What are the chances you actually have the disease? Most people say 99%. The real answer depends on how rare the disease is. If 1 in 10,000 people have it, a positive result only gives you about a 1% chance of being sick. The other 99% of positive results are false alarms from healthy people. This is not a trick question. It is Bayes' theorem. Every spam filter, every medical diagnostic, every machine learning model that quantifies uncertainty uses this exact reasoning. You start with a belief. You see evidence. You update. If you build ML systems without understanding this, you will misinterpret model outputs, set bad thresholds, and ship overconfident predictions. You already know from Lesson 06 that conditional probability is: And symmetrically: Both expressions share the same numerator: P(A and B). Set them equal and rearrange: That is Bayes' theorem. Four quantities, one equation.…
Bayes' Theorem: Probability is about what you expect. Bayes' theorem is about what you learn. Language: Python Apply Bayes' theorem to compute posterior…
This free lesson is part of the AI Engineering from Scratch curriculum. Read the full explanation, run the lesson code, and verify the result in the interactive reader or from the repository source.
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