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Stats 3.3Concept7 parts

Bayes' Theorem

Turn "how likely is the evidence given the class" into "how likely is the class given the evidence".

Loading your progress…Next: 3.4 Random Variables, Expectation and Variance

In this lesson7 parts

  1. 01The result we need to explain
  2. 02All the ways a flag can occur
  3. 03Build Bayes' theorem from those counts
  4. 04Change only the starting rate
  5. 05Update when new evidence arrives
  6. 06Check the assumption and run the update
  7. 07Use the reasoning independently

Key terms

The words this lesson introduces, each in one line. The module’s glossary collects them all.

prior
Probability before the new evidence: 1% spam in the constructed inbox.
likelihood
Probability of this evidence given a specified class: P(flagged given spam) = 90%.
false-positive rate
Probability of a positive flag when the class is real: 10% in the construction.
law of total probability
The probability of the evidence is the sum over all disjoint paths that produce it: 108 flags per 1,000 messages, from spam and from real mail.
posterior
Probability after incorporating the stated evidence: 8.33% after one flag.
Bayes' theorem (narration)
The update from a prior and the likelihoods in each class to a posterior: likelihood times prior, divided by the total probability of the evidence.
conditional independence
Within each class, one flag result does not alter another flag's probability. An assumption the construction does not establish.

Quiz 5 questions

Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.

Practice

Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.

The self-checking notebook for this lesson is Conditional probability, independence and Bayes' theorem.

Common mistakes

What you will see when it goes wrong, why it happens, and the fix.

Where it’s used

Where this lesson’s ideas turn up in real work.