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Bayesian Machine Learning for Optimization in Python

Bayes’ Theorem

Explore Bayes’ Theorem to learn how prior knowledge and new evidence can be combined to revise event probabilities. This lesson demonstrates the theorem’s practical use in diagnosis and weather forecasting, helping you apply Bayesian concepts to real-world predictive modeling.

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What is Bayes’ theorem?

Bayes’ theorem describes the probability of an event based on prior knowledge of conditions that might be related to the event. Named after English statistician Thomas Bayes, it provides a way to revise existing predictions or theories when new evidence becomes available. Bayes’ theorem is used in many fields, from medicine to economics and artificial intelligence to psychology.

Bayes’ theorem can be stated as follows:

Here:

  • P(A∣B)P(A|B) is the probability of event AA, given that event BB has occurred.

  • P(B∣A)P(B|A) is the probability of event BB, given that event AA has occurred.

  • P(A)P(A) is the probability of event AA occurring independently of event ...