Bayes Theorem Demystified
Do we really need the Bayes theorem? Can we do everything with the conditionals and marginals?
This is a fictional story of a high school student Ken, and his math teacher Dr. Demystifier (Dr. D). Ken has just learned the Bayes theorem but he was completely mystified by the formula, not knowing how to make use of it.
They will discuss the following topics:
- Bayes Theorem Derivation
- Belief Update Once
- Belief Update Twice
- Belief Update Forever
Bayes Theorem Derivation
Ken asked Dr. D, “May I ask a question about the Bayes theorem?”
Dr. D nodded and said, “Please do”.
Ken continued, “The Bayes theorem says:
I know how to derive it using the conditional probabilities, which we define using the joint probabilities:
We can re-arrange them to derive the following equality:
Re-arranging them further yields the Bayes theorem:
