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2. Conditioning and Independence

Conditioning leads to revised ("conditional") probabilities that take into account partial information on the outcome of a probabilistic experiment. Conditioning is a very useful tool that allows us to "divide and conquer" complex problems. Independence is used to model situations involving non-interacting probabilistic phenomena and also plays an important role in building complex models from more elementary ones.

Conditioning and Bayes' rule​

  • Conditional Probability

The conditional probability of an event given another event is the probability of their intersection divided by the probability of the conditioning event.

  • Three important tools
    • Multiplication rule
    • Total probability theorem
    • Bayes' rule - provides a systematic way for incorporating new evidence into a probability model. Foundation of the field of inference. It is a guide on how to process data and make inferences about unobserved quantities or phenomena.

P ( A | B ) = Probability of A given B

P ( A | B ) = Here B is called the conditioning event

Conditional Probabilities share probabilities of ordinary probabilities​

  • Conditional probabilities must be non-negative

Inference - Having observed B, we make inferences as to how likely a particular scenario Ai, is going to be.