Probability - Caltech

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Review: Probability ! Describe probability of events ! P( Pit at [2,2] ) ! P( Wumpus dead ) ! P( A v B ) ! Formally: Probability Space ! Set of “atomic events”: ! Set of all non-‐atomic events: is a σ-‐Algebra (closed under complements and countable unions) ! Probability measure For , is the probability that event happens 8
Why use probabili)es? Related events must have related probabili)es Ω Agents that bet according to beliefs that violate probability axioms can be forced to lose in expecta)on (de Fineq 1931) 9
Page 1 and 2: Introduc)on to Ar)ficial Intellig
Page 3 and 4: Announcements ! Grading: AvianAske
Page 5 and 6: Quan)fying Uncertainty ! So far,
Page 7: Decision making under uncertaint
Page 11 and 12: Interpreta)on of probabili)es ! P
Page 13 and 14: Examples ! Bernoulli distribu)on:
Page 15 and 16: Example: Gaussian distribu)on !
Page 17 and 18: Example: Mul)variate Gaussian 17
Page 19 and 20: Marginal distribu)ons What is P(
Page 21 and 22: Condi)onal distribu)ons ! Formal
Page 23 and 24: Posterior inference ! Suppose we
Page 25 and 26: Independent RVs ! What if RVs a

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