# Lecture 8 - Uncertainty Let action At = leave for airport t...

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Uncertainty Let action A t = leave for airport t minutes before flight Will A t get me there on time? Problems: 1. partial observability (road state, other drivers' plans, etc.) 2. noisy sensors (traffic reports) 3. uncertainty in action outcomes (flat tire, etc.) 4. immense complexity of modeling and predicting traffic Hence a purely logical approach either 1. risks falsehood: “ A 75 will get me there on time”, or 2. leads to conclusions that are too weak for decision making: A 75 will get me there on time if there's no accident on the bridge and it doesn't rain and my tires remain intact etc etc.” ( A 1440 might reasonably be said to get me there on time but I'd have to stay overnight in the airport …)

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Probability Probabilistic assertions summarize effects of laziness : failure to enumerate exceptions, qualifications, etc. ignorance : lack of relevant facts, initial conditions, etc. Subjective probability: Probabilities relate propositions to agent's own state of knowledge e.g., P(A 75 | no reported accidents) = 0.06 These are not assertions about the world Probabilities of propositions change with new evidence: e.g., P(A 75 | no reported accidents, 5 a.m.) = 0.15
Making decisions under uncertainty Suppose I believe the following: P(A 75 gets me there on time | …) = 0.04 P(A 90 gets me there on time | …) = 0.70 P(A 120 gets me there on time | …) = 0.95 P(A 1440 gets me there on time | …) = 0.9999 Which action to choose? » Depends on my preferences for missing flight vs. time spent waiting, etc. » Utility theory is used to represent and infer preferences

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Syntax Basic element: random variable Similar to propositional logic: possible worlds defined by assignment of values to random variables. Boolean random variables e.g., Cavity (do I have a cavity?) Discrete random variables e.g., Weather is one of < sunny, rainy, cloudy, snow > Domain values must be exhaustive and mutually exclusive Elementary proposition constructed by assignment of a value to a random variable: e.g., Weather = sunny , Cavity = false (abbreviated as ¬ cavity ) Complex propositions formed from elementary propositions and standard logical connectives e.g., Weather = sunny Cavity = false
Syntax Atomic event : A complete specification of the

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Lecture 8 - Uncertainty Let action At = leave for airport t...

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