Uncertainty Chapter 13
Uncertainty Chapter 13
Outline 。Uncertainty ·Probability ·Syntax and Semantics ·Inference Independence and Bayes'Rule
Outline • Uncertainty • Probability • Syntax and Semantics • Inference • Independence and Bayes' Rule
Uncertainty Let action At leave for airportt minutes before flight Will A:get me there on time? Problems: 1. partial observability(road state,other drivers'plans,etc.) 2. 2. noisy sensors (traffic reports) 3. uncertainty in action outcomes(flat tire,etc.) 4. 4. immense complexity of modeling and predicting traffic Hence a purely logical approach either 1. risks falsehood:"A2swill get me there on time",or 2.leads to conclusions that are too weak fordecision making: "A2s 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
Uncertainty Let action At = leave for airport t minutes before flight Will At get me there on time? Problems: 1. partial observability (road state, other drivers' plans, etc.) 2. 2. noisy sensors (traffic reports) 3. 3. uncertainty in action outcomes (flat tire, etc.) 4. 4. immense complexity of modeling and predicting traffic 5. Hence a purely logical approach either 1. risks falsehood: “A25 will get me there on time”, or 2. leads to conclusions that are too weak for decision making: “A25 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 might reasonably be said to get me there on time but I'd have to stay overnight in
Methods for handling uncertainty Default or nonmonotonic logic: Assume my car does not have a flat tire Assume A25 works unless contradicted by evidence Issues:What assumptions are reasonable?How to handle contradiction? ● Rules with fudge factors: ● -A251-0.3 get there on time Sprinkler0.99 WetGrass -VetGrass→o.7Rain Issues:Problems with combination,e.g.,Sprinkler causes Rain??
Methods for handling uncertainty • Default or nonmonotonic logic: • – Assume my car does not have a flat tire – – Assume A25 works unless contradicted by evidence • Issues: What assumptions are reasonable? How to handle contradiction? • • Rules with fudge factors: • – A25 |→0.3 get there on time – – Sprinkler |→ 0.99 WetGrass – – WetGrass |→ 0.7 Rain • Issues: Problems with combination, e.g., Sprinkler causes Rain?? •
Probability Probabilistic assertions summarize effects of laziness:failure to enumerate exceptions,qualifications,etc. 一 ignorance:lack of relevant facts,initial conditions,etc. Subjective probability: Probabilities relate propositions to agent's own state of knowledge e.g.,P(A25 I no reported accidents)=0.06 These are not assertions about the world
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(A25 | no reported accidents) = 0.06 These are not assertions about the world Probabilities of propositions change with new evidence: