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Judgement Summary 09

# Judgement Summary 09 - Judgement Probability and Belief...

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Judgement Probability and Belief Revision What does ‘probability’ mean? Logical possibility . Mostly applies to true games of chance, e.g. probability of drawing an ace from a fair deck is 4 in 52, or .077 (7.7%) Frequency As proportion of possible occurrences; natural sampling Degree of belief Subjective likelihood of unique events Propensity e.g. of a coin to come down heads or tails Bayesian theory Bayes’ rule enables you to work out how beliefs change in response to information. Estimating your degree of belief and the likelihood of the new information [p(D)] given this prior probability [p(H)] and the probability of alternative hypotheses [p(¬H)]. Bayes’ rule looks like this: P(H|D) = _______p(D|H) x p(H) _________ [p(D|H) x p(H)] + p(D¬|H) x p(¬H)] Are people good Bayesians? Kahneman & Tversky’s cab problem: A taxi is involved in an accident. There are two taxi firms, Blue and Green. 85% of the taxis are Green and the rest are Blue. A witness identifies the cab as Blue. Under tests, he correctly identified cab colour 80% of the time. What is the probability that the cab actually was Blue?

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Judgement Summary 09 - Judgement Probability and Belief...

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