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Unformatted text preview: Review Interpretations of Probabilty Probability and Forecasts Eco331: Subjective Probability as a Rational Forecast Marciano Siniscalchi September 27, 2009 Review Interpretations of Probabilty Probability and Forecasts Probability, Random Variables, Expectation Definition A probability over a finite set S of states is a function P : P ( S ) → R such that: 1 P ( E ) ≥ 0; 2 P ( ∅ ) = 0; P ( S ) = 1. 3 If E ∩ F = ∅ , then P ( E ∪ F ) = P ( E ) + P ( F ) [ additivity ]. Definition Consider a finite state space S . A (realvalued) random variable is a function X : S → R that associates a real number X ( s ) to each state s ∈ S . Its expectation (or expected value ) is E [ X ] = X s ∈ S X ( s ) P ( { s } ) . Review Interpretations of Probabilty Probability and Forecasts Three Views of Probability Classical: Probability describes the “physical” chance that an experiment produces some outcome. P (event) = #“favorable” outcomes #possible outcomes . Selfreferential, because it assumes equally “likely” outcomes. Frequentist: Probability is the longrun frequency of an event in an infinite sequence of repetitions of the experiment. What if experiment cannot be repeated? Subjectivist / Bayesian: Probability is a numerical representation of the individual ’s beliefs, as revealed by her behavior . Review Interpretations of Probabilty Probability and Forecasts Subjective Probability “The individual” is whoever is making the decision. Maybe you! That’s why it’s called “subjective”... Actually, (subjective) probability only makes sense in a decision context. Subjective Probability is based on behavior. “Belief” is a psychological concept. We need an operational definition . Probability is just a function, but we must be able to derive (elicit) it from the individual’s choices in suitable settings. Review Interpretations of Probabilty Probability and Forecasts DecisionTheoretic Foundations (1) A simple idea that requires a lot of work to get right....
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This note was uploaded on 11/17/2009 for the course ECONOMICS 331 taught by Professor Marciano during the Spring '09 term at Northwestern.
 Spring '09
 Marciano
 Economics

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