Dear Paul,
if you consider TWC prediction as a part of the probabilistic model, you get 4 probabilities for modelling a model which needs 3 probabilities to be specified. (the model is given by the 2-way table given by (Snow/not snow and snow prediction of 70%/not snow prediction of 70%).
The problem is that in this model the 4 numbers you give are inconsistent, so, when you accept the probabilities 2,5, and 6, you find that P(S/prediction of snow is 70%) = 0.34, which is not consistent with propositions 3 and 4.
If you accept probabilities 2,3 and 5, for example, you find that Pr(prediction of snow = 70% / not snow) = 0.002, and not 0.01 as given in the problem.
Hope that helps also, Jean-Louis
2009/2/13 Lehner, Paul E. <pleh...@mitre.org>:I was working on a set of instructions to teach simple two-hypothesis/one-evidence Bayesian updating. I came across a problem that perplexed me. This can't be a new problem so I'm hoping someone will clear things up for me. The problem 1. Question: What is the chance that it will snow next Monday? 2. My prior: 5% (because it typically snows about 5% of the days during the winter) 3. Evidence: The Weather Channel (TWC) says there is a "70% chance of snow" on Monday. 4. TWC forecasts of snow are calibrated. My initial answer is to claim that this problem is underspecified. So I add 5. On winter days that it snows, TWC forecasts "70% chance of snow" about 10% of the time 6. On winter days that it does not snow, TWC forecasts "70% chance of snow" about 1% of the time. So now from P(S)=.05; P("70%"|S)=.10; and P("70%"|S)=.01 I apply Bayes rule and deduce my posterior probability to be P(S|"70%") = .3448. Now it seems particularly odd that I would conclude there is only a 34% chance of snow when TWC says there is a 70% chance. TWC knows so much more about weather forecasting than I do. What am I doing wrong? Paul E. Lehner, Ph.D. Consulting Scientist The MITRE Corporation (703) 983-7968 pleh...@mitre.org _______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai_______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai
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