12) In planning for the next year\'s losses, one predictive modeler for an insur

Question

12) In planning for the next year's losses, one predictive modeler for an insurance company claims that there is an 80% chance of a severe weather event in any given month, independent of all other months. Another predictive modeler claims that the true chance of a severe monthly weather event is actually 60%. These two analysts are equally reliable, so barring any evidence to contrary, we assign their judgements equal weight. If one of the two has to be right, what probabilities would we assign to their claims if only six months of the following year actually had severe weather events?

Explanation / Answer

Two anaysts are equally reliable and equal weighttotheir judgement.

So, Pr(Model I) = Pr(Model II) = 0.5 (prior distribution)

If one of two has to be right. that means either of model is correct)

so,

Pr(6 severe mmonth out of 12) = Pr(First model is true) * Pr [BIN (X = 6; 12; 0.8)] + Pr( Second Model is true) * Pr [ BIn ( X = 6 ; 12; 0.6)]

= 0.5 * 12C6 * (0.8)6 (0.2)6 + 0. 5 * 12C6 * (0.6)6 (0.6)6

= 0.5 * 0.0155 + 0.5 * 0.1766

= 0.096

so Probability assigned to Model 1 = 0.0155 * 0.5/ 0.096 = 0.08

Probability assigned to Model 2 = 0.1766 * 0.5/ 0.096 = 0.92

so 8% probability assigned to model1 and 92% probability to model 2

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