Utility Calculation Mistake

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Andy
Posts: 1
Joined: Fri Aug 12, 2016 11:21 am

Utility Calculation Mistake

Post by Andy »

Hello,

i'm a little bit confused about the utility calculation. In the attachment i have constructed two simple scenarios with a utility node U1 and two chance nodes as parents (S1,S2). I thought, that the Utility is an expected value, calculated by the parent's propagated evidence. So let's say we have only one chance node weather with states rainy, and sunny and it is a parent node of U, it is calculating

Code: Select all

U(weather=rainy)=-10; U(weather=sunny)=20 -> Expected Value: P(weather=rainy)*-10 + P(weather=sunny)*20


This approach worked fine, also with more than one parent node. But since i have connected these parents like in the scenarios (S1->S2), this approach is not working anymore. It is only working for case 1. In case 2 i have only changed one utility-table-entry from 10 to 100. So i think i have done a mistake in this approach. Can someone tell me, what is wrong in my calculation approach?

Image

I would be really grateful, if you could help me. Thanks a lot!
Attachments
utilitycalculation_understanding.png
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adam
Posts: 25
Joined: Thu Jan 17, 2008 11:01 pm
Location: Shrivenham, UK
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Re: Utility Calculation Mistake

Post by adam »

Andy,

There's no mistake in SMILE -- the result should be 54. In your calculations you make incorrect assumption that S1 and S2 are independent, while clearly in your model they aren't.

Instead of P(S1=state_x1)*P(S2-state_x2)*U(S1=state_x1,S2=state_x2) you should use P(S1=state_x1)*P(S2-state_x2|S1=state_x1)*U(S1=state_x1,S2=state_x2).

You would get:
0.4*0.8*100 + 0.4*0.2*20 + 0.6*0.6*30 + 0.6*0.4*40 = 54

Cheers,
Adam
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