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Bayesian inference 
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#1
Feb2510, 02:54 PM

P: 103

(Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics")
Hi guys, Say outside of my house, there are 20% chance of rain, and 40% chance the sprinker is on. When it is rain the pavement outside of house must be wet. And if the sprinkler is on, it also wet my pavement. If there is no rain and the sprinkler is off, my pavement is just dry. How do I calculate the probability of my pavement is dry? And I got the answer 52% from Netica. I think you all know netica is for bayesian network. 


#2
Feb2510, 05:36 PM

P: 106

Let's consider the chance of rain and no rain:
 20% chance of rain  20% chance of pavement wet (it doesn't matter if the sprinkler is on or off)  80% chance of no rain  80% * 40% chance of pavement wet due the sprinkler 80% * 60% chance of pavement dry (cause there is no rain, and the sprinkler is off) So, the chance of pavement wet is 20% + 80% * 40% = 52% 


#3
Feb2510, 06:18 PM

P: 2,504

Realistically P(R) and P(S) should not be independent and you would need some additional information on this such as P(RS) or P(SR). 


#4
Feb2510, 06:31 PM

P: 103

Bayesian inference
Thanks guys. I should worked it out. I was just spent whole afternoon working til brain damaged. :p



#5
Mar310, 12:31 PM

P: 2,504

What is the maximum value that P(W) can have? Set P(SR)= 0 and use Bayes' Theorem to calculate the max P(W). What is the minimum value that P(W) can have? Set P(SR) = 1 and repeat the calculation for min P(W). Hint: Note the role of the "interaction" term P(S)P(R) in the original calculation under the assumption of independence. 


#6
Mar310, 02:58 PM

P: 1,822




#7
Mar310, 09:10 PM

P: 2,504




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