Bayesian exercise

#1
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I cant get my head round the following exercise:

You are testing dice for a casino to make sure that sixes do not come up more frequently than expected. Because you do not want to manually roll dice all day, you design a machine to roll a die repeatedly and record the number of sixes that come face up. In order to do a Bayesian analysis to test the hypothesis that p = 1/6 versus p = .175 , you set the machine to roll the die 6000 times. When you come back at the end of the day, you discover to your horror that the machine was unable to count higher than 999. The machine says that 999 sixes occurred. Given a prior probability of 0.8 placed on the hypothesis p = 1/6 , what is the posterior probability that the die is fair, given the censored data? Hint - to find the probability that at least x sixes occurred in N trials with proportion p (which is the likelihood in this problem), use the R command :

1-pbinom(x-1,N,p)

The possible answers are 0.5, 0.684, 0.8 or 0.881.

I would really appreciate if someone could help me here! I need to understand this approach!

Cheers and thanks in advance! Markus
 

hlsmith

Omega Contributor
#2
Yeah, they provide a lot of jumbled up text. Big picture:


posterior probability = prior probability * likelihood of outcome.
 

Dason

Ambassador to the humans
#3
Yeah, they provide a lot of jumbled up text. Big picture:


posterior probability = prior probability * likelihood of outcome.
That's not quite correct. The posterior is proportional to prior*likelihood but it isn't an equality unless you divide by the probability of the data.
 

hlsmith

Omega Contributor
#5
Dason, please make the Purdy open infinity sign (proportionality) for me and I will correct all that is wrong :)


Thanks.