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Math Help - Bayes estimator

  1. #1
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    Bayes estimator

    An urn contain 5 balls,  \theta  white and  5 - \theta green. The experiment consists in grab 2 balls from the urn and register the pair  (x_1, x_2) , where  x_i = 1 we observe a white ball and  x_i = 0 otherwise. What is the bayes estimator  \theta^* for   \theta considering the squared loss function? (i.e  l(\theta,\theta^*) = (\theta - \theta^*)^2 )


    I can't figure out which posterior distribution I should use or even if I need to use one. I calculated my loss function considering all the possible values for  \theta and $ \theta^* but I can't calculate the risk function without the posterior function.
    Can someone help me with it?


    I can't find out what to do with the ordered pair, I just calculated the probability of each pair
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  2. #2
    MHF Contributor
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    Re: Bayes estimator

    Hey Giiovanna.

    Under squared loss, the best estimator is always the mean (its a standard result).

    Hint: Take a look at the conjugate prior for a hyper-geometric distribution and use this to form your prior. Once you have your prior*likelihood distribution you can use this to get your posterior and then your mean from this distribution.
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