# Bayes estimator

• Sep 28th 2013, 06:06 AM
Giiovanna
Bayes estimator
An urn contain 5 balls, $\displaystyle \theta$ white and $\displaystyle 5 - \theta$ green. The experiment consists in grab 2 balls from the urn and register the pair $\displaystyle (x_1, x_2)$ , where $\displaystyle x_i = 1$ we observe a white ball and $\displaystyle x_i = 0$ otherwise. What is the bayes estimator $\displaystyle \theta^*$ for $\displaystyle \theta$ considering the squared loss function? (i.e $\displaystyle l(\theta,\theta^*) = (\theta - \theta^*)^2$ )

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 $\displaystyle \theta$ and \displaystyle \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
• Sep 28th 2013, 05:11 PM
chiro
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.