#StackBounty: #hypothesis-testing #bayesian #estimation #inference Posterior calculation on binomial distribution using quadratic loss …

Bounty: 50

Que

Let x be a binomial variate with parameters n and p (0<p<1). using a quadratic error loss function and a priori distribution of p as $ pi(p) $ = 1, obtain the bayes’ estimate for p.

Hey lately I have been teaching myself bayes estimator( in relation to statistical inference) ,
$ f(x| p ) = C^{n}_{x} p^x (1-p)^{n-x } $

Since prior distribution is 1

So joint distribution of x, p

f(x,p) = $ C^{n}_{x} p^x (1-p)^{n-x } $ only

Now posterior distribution is directly proportional to joint distribution of x and p

f(p|x) $ propto C^{n}_{x} p^x (1-p)^{n-x } $

f(p|x) $ propto p^x (1-p)^{n-x } $

f(p|x) $ propto p^{x+1-1} (1-p)^{n-x+1-1 } $

f(p|x) $ ~ beta({x+1, n-x+1 )} $

As we know Expected value of posterior distribution is

E(f(p|x)) $ = frac{x+1}{ n+2 } $

Now can someone help in calculating bayes risk using quadratic loss function , because I have no idea on how to proceed .


Get this bounty!!!

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