The Beta-Binomial model. Let X_1, X_2, . . ., X_n be independent Bernoulli rando

Question

The Beta-Binomial model. Let X_1, X_2, . . ., X_n be independent Bernoulli random variables with probability of success (i.e. of being 1) given by p. Assume the prior distribution of p is given by a beta(alpha; beta) distribution. Derive the posterior distribution of p. Romney (1999) looks at the level of consensus among 24 Guatemalan women on whether they think polio is non-contagious. The survey data are given below: where 1 indicates that the respondent believes polio to be non-contagious and 0 indicates that the respondent believes polio to be contagious. Let p denote the probability of each woman believing polio to be non-contagious. Apply the beta-binomial model with a beta( 1; 1) prior to find the posterior distribution of p. For the above data, find a Bayes point estimate and a 90% credible interval for p.

Explanation / Answer

a)

posterior distribution of P : BETA

b)

for this exercise I can gladly help you but you shoudl post it in a new quiestion

c)

alpha = 1 - 0.90 = 0.10

alpha /2 = 0.05

Z= 1.64

I: p +/- 1.64 * srqt ( [p*q] / n )

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