obtain the point estimate and 95% credible interval for μ.

Suppose that we are interested in the proportion of population affected by diabetes among Pima Indian women. Let us represent the diabetes status of each person by random variable X, where X=1 if the person has diabetes and X=0 if the person does not. Then we can assume that X has a Bernoulli distribution with parameter μ. We know that the population proportion of diabetic women in the whole US is about 10%. We want to use this information to specify our prior for μ. Use R-Commander to find a beta distribution that has relatively high probability density values around 0.1. For this, plot different beta distribution by changing the parameters until you find a distribution for which the area under the probability density curve is large over the interval from 0.05 to 0.15. Then use the Pima.tr data (available from the MASS package) to find the posterior probability distribution of μ. Use the posterior probability distribution to obtain the point estimate and 95% credible interval for μ.

 

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