What is the posterior mean? Report your answer to three decimal places. What is the lower bound of an equal tail 95% credible interval for p? That is, report the 0.025 quantile of the posterior distribution.
Suppose we take the Bayesian viewpoint.
We want to understand the probability of someone responding positively to a vaccine. Our parameter of interest is p the probability of a positive reaction.
We specify our prior belief on p using a Beta distribution with parameters (shape 1 and shape 2) given by 4 and 8.
We take 100 people (assumed to be a random sample), administer the vaccine, and see how many successes we have. We can reasonably model our data using a Binomial distribution with parameters 100 and p.
Our updated belief follows a new Beta distribution with parameters (shape 1 and shape 2) given by 44 and 68.
What is the posterior mean? Report your answer to three decimal places.
What is the lower bound of an equal tail 95% credible interval for p? That is, report the 0.025 quantile of the posterior distribution.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 21 images
