Question: When observed data are used to develop the prior distribution in Bayesian procedures, the methods are often referred to as empirical Bayes methods. These methods
When observed data are used to develop the prior
distribution in Bayesian procedures, the methods are often referred to as empirical Bayes methods. These methods are in contrast to standard Bayesian methods, which assume the prior
distribution is fixed before any data are observed. In Exercise 10, a beta(60, 38) prior
distribution was assigned to the 2010 completion rate for Drew Brees. The prior parameters were derived from pass completion data from other quarterbacks, making this an empirical Bayes problem. The average pass completion rate among all starting quarterbacks for the first five games was 61%, and the variance of the completion rates for the first five games (measured as a decimal) was 0.0024. We will assign a beta prior
distribution for p with prior mean E(π) = 0.61 and prior variance Var(π) = 0.0024. Use the approach for finding the prior
distribution parameters discussed in Exercise 12 to show that the parameters for the beta prior assigned to Brees’ 2010 completion rate are α = 60 and β = 38 (rounding to the nearest integer values).