Let the unknown probability that a basketball player makes a shot successfully be θ. Suppose your prior on θ is uniform and that she makes two shots in a row. Assume that the outcomes of the two shots are independent. (a) What is the posterior density of θ? (b) What is the Bayes estimator under squared error loss for θ? (c) What is the Bayes estimator under absolute error loss for θ? (d) Consider the impact of

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
icon
Related questions
Question

Let the unknown probability that a basketball player makes a shot successfully be θ. Suppose your prior on θ is uniform and that she makes two shots in a row. Assume that the outcomes of the two shots are independent. (a) What is the posterior density of θ? (b) What is the Bayes estimator under squared error loss for θ? (c) What is the Bayes estimator under absolute error loss for θ? (d) Consider the impact of the prior choice θ ∼ Beta(1, 1). How would your answer in (b) change if you instead used Beta(0.1, 0.1)? Beta(10,10)?

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 7 steps with 7 images

Blurred answer
Similar questions
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill