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
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
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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)?
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