Let 0 denote the proportion of patients with ulcers who are cured using a newly developed...
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Let 0 denote the proportion of patients with ulcers who are cured using a newly developed drug, assuming a Bernoulli model holds. Suppose the value of 0 is unknown. Two researchers, Leonard and Sheldon, assign different prior distributions to 0: Leonard assigns 1(0)=1f0<0 <1 Sheldon assigns 2(0) = 40^3 f 0<0 <1 a. Explain what Leonard's and Sheldon's choices of prior indicate about their beliefs of the likely values of 0. b. Suppose a random sample of 500 ulcer patients are administered the new drug. Find the posterior distribution that each researcher would derive for 0. Justify your response here. c. Using a squared error loss, compute the Bayes estimator for each researcher. What is the largest possible difference between the estimates that Leonard and Sheldon would obtain based on a sample of 500? Justify your response. d. Suppose that in the sample of 500 it is observed that 365 are cured. Using a squared error loss, find Leonard's and Sheldon's Bayes estimates. How do they compare? e. Suppose that in the sample of 20 it is observed that 15 are cured. Using a squared error loss, find Leonard's and Sheldon's Bayes estimates. How do they compare? Let 0 denote the proportion of patients with ulcers who are cured using a newly developed drug, assuming a Bernoulli model holds. Suppose the value of 0 is unknown. Two researchers, Leonard and Sheldon, assign different prior distributions to 0: Leonard assigns 1(0)=1f0<0 <1 Sheldon assigns 2(0) = 40^3 f 0<0 <1 a. Explain what Leonard's and Sheldon's choices of prior indicate about their beliefs of the likely values of 0. b. Suppose a random sample of 500 ulcer patients are administered the new drug. Find the posterior distribution that each researcher would derive for 0. Justify your response here. c. Using a squared error loss, compute the Bayes estimator for each researcher. What is the largest possible difference between the estimates that Leonard and Sheldon would obtain based on a sample of 500? Justify your response. d. Suppose that in the sample of 500 it is observed that 365 are cured. Using a squared error loss, find Leonard's and Sheldon's Bayes estimates. How do they compare? e. Suppose that in the sample of 20 it is observed that 15 are cured. Using a squared error loss, find Leonard's and Sheldon's Bayes estimates. How do they compare?
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Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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