1. A new drug has been developed to cure a rare disease. 20 people infected with...

 

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1. A new drug has been developed to cure a rare disease. 20 people infected with the disease are randomly selected and 16 of them are cured. a) Use the following uniform prior: define 101 hypotheses where 0, the proportion of the population of infected individuals that would be cured by the drug, is 0, 0.01, 0.02, ..., 0.99, 1, and is equally likely to be any of these values. i) Calculate the posterior distribution of and plot it. ii) What is the mean of this posterior distribution? iii) Give a 95% credible interval for 0. iv) What is the probability that the drug will cure over 70% of the infected population? b) Repeat part a) but this time using a continuous prior: 0~Uniform(0,1)= Beta (1,1). c) Suppose an expert suggests that he thinks the probability of an infected individual being cured is about 0.7, and he is 95% sure that the probability is between 0.5 and 0.9. Specify a Beta prior that takes into account the expert's opinion. Repeat part a) using the new posterior distribution. 1. A new drug has been developed to cure a rare disease. 20 people infected with the disease are randomly selected and 16 of them are cured. a) Use the following uniform prior: define 101 hypotheses where 0, the proportion of the population of infected individuals that would be cured by the drug, is 0, 0.01, 0.02, ..., 0.99, 1, and is equally likely to be any of these values. i) Calculate the posterior distribution of and plot it. ii) What is the mean of this posterior distribution? iii) Give a 95% credible interval for 0. iv) What is the probability that the drug will cure over 70% of the infected population? b) Repeat part a) but this time using a continuous prior: 0~Uniform(0,1)= Beta (1,1). c) Suppose an expert suggests that he thinks the probability of an infected individual being cured is about 0.7, and he is 95% sure that the probability is between 0.5 and 0.9. Specify a Beta prior that takes into account the expert's opinion. Repeat part a) using the new posterior distribution.

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a i P 0 x P x 0 P 0 P x P 0 x 16 20 1 101 0 01 ii E 0 x sum i P 0 x i E 0 x 0 01 0 0 01 ... View the full answer