General Studies · Bayesian Inference
Consider a small clinical trial to study the effectiveness of a treatment for a particular illness. 10 patients are enrolled in this experiment. Let θ denote the probability that a randomly chosen patient in the population recovers from this illness due to this treatment. For a standard Bayesian analysis, consider the Beta(0.5, 0.5) prior on θ. Suppose exactly 6 out of the 10 patients recover. Which of the following is the Bayes estimate of θ under the squared error loss function?
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