Statistics | Part IB, 2002

Explain what is meant by a prior distribution, a posterior distribution, and a Bayes estimator. Relate the Bayes estimator to the posterior distribution for both quadratic and absolute error loss functions.

Suppose X1,,XnX_{1}, \ldots, X_{n} are independent identically distributed random variables from a distribution uniform on (θ1,θ+1)(\theta-1, \theta+1), and that the prior for θ\theta is uniform on (20,50)(20,50).

Calculate the posterior distribution for θ\theta, given x=(x1,,xn)\mathbf{x}=\left(x_{1}, \ldots, x_{n}\right), and find the point estimate for θ\theta under both quadratic and absolute error loss function.

Typos? Please submit corrections to this page on GitHub.