# Bayesian estimate

Suppose theta is a parameter that takes values on the real line. Consider the loss function

l(theta, theta_hat) = 0 if |q-theta_hat|<=c, 1 otherwise

Show that the Bayes estimate of theta is the midpoint of the interval I of length 2c that maximizes P(theta in I|x).

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#### Solution Summary

This solutions shows that the Bayes estimate of theta is the midpoint of the interval I of length 2c that maximizes P(theta in I|x).

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