Question

Bayesian Estimation and Confidence Regions: Concept Questions Σχ.-12 Consider the scenario where we observe n 10 random variable with sum AMAP M. Bayes Compare the values of the Bayes' estimator A0.833 and the maximum a-poster estimator -0.75 calculated earlier. Which of the following statements correctly describes the relative values and provides an accurate justification for it? (a) because this inequality will always hold regardless of the prior or model choice 1 ABaves AMAP (b) A< 1 because this inequality will always hold regardless of the prior or model choice λ>λ because of posterior distribution is skewed to the left (cl A Baes MAP X < 1 because of posterior distribution is skewed to the left (e) 1 > A because the posterior distribution is skewed to the right ABaves AMAP λ λ < because the posterior distribution is skewed to the right

Answer 1

(e) is the correct answer. Bayes estimator is the posterior mean and MAP estimator is the posterior mode.

Since Mean>Mode for the given data, posterior distribution is expected to be skewed to the right.