Assume Y,..., Y02 id Normal(0, ) and ~ InvGamma(a, b). (a) Give an expression for...

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Assume Y₁,..., Y₁02 id Normal(0, ²) and ² ~ InvGamma(a, b). (a) Give an expression for two estimators of o²: the posterior mean and the posterior mode. (b) Plot the posterior density functions and the give the two es timators for a sample with n = 10 and ² = 200 and a = b = 0.001. (c) Argue that both estimators are consistent (i.e., their MSE goes to zero as n increases) for any a and b. Assume Y₁,..., Y₁02 id Normal(0, ²) and ² ~ InvGamma(a, b). (a) Give an expression for two estimators of o²: the posterior mean and the posterior mode. (b) Plot the posterior density functions and the give the two es timators for a sample with n = 10 and ² = 200 and a = b = 0.001. (c) Argue that both estimators are consistent (i.e., their MSE goes to zero as n increases) for any a and b.

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a The posterior distribution of 2 is Inverse Gammaan2 bYi22 The po... View the full answer