Let us have observations zj, j = 1,2,..., M of the scalar parameter 0. The observations...

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Let us have observations zj, j = 1,2,..., M of the scalar parameter 0. The observations are corrupted by Gaussian noise v = RM, where the components v; are independent and indentically distrbuted with the parameters nvj 0 and 2 = for all j. Let us assume that the prior density f(0) is Gaussian with the parameters no and off. Moreover, the noise v and parameter 0 are assumed to be uncorrelated. = 2 (a) Specify the observation model and calculate the posterior density f(z) using the Bayes formula. (b) Prove that the MS-estimator MS is of the form MS M i=1zj + -no M+ M + What happens when M is large? Let us have observations zj, j = 1,2,..., M of the scalar parameter 0. The observations are corrupted by Gaussian noise v = RM, where the components v; are independent and indentically distrbuted with the parameters nvj 0 and 2 = for all j. Let us assume that the prior density f(0) is Gaussian with the parameters no and off. Moreover, the noise v and parameter 0 are assumed to be uncorrelated. = 2 (a) Specify the observation model and calculate the posterior density f(z) using the Bayes formula. (b) Prove that the MS-estimator MS is of the form MS M i=1zj + -no M+ M + What happens when M is large?