Suppose that X1, , Xn form a random sample from a Poisson distribution for which the value of the mean is unknown, and that the prior distribution of is a certain specified gamma distribution Is the Bayes estimator of with respect to the squared error loss function a minimal sufficient statistic

Question: Suppose that X1, . . . , Xn form a random sample from a Poisson distribution for which the value of the mean is

Suppose that X1, . . . , Xn form a random sample from a Poisson for which the value of the mean λ is unknown, and that the prior of λ is a certain specified gamma Is the Bayes estimator of λ with respect to the squared error loss function a minimal sufficient statistic?

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