Comparison of classical and Bayesian estimates of Normal distribution parameters


The following topics compare the derivation and results from classical and Bayesian approaches to estimating the parameters of a Normal distribution.

Estimates of the mean of a Normal distribution when the standard deviation is known

The classical statistics estimate and the Bayesian estimate with a Uniform(uninformed) prior produce exactly the same estimate, namely:

                

Estimates of the mean of a Normal distribution when the standard deviation is unknown

The classical statistics estimate and the Bayesian estimate with a Uniform(uninformed) prior produce exactly the same estimate, namely:

                

Estimates of the standard deviation of a Normal distribution when the mean is unknown

The result is exactly the same as the classical statistics estimate with a 1/s uninformed prior, namely:

                

Proof of Bayesian result

Estimates of the standard deviation of a Normal distribution when the mean is known

The result is exactly the same as the classical statistics estimate with a 1/s uninformed prior, namely:

                

Proof of Bayesian result

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