Comparison of classical and Bayesian estimates of Normal distribution parameters | Vose Software

# 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