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In Example 7.3.1, prove that the posterior mean of ψ = σ/µ does not exist. Example 7.3.1…

In Example 7.3.1, prove that the posterior mean of ψ = σ/µ  does not exist.

Example 7.3.1

In many circumstances, it turns out that the posterior distribution of is approximatel normally distributed. We can then use this to compute approximate credible regions for the true value of  θ , carry out hypothesis assessment, etc. One such result  says that, under conditions that we will not describe here, where

In Example 7.3.1, prove that the posterior mean of ψ = σ/µ does not exist. Example 7.3.1...

Note that this result is similar to Theorem 6.5.3 for the MLE. Actually, we can replace In Example 7.3.1, prove that the posterior mean of ψ = σ/µ does not exist. Example 7.3.1... by the observed information (see Section 6.5), and the result still holds. When θ is k-dimensional, there is a similar but more complicated result.