Suppose that the results of a certain test are known, on the basis of general theory, to be normally distributed about the same mean with the same variance , neither of which is known Suppose further that your prior beliefs about (,) can be represented by a normal chi squared distribution with Now ...

To find the posterior distribution of given the prior distribution and the observed data we can appl ...

Suppose that the results of a certain test are known, on the basis of general theory, to

Question:

Suppose that the results of a certain test are known, on the basis of general theory, to be normally distributed about the same mean μ with the same variance ϕ, neither of which is known. Suppose further that your prior beliefs about (μ,ϕ) can be represented by a normal/chi-squared distribution with

10 = 4, So = 350, no = 1 and 00 85. -

Now suppose that 100 observations are obtained from the population with mean 89 and sample variance s² = 30. Find the posterior distribution of (μ,ϕ). Compare 50% prior and posterior HDRs for μ.

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