Applied Bayesian Statistics by Mary Kathryn Cowles

Author:Mary Kathryn Cowles
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Indeed, the normal-inverse gamma prior density was conjugate for the normal likelihood, since the resulting posterior density is in the same family as the prior.

Recall that the parameters of the inverse gamma density can be thought of as and . With that reparameterization, the joint posterior density becomes

(7.13)

It is clear that n 0 is the equivalent prior sample size with respect to the variance, and κ is the equivalent prior sample size with respect to the mean μ.

By an integration process analogous to that in (7.6), we can find that the posterior marginal density p(μ | { y}) is a t density with: mean

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