statistics - For the multivariate normal model, why is jeffreys' prior distribution not a probability density? -


for multivariate normal model, jeffreys' rule generating prior distribution on (theta, sigma) gives p_j(theta, sigma) proportional |sigma|^{-(p+2)/2}.

my book notes in footnote p_j cannot probability density theta, sigma. why this?

it's "improper", meaning doesn't integrate 1 probability distributions have do. example, marginal density respect theta constant, integral on real line infinite. it's ok use improper distributions priors in bayesian inference, long posterior proper probability distribution.


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