James Berger, Victor De Oliveira and Bruno Sanso
We first show that common choices of default prior distributions, such as the constant prior and the independent Jeffreys prior, typically result in improper posterior distributions for this model. Next, the reference prior for the model is developed, and is shown to yield a proper posterior distribution. A further attractive property of the reference prior is that it can be used directly for computation of Bayes factors or posterior probabilities of hypotheses to compare different correlation functions, even though the reference prior is improper. An illustration is given using a spatial data set of topographic elevations.
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