Bayesian inference computes the posterior probability according to Bayes' theorem: – the posterior probability of a hypothesis is proportional to its prior probability (its inherent likeliness) and the newly acquired likelihood (its compatibility with the new observed evidence). If the evidence does not match up with a hypothesis, one should reject the hypothesis.
But if a hypothesis is extremely unlikely a priori, one should also reject it, even if the evidence does appear to match up.
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An explicit link between Gaussian ﬁelds and Gaussian Markovrandom ﬁelds: The SPDE approach (with discussion).
In this way, you are comparing the results obtained from the same model.
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