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On the Flatland Paradox

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Abstract:

We revisit the flatland paradox proposed by Stone (1976). We show that the choice of a flat prior is not adapted to the structure of the parameter space and that the impropriety of the prior is not directly involved in the paradox. We also propose an analysis of the paradox by using proper uniform priors and taking the limit on the hyper-parameter. Then, we construct an improper prior based on reference priors that take into account the structure of the parameter space and the partial knowledge of the random process that generates the parameter. For this prior, the paradox disappear and the Bayesian analysis matches the intuitive reasoning.

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