Review and Analysis of Some Inconsistencies Related to Improper Priors and Finite Additivity

Publisher Summary This chapter explains two paradoxes in nontechnical manner and discusses some reactions to them. Their analysis is emphasized in terms of the approximability of posteriors, from improper priors by those from proper priors for the relevant class of data, adopting the conventional view of infinity as an approximator of necessary finiteness. The chapter explains the connections between impropriety and finite additivity. The chapter discusses the Flatland example that is essentially a Bayesian version of a classical counterexample to invariant statistical procedures. An easily appreciated variant is provided by the inferential game. An unemployed nuclear physicist is asked to toss a regular tetrahedral die a number of times. The chapter also reviews that the finitely additive theory of de Finetti is the only theory without gaping holes.

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