Coherent Distributions and Lindley’s Paradox
A Bayesian test of the simple null hypothesis H0:θ=θ0 versus the composite alternative H1:θ≠θ0 is performed using finitely additive prior distributions in order to investigate the so-called Lindley’s paradox. In particular two priors for θ under H1 are considered. The first represents a coherently non-informative distribution which is shown to correctly yield the “paradox” because of the overall induced distribution of θ. The second, through the use of adherent masses to θ0, does instead avoid Lindley’s paradox.
KeywordsPosterior Distribution Loss Function Prior Distribution Exponential Family Posterior Odds
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