Geometric properties of noninformative priors based on the chi-square divergence

Abstract

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Recently, a noninformative prior distribution that is different from the Jeffreys prior was derived as an extension of Bernardo's reference prior based on the chi-square divergence. We summarize this result in terms of information geometry and clarify some geometric properties. Specifically, we show that it corresponds to a parallel volume element and can be written as a power of the Jeffreys prior in flat model manifolds.

Keywords

• noninformative prior
• Jeffreys prior
• reference prior
• alpha-parallel prior
• objective prior
• chi-square divergence