AUTHOR=Tanaka Fuyuhiko TITLE=Geometric properties of noninformative priors based on the chi-square divergence JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=9 YEAR=2023 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2023.1141976 DOI=10.3389/fams.2023.1141976 ISSN=2297-4687 ABSTRACT=

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.