Higher Order Expansions for Posterior Distributions Using Posterior Modes

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  • Miyata Yoichi
    Faculty of Economics, Takasaki City University of Economics, 1300 Kaminamie, Takasaki, Gunma 370-0801, Japan. Email: ymiyatagbt@tcue.ac.jp

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The (arbitrary) higher order asymptotic expansion for posterior distributions of a single parameter is derived by using posterior modes, and its validity is shown. An asymptotic expansion for the Bayes risk with squared error loss of a posterior mode is derived.

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