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自然参数的广义贝叶斯估计量刻画AI 解读

Let X be a real-valued random variable with a family of possible densities (with respect to σ-finite μ) belonging to a one-parameter exponential family with the natural parameter θ ∈ Ω = natural parameter space. Let C(μ) = convex hull of the support of μ. Fix x 0> in the interior of C(μ), then δ is generalized Bayes for θ (with squared error loss) if and only if g(t) = exp { f 0 t δ(y + x 0)dy} (< ∞ for t + x 0 ∈ C(μ)) is a moment-generating function for a probability…

自然参数的广义贝叶斯估计量刻画AI 解读

Let X be a real-valued random variable with a family of possible densities (with respect to σ-finite μ) belonging to a one-parameter exponential family with the natural parameter θ ∈ Ω = natural parameter space. Let C(μ) = convex hull of the support of μ. Fix x 0> in the interior of C(μ), then δ is generalized Bayes for θ (with squared error loss) if and only if g(t) = exp { f 0 t δ(y + x 0)dy} (< ∞ for t + x 0 ∈ C(μ)) is a moment-generating function for a probability…