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后验密度形式 Edgeworth 展开的有效性AI 解读

We consider a fundamental open problem in parametric Bayesian theory, namely the validity of the formal Edgeworth expansion of the posterior density. While the study of valid asymptotic expansions for posterior distributions constitutes a rich literature, the validity of the formal Edgeworth expansion has not been rigorously established. Several authors have claimed connections of various posterior expansions with the classical Edgeworth expansion, or have simply assumed its…

多元尾概率的鞍点近似AI 解读

This paper presents a saddlepoint approximation to the cumulative distribution function of a random vector. The proposed approximation has accuracy comparable to that of existing expansions valid in two dimensions, and may be applied to random vectors of arbitrary length, subject only to the requirement that the distribution approximated either have a density or be confined to a lattice, and have a cumulant generating function. The result is derived by directly inverting the…

广义线性模型条件分布的 Gibbs 抽样收敛性与精度AI 解读

This paper presents convergence conditions for a Markov chain constructed using Gibbs sampling, when the equilibrium distribution is the conditional sampling distribution of sufficient statistics from a generalized linear model. For cases when this unidimensional sampling is done approximately rather than exactly, the difference between the target equilibrium distribution and the resulting equilibrium distribution is expressed in terms of the difference between the true and…

条件分布函数的高阶近似AI 解读

This paper derives higher-order terms in the double-saddlepoint expansion of Skovgaard for a unidimensional conditional cumulative distribution function. Expansions for continuous and lattice random variables are derived. Results are applied to the sufficient statistic in logistic regression.

利用 Gibbs 抽样进行指数族近似条件推断AI 解读

This article presents the Gibbs-Skovgaard algorithm for approximate frequentist inference. The method makes use of the double saddlepoint approximation of Skovgaard to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics. This approximation is then used in the Gibbs sampler to generate a Markov chain. The equilibrium distribution of this chain approximates the joint distribution of the sufficient statistics…

格点分布的 Edgeworth 展开AI 解读

This paper investigates the use of Edgeworth expansions for approximating the distribution function of the normalized sum of $n$ independent and identically distributed lattice-valued random variables. We prove that the continuity-corrected Edgeworth series, using Sheppard-adjusted cumulants, is accurate to the same order in $n$ as the usual Edgeworth approximation for continuous random variables. Finally, as a partial justification of the Sheppard adjustments, it is shown…