Approximate Conditional Inference in Exponential Families Via the Gibbs Sampler
本文提出Gibbs-Skovgaard算法，利用双鞍点近似和吉布斯采样器生成马尔可夫链，近似充分统计量的条件分布，适用于逻辑回归和泊松回归的推断。
Abstract 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 associated with the parameters of interest conditional on the observed values of the sufficient statistics associated with the nuisance parameters. This Gibbs-Skovgaard algorithm is applied to the cases of logistic and Poisson regression.