Another Look at the Salamander Mating Data: A Modified Laplace Approximation Approach
本文针对McCullagh和Nelder的蝾螈交配数据集，采用修正的拉普拉斯近似方法重新分析，重点研究得分函数的渐近阶和计算，解决了标准方法因积分维数等于样本量平方根而失效的问题。
Abstract The salamander mating dataset of McCullagh and Nelder has drawn the attention of statisticians because of its challenging structure: the design is crossed rather than nested. The standard Laplace approximation used to evaluate marginal likelihood functions fails in this case because the dimension of the integral is the square root of the sample size. A modification has been proposed by Shun and McCullagh. This article reanalyzes the salamander data using this modified Laplace approximation and focuses on the asymptotic order and computation of the score function.