Han Zifei, De Oliveira Victor
Vertex Pharmaceuticals, Boston MA 02210, USA,
Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA,
Commun Stat Simul Comput. 2020;49(8):1957-1981. doi: 10.1080/03610918.2018.1508705. Epub 2019 Jan 12.
This work investigates the computation of maximum likelihood estimators in Gaussian copula models for geostatistical count data. This is a computationally challenging task because the likelihood function is only expressible as a high dimensional multivariate normal integral. Two previously proposed Monte Carlo methods are reviewed, the Genz-Bretz and Geweke-Hajivassiliou-Keane simulators, and a new method is investigated. The new method is based on the so-called algorithm, which uses Markov chain Monte Carlo algorithms to approximate maximum likelihood estimators and their (asymptotic) variances in models with computationally challenging likelihoods. A simulation study is carried out to compare the statistical and computational efficiencies of the three methods. It is found that the three methods have similar statistical properties, but the Geweke-Hajivassiliou-Keane simulator requires the least computational effort. Hence, this is the method we recommend. A data analysis of Lansing Woods tree counts is used to illustrate the methods.
本文研究了用于地质统计计数数据的高斯Copula模型中最大似然估计量的计算。这是一项计算上具有挑战性的任务，因为似然函数只能表示为高维多元正态积分。回顾了两种先前提出的蒙特卡罗方法，即Genz-Bretz模拟器和Geweke-Hajivassiliou-Keane模拟器，并研究了一种新方法。新方法基于所谓的算法，该算法使用马尔可夫链蒙特卡罗算法来近似具有计算挑战性的似然模型中的最大似然估计量及其（渐近）方差。进行了一项模拟研究，以比较这三种方法的统计和计算效率。结果发现，这三种方法具有相似的统计性质，但Geweke-Hajivassiliou-Keane模拟器所需的计算量最少。因此，这是我们推荐的方法。通过对兰辛森林树木计数的数据分析来说明这些方法。
