Miscellanea A note on the accuracy of adaptive Gauss-Hermite quadrature

• 成果类型: Article
• 署名作者: Jin, Shaobo; Andersson, Bjorn
• 署名单位: Uppsala University; University of Oslo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz080
• 发表日期: 2020
• 页码: 737744
• 关键词: laplace approximation; models

摘要

Numerical quadrature methods are needed for many models in order to approximate integrals in the likelihood function. In this note, we correct the error rate given by Liu & Pierce (1994) for integrals approximated with adaptive Gauss-Hermite quadrature and show that the approximation is less accurate than previously thought. We discuss the relationship between the error rates of adaptive Gauss-Hermite quadrature and Laplace approximation, and provide a theoretical explanation of simulation results obtained in previous studies regarding the accuracy of adaptive Gauss-Hermite quadrature.