Spherical-radial integration rules for Bayesian computation

• 成果类型: Article
• 署名作者: Monahan, J; Genz, A
• 署名单位: Washington State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• 发表日期: 1997
• 页码: 664-674
• 关键词: monte-carlo integration; inference; approximations; models

摘要

The common numerical problem in Bayesian analysis is the numerical integration of the posterior. In high dimensions, this problem becomes too formidable for tired quadrature methods, and Monte Carlo integration is the usual approach. Through the use of modal standardization and a spherical-radial transformation, we reparameterize in terms of a radius r and point z on the surface of the sphere in d dimensions. We propose two types of methods for spherical-radial integration. A completely randomized method uses randomly placed abscissas for the radial integration and for the sphere surface. A mixed method uses fixed quadrature (i.e.,, Simpson's rule) on the radius and randomized spherical integration. The mixed methods show superior accuracy in comparisons, require little or no assumptions, and provide diagnostics to detect difficult problems. Moreover, if the posterior is close: to the multivariate normal, then the mixed methods can give remarkable accuracy.