Fully exponential Laplace approximations using asymptotic modes
成果类型：
Article
署名作者：
Miyata, Y
署名单位：
Waseda University
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/016214504000001673
发表日期：
2004
页码：
1037-1049
关键词：
摘要：
Posterior means of positive functions can be expressed as the ration integrals which is called fully exponential form. When approximating the posterior means analytically, we usually use Laplace's method. Tierney and Kadane presented a second-order approximation by using the Laplace approximations in each of the numerator and denominator of the fully exponential form. However, Laplace's method requires the exact mode of the integrand. In this article we introduce the concept of asymptotic modes and present the Laplace method via an asymptotic mode under regularity conditions. Furthermore, we propose second-order approximations to the posterior means of positive functions without evaluating the third derivatives of a log-likelihood function and the exact modes of integrands. We also give an Edgeworth-like expansion for the random variable according to a poster or distribution using the Laplace method via an asymptotic mode.