首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Quasi Bayesian likelihood
Authors:Lu Lin  
Institution:

aSchool of Mathematics and System Sciences, Shandong University, Jinan, Shandong Province, 250100, PR China

Abstract:If the form of the distribution of data is unknown, the Bayesian method fails in the parametric inference because there is no posterior distribution of the parameter. In this paper, a theoretical framework of Bayesian likelihood is introduced via the Hilbert space method, which is free of the distributions of data and the parameter. The posterior distribution and posterior score function based on given inner products are defined and, consequently, the quasi posterior distribution and quasi posterior score function are derived, respectively, as the projections of the posterior distribution and posterior score function onto the space spanned by given estimating functions. In the space spanned by data, particularly, an explicit representation for the quasi posterior score function is obtained, which can be derived as a projection of the true posterior score function onto this space. The methods of constructing conservative quasi posterior score and quasi posterior log-likelihood are proposed. Some examples are given to illustrate the theoretical results. As an application, the quasi posterior distribution functions are used to select variables for generalized linear models. It is proved that, for linear models, the variable selections via quasi posterior distribution functions are equivalent to the variable selections via the penalized residual sum of squares or regression sum of squares.
Keywords:Quasi Bayesian likelihood  Quasi posterior distribution  Quasi posterior score function  Variable selection
本文献已被 ScienceDirect 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号