摘要
本文主要讨论了变点的先验分布为beta-binomial分布和Ibrahim等(2003)提出的幂型先验的条件下,有一个变点的线性模型的贝叶斯统计推断问题,并且我们假定变点两边的观测值的方差是相等的.我们得到变点、回归系数、共同方差的后要分布的显示表达式.本论文不仅把Ferrira(1975)论文从变点先验分布服从离散均匀分布推广到了更好描述变点的形状的beta-binomial分布,而且进一步将变点的先验分布推广到包含的历史信息的幂型先验.当变点的先验分布为beta-binomial分布和幂型先验时,模拟结果显示了贝叶斯方法具有更高的准确性.
This article considers Bayesian inference of the linear regression model with one change point in observations, provided that the prior distribution of the change point is the beta-binomial distri- bution or the power prior introduced by Ibrahim et al. （2003） and the variances of the observations on two sides of the change point are the same. We get closed forms of the posterior distributions of the change point, the regression coefficients and the common variance. This not only generalizes the result of Ferreira （1975） from the the discrete uniform prior distribution of the change point t to the beta-binomial distribution which can well describe the shape of the change point distri- bution, but also can be further generalized to the power prior distribution of the change point, which included the historical information. Simulation shows higher performance or accuracy of the Bayesian method when the change point follows the beta-binomial and power prior.
出处
《应用概率统计》
CSCD
北大核心
2015年第1期89-102,共14页
Chinese Journal of Applied Probability and Statistics
基金
supported by Natural Science Foundation of China(11271136)
Program of Shanghai Subject Chief Scientist(14XD1401600)
the 111 Project(B14019)
