| 基于Gibbs抽样法的边际密度估计 |
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| 引用本文： | 林秀光,程杞元.基于Gibbs抽样法的边际密度估计[J].北京理工大学学报,2002,22(1):16-19. |
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| 作者姓名： | 林秀光 程杞元 |
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| 作者单位： | 北京理工大学,应用数学系,北京,100081 |
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| 摘 要： | 证明利用Gibbs抽样法从后验分布p(*|y)产生的Markov链转移核有不变概率测度p(*|y).利用Gibbs抽样法、Monte Carlo积分和条件概率公式相结合的方法对多元分布的边际密度进行了估计,并且证明了在一定条件下所得的边际密度估计几乎处处收敛到真实的边际密度.最后用两个实例对该结论进行说明.
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| 关 键 词： | Gibbs抽样 正条件 Monte Carlo积分 |
| 文章编号： | 1001-0645(2002)01-0016-04 |
| 收稿时间： | 2001/6/11 0:00:00 |
| 修稿时间： | 2001年6月11日 |
Gibbs Sampling-Based Approaches in Estimating Marginal Densities |
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| LIN Xiu guang and CHENG Qi yuan.Gibbs Sampling-Based Approaches in Estimating Marginal Densities[J].Journal of Beijing Institute of Technology(Natural Science Edition),2002,22(1):16-19. |
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| Authors: | LIN Xiu guang and CHENG Qi yuan |
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| Institution: | Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing100081, China;Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing100081, China |
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| Abstract: | A proof was given that a Markov transition kernal from posterior distribution p(·|y) by Gibbs sampling has an invariant distribution p(·|y) . To estimate the marginal densities of multidimensional distribution, Gibbs sampler in conjunction with Monte Carlo inte gration and conditional probability formula was used. Under some conditions, the estimated marginal densities almost converge to the true marginal densities everywhere. Two examples were given to illustrate this result. |
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| Keywords: | Gibbs sampler positivity condition Monte Carlo integration |
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