Estimation of Binary Markov Random Fields Using Markov chain Monte Carlo
Estimation of Binary Markov Random Fields Using Markov chain Monte Carlo
复制标题
使用马尔可夫链蒙特卡罗估计二元马尔可夫随机场
DOI：
10.1198/106186006x97817
复制
发表时间：
2006
影响因子：
2.4
通讯作者：
M. Smith
中科院分区：
文献类型：
--
作者：
Daniel Smith;M. Smith
本文比较了三个二进制马尔可夫随机场（MRF），这是流行的贝叶斯先验空间平滑。这些是基于潜在高斯MRF的Ising先验和两个先验。关注的是选择一个合适的马尔可夫链蒙特卡罗（MCMC）抽样方案为每个先验。三个先验和抽样方案的属性进行了研究的背景下，三个经验的例子。第一个是模拟数据集，第二个涉及共聚焦荧光显微镜数据集，而第三个是基于功能性磁共振成像（fMRI）数据的分析。在伊辛先验的情况下，单站点和多站点Swendsen-Wang抽样计划都被认为是。单站点计划的工作一贯良好，而它表明，Swendsen-Wang算法可以有收敛问题。先验的采样方案被扩展以生成平滑参数，使得估计变得完全自动。虽然这很好地工作，它被发现，对于高度连续的图像固定平滑参数非常高的值可以通过注入额外的先验信息，有关的图像中的邻接水平，以改善结果。研究了三个二进制MRF的相对属性，并展示了Ising先验如何特别定义锐边并促进聚类。此外，潜在的高斯MRF先验之一是无法区分更高水平的平滑。在功能磁共振成像的例子，我们也进行了模拟研究。
This article compares three binary Markov random fields (MRFs) which are popular Bayesian priors for spatial smoothing. These are the Ising prior and two priors based on latent Gaussian MRFs. Concern is given to the selection of a suitable Markov chain Monte Carlo (MCMC) sampling scheme for each prior. The properties of the three priors and sampling schemes are investigated in the context of three empirical examples. The first is a simulated dataset, the second involves a confocal fluorescence microscopy dataset, while the third is based on the analysis of functional magnetic resonance imaging (fMRI) data. In the case of the Ising prior, single site and multi-site Swendsen-Wang sampling schemes are both considered. The single site scheme is shown to work consistently well, while it is shown that the Swendsen-Wang algorithm can have convergence problems. The sampling schemes for the priors are extended to generate the smoothing parameters, so that estimation becomes fully automatic. Although this works well, it is found that for highly contiguous images fixing smoothing parameters to very high values can improve results by injecting additional prior information concerning the level of contiguity in the image. The relative properties of the three binary MRFs are investigated, and it is shown how the Ising prior in particular defines sharp edges and encourages clustering. In addition, one of the latent Gaussian MRF priors is shown to be unable to distinguish between higher levels of smoothing. In the context of the fMRI example we also undertake a simulation study.