Variational Bayes for estimating the parameters of a hidden Potts model
Variational Bayes for estimating the parameters of a hidden Potts model
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DOI：
10.1007/s11222-008-9095-6
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发表时间：
2009-09-01
影响因子：
2.2
通讯作者：
Pettitt, A. N.
中科院分区：
文献类型：
--
作者：
McGrory, C. A.;Titterington, D. M.;Pettitt, A. N.
隐马尔可夫随机场模型提供了一个有吸引力的图像和其他空间问题的表示。缺点是，这些模型的推理并不简单，因为除了非常小的观察集之外，可能性的归一化常数通常是难以处理的。变分方法是贝叶斯推理的一种新兴工具，它们已经成功地应用于其他环境中。聚焦于一个特殊的情况下，隐波茨模型与高斯噪声，我们展示了如何变分贝叶斯方法可以应用于隐马尔可夫随机场的推断。为了解决棘手的归一化常数的可能性的障碍，我们探索替代的估计方法纳入变分贝叶斯算法。我们考虑一个伪似然方法，以及最近减少依赖近似的归一化常数。为了说明这些方法的有效性，我们提出了模拟数据集的分析实证结果。我们还分析了一个真实的数据集，并将结果与以前的分析以及最近开发的辅助变量MCMC方法和递归MCMC方法的结果进行了比较。我们的研究结果表明，变分贝叶斯分析可以进行得更快，比MCMC分析，并产生良好的估计模型参数。我们还发现，在我们对真实的和合成数据集的分析中，归一化常数的降低依赖近似优于伪似然近似。
Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets.