Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses
Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses
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DOI：
10.1111/j.1365-2966.2007.12353.x
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发表时间：
2008-02-21
影响因子：
4.8
通讯作者：
Hobson, M. P.
中科院分区：
文献类型：
--
作者：
Feroz, F.;Hobson, M. P.
在对天文数据进行贝叶斯分析时，经常会出现两个难题。首先，在估计某些数据模型的参数时，得到的后验分布可能是多模态的或表现出明显的（曲线）退化，这可能会给传统的马尔可夫链蒙特卡罗（MCMC）抽样方法带来问题。其次，在一组相互竞争的模型之间进行选择时，使用现有的方法（如热力学积分）计算每个模型的贝叶斯证据的计算成本很高。Skilling引入的嵌套抽样方法大大减少了计算证据的计算费用，同时也产生了后验推理。这种方法已经被Mukherjee、Parkinson和Liddle成功地应用于宇宙学应用中，但他们的实现只对没有明显简并的单峰分布有效。Shaw， Bridges & Hobson最近引入了一种聚类嵌套采样方法，该方法在从多模态后验中采样时效率显著提高，并且还确定了单次运行算法的最终证据的期望和方差，从而进一步提高了效率。在本文中，我们以Shaw等人的工作为基础，提出了三种新的方法，用于从可能包含多个模式和非常高维的显著退化的分布中进行抽样和证据评估；我们还提出了一种更有效的技术来估计评估证据的不确定性。这些方法进一步提高了采样效率和鲁棒性，并应用于两个toy问题，以证明证据计算和参数估计的准确性和经济性。最后，我们讨论了这些方法在天文数据集中执行贝叶斯目标检测中的应用，并表明它们明显优于现有的MCMC技术。我们的方法的实现将很快公开发布。
In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to two toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical data sets, and show that they significantly outperform existing MCMC techniques. An implementation of our methods will be publicly released shortly.