arXiv 1402.17632014-02-07astro-ph.COphysics.data-an

宇宙学中的无矩阵大规模贝叶斯推断

Matrix-free Large Scale Bayesian inference in cosmology

Jens Jasche, Guilhem Lavaux

备注：: 9 pages, 2 figures, submitted to MNRAS
DOI：: 10.1093/mnras/stu2479

摘要：

在这项工作中，我们提出了一个新的矩阵的维纳采样器，传统上适用于高维分析时，信号协方差是未知的实现。具体而言，所提出的方法解决了联合推断高维信号及其相应的协方差矩阵从一组观察的问题。我们的方法实现了吉布斯采样适应先前提出的信使的方法，允许铸造复杂的多变量推理问题到一个序列的单变量随机过程。以这种方式，传统的要求，反高维矩阵是完全消除了推理过程中，导致在一个有效的算法，是微不足道的实现。使用宇宙大尺度结构数据作为展示，我们展示了我们的吉布斯抽样方法的能力，通过执行一个联合分析的三维密度场和相应的功率谱从高斯模拟目录。这些测试清楚地证明了该算法能够准确地提供三维密度场及其功率谱的测量以及相应的不确定性量化。此外，这些测试显示出良好的数值和统计效率，这将使所提出的算法在宇宙学和天体物理学的大规模贝叶斯推断的工具箱中的一个有价值的补充。

英文摘要：

In this work we propose a new matrix-free implementation of the Wiener sampler which is traditionally applied to high dimensional analysis when signal covariances are unknown. Specifically, the proposed method addresses the problem of jointly inferring a high dimensional signal and its corresponding covariance matrix from a set of observations. Our method implements a Gibbs sampling adaptation of the previously presented messenger approach, permitting to cast the complex multivariate inference problem into a sequence of uni-variate random processes. In this fashion, the traditional requirement of inverting high dimensional matrices is completely eliminated from the inference process, resulting in an efficient algorithm that is trivial to implement. Using cosmic large scale structure data as a showcase, we demonstrate the capabilities of our Gibbs sampling approach by performing a joint analysis of three dimensional density fields and corresponding power-spectra from Gaussian mock catalogues. These tests clearly demonstrate the ability of the algorithm to accurately provide measurements of the three dimensional density field and its power-spectrum and corresponding uncertainty quantification. Moreover, these tests reveal excellent numerical and statistical efficiency which will generally render the proposed algorithm a valuable addition to the toolbox of large scale Bayesian inference in cosmology and astrophysics.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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