计算引力波模型证据的垫脚石抽样算法
The stepping-stone sampling algorithm for calculating the evidence of gravitational wave models
摘要：
贝叶斯统计推断对于分析Advanced LIGO和Advanced Virgo引力波探测器的观测结果变得越来越重要。为此，迭代模拟技术，特别是嵌套采样和并行回火，已在软件库LALInference中实现，以从紧凑型二元聚结事件的波形参数的后验分布中采样。嵌套抽样主要用于计算模型的边际似然，但也会产生后验样本。采用热力学积分计算的证据，使用平行回火产生的样品，但已被发现是计算要求。在这里，我们提出了垫脚石采样算法，最初由Xie et al.（2011）在遗传学和路径采样的特殊情况下提出，作为热力学积分的替代方案。垫脚石采样算法也是基于来自并行回火的功率后验的样本，但具有更好的性能，因为温度步长更少，因此需要计算资源来实现相同的精度。我们证明了它的性能和计算成本相比，热力学集成和嵌套采样的模拟研究和计算的边缘可能性的二元黑洞信号模型应用于模拟数据的高级LIGO和高级处女座引力波探测器的案例研究。为了解决目前基于幂后验技术估计证据估计标准误的方法不足的问题，我们提出了一种新的块引导方法，并在我们的模拟研究和LIGO应用中显示了其潜力。
英文摘要：
Bayesian statistical inference has become increasingly important for the analysis of observations from the Advanced LIGO and Advanced Virgo gravitational-wave detectors. To this end, iterative simulation techniques, in particular nested sampling and parallel tempering, have been implemented in the software library LALInference to sample from the posterior distribution of waveform parameters of compact binary coalescence events. Nested sampling was mainly developed to calculate the marginal likelihood of a model but can produce posterior samples as a by-product. Thermodynamic integration is employed to calculate the evidence using samples generated by parallel tempering but has been found to be computationally demanding. Here we propose the stepping-stone sampling algorithm, originally proposed by Xie et al. (2011) in phylogenetics and a special case of path sampling, as an alternative to thermodynamic integration. The stepping-stone sampling algorithm is also based on samples from the power posteriors of parallel tempering but has superior performance as fewer temperature steps and thus computational resources are needed to achieve the same accuracy. We demonstrate its performance and computational costs in comparison to thermodynamic integration and nested sampling in a simulation study and a case study of computing the marginal likelihood of a binary black hole signal model applied to simulated data from the Advanced LIGO and Advanced Virgo gravitational wave detectors. To deal with the inadequate methods currently employed to estimate the standard errors of evidence estimates based on power posterior techniques, we propose a novel block bootstrap approach and show its potential in our simulation study and LIGO application.
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