论文标题
比较贝叶斯因子和分层推断，用于测试与重力波的一般相对性
Comparing Bayes factors and hierarchical inference for testing general relativity with gravitational waves
论文作者
论文摘要
在用引力波测试一般相对性的背景下，通常通过分层形式主义或组合乘法贝叶斯因子将多个事件获得的约束结合在一起。我们表明，贝叶斯因素对参数空间区域中分析先验的众所周知的依赖性而无需可能支持，这可能会导致强烈的信心，而当人们采用多重贝叶斯因子时，有利于不正确的结论。贝叶斯因素$ \ Mathcal {o}（1）$是矛盾的，因为它们敏感地依赖于分析先验，这些分析很少以有原则的方式设置；此外，合并的贝叶斯因子$> \ MATHCAL {O}（10^3）$可以根据分析先验而获得不正确的结论，而当许多$ \ Mathcal {o}（1）$ bayes因子被乘坐时，当先生的范围比基础人群较宽时，可以获得不正确的结论。层次分析是渗透到个人超越派利率约束的集合分布并不遭受此问题的损失，并且一般会收敛以有利于正确的结论。可以从分层分析中计算出更可靠的贝叶斯因子，而不是幼稚的乘法。我们提供了许多玩具模型，表明乘以贝叶斯因素的实践可能导致结论不正确。
In the context of testing general relativity with gravitational waves, constraints obtained with multiple events are typically combined either through a hierarchical formalism or though a combined multiplicative Bayes factor. We show that the well-known dependence of Bayes factors on the analysis priors in regions of the parameter space without likelihood support can lead to strong confidence in favor of incorrect conclusions when one employs the multiplicative Bayes factor. Bayes factors $\mathcal{O}(1)$ are ambivalent as they depend sensitively on the analysis priors, which are rarely set in a principled way; additionally, combined Bayes factors $>\mathcal{O}(10^3)$ can be obtained in favor of the incorrect conclusion depending on the analysis priors when many $\mathcal{O}(1)$ Bayes factors are multiplied, and specifically when the priors are much wider than the underlying population. The hierarchical analysis that instead infers the ensemble distribution of the individual beyond-general-relativity constraints does not suffer from this problem, and generically converges to favor the correct conclusion. Rather than a naive multiplication, a more reliable Bayes factor can be computed from the hierarchical analysis. We present a number of toy models showing that the practice of multiplying Bayes Factors can lead to incorrect conclusions.
