An introduction to Bayesian inference in gravitational-wave astronomy: parameter estimation, model selection, and hierarchical models—Corrigendum
An introduction to Bayesian inference in gravitational-wave astronomy: parameter estimation, model selection, and hierarchical models—Corrigendum
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DOI：
10.1017/pasa.2020.23
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发表时间：
2020-09
影响因子：
6.3
通讯作者：
E. Thrane;C. Talbot
中科院分区：
文献类型：
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作者：
E. Thrane;C. Talbot
1.在本文的原始版本中，我们在附录E中包括了一个小节，“单一事件的选择效应”。本节包括有错误的公式，包括Eq. 89、Eq. 95的arxiv版本（方程。E2和Eq。在PASA中发布的版本中的E8）。此外，该节还包括一个概念错误，因为单一事件的选择效应的想法没有意义。选择效应与群体研究有着内在的联系，因此它们根本不影响单个检测的分析。考虑这是如何在数学上产生的是很有趣的。虽然单事件det似然获得了p-1 det的因子（正如在原始文章中正确指出的那样），但单事件det先验获得了pdet的补偿因子，因为检测到的事件的先验与原始（无det）先验不同。由于det后验概率与似然概率和先验概率的乘积成比例，这两个因素抵消，得到原始（无det）似然概率。附录修订本见下文。2.在八个地方，我们提到了“优势比”。然而，我们应该简单地提到“几率”。在统计学中，赔率是指概率的比率。当我们将贝叶斯因子乘以先验概率时，我们得到后验概率。比值比，也是一个统计学术语，指的是比率的比率。
1. In the original version of this article, we included a subsection in Appendix E, “Selection effects with a single event.” This section included formulas with errors including Eq. 89 and Eq. 95 of the arxiv version (Eq. E2 and Eq. E8 in the version published in PASA). Moreover, the section included a conceptual error since the idea of selection effects for single events does not make sense. Selection effects are intrinsically related to population studies, so they simply do not affect the analysis of single detections. It is interesting to consider how this comes about mathematically. While the single-event det likelihood gains a factor of p−1 det (as correctly noted in the original article), the single-event det prior picks up a compensating factor of pdet, because the prior for detected events is not the same as the original (no det) prior. Since the det posterior is proportional to the product of the likelihood and the prior, these two factors cancel, giving the original (no det) likelihood. A revised version of the appendix is presented below. 2. In eight places we referred to “the odds ratio.” However, we should have referred simply to “the odds.” In statistics, the odds refers to a ratio of probabilities. When we multiply the Bayes factor by the prior odds, we obtain the posterior odds. The odds ratio, which is also a statistical term, refers to a ratio of ratios.