用射电双星检验广义相对论
On tests of general relativity with binary radio pulsars
摘要：
双星系统中射电望远镜的计时为广义相对论提供了一个极好的试验场。在这里，我们提出了一种贝叶斯方法来进行这些测试，以及相关的有效数值实现，相对于迄今为止使用的基于最小二乘拟合的传统方法，该方法具有几个概念和实际优势：（i）它说明了似然函数的实际结构-而且它不是以拉普拉斯近似为基础的，拉普拉斯近似隐含地建立在最小-平方拟合可能会使推断产生偏差-（ii）它提供了所考虑的任何两个模型的证据的比率作为统计量来比较不同的理论，以及（iii）它允许我们从多个系统的监测中提出联合约束，这可以用证据的比率或理论的全局（因此不依赖于系统）参数的概率区间来表示，如果存在的话。我们提出的方法最佳地利用了无线电信标的定时和观测系统数量的增加。我们展示了这个框架的力量，使用模拟的数据集，是目前的观察代表。
英文摘要：
The timing of radio pulsars in binary systems provides a superb testing ground of general relativity. Here we propose a Bayesian approach to carry out these tests, and a relevant efficient numerical implementation, that has several conceptual and practical advantages with respect to traditional methods based on least-square-fits that have been used so far: (i) it accounts for the actual structure of the likelihood function - and it is not predicated on the Laplace approximation which is implicitly built in least-square fits that can potentially bias the inference - (ii) it provides the ratio of the evidences of any two models under consideration as the statistical quantity to compare different theories, and (iii) it allows us to put joint constraints from the monitoring of multiple systems, that can be expressed in terms of ratio of evidences or probability intervals of global (thus not system-dependent) parameters of the theory, if any exists. Our proposed approach optimally exploits the progress in timing of radio pulsars and the increase in the number of observed systems. We demonstrate the power of this framework using simulated data sets that are representative of current observations.
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