天文数据中的黑天鹅
Black Swans in Astronomical Data
摘要：
天文学总是被发现缺乏先例的新现象所推动，通常是新的理论来解释它们的存在和性质。在以更高的精度和采样率对天空进行大规模调查的现代，这些偶然发现似乎将继续下去，最近的例子包括Boyajian星，快速射电暴和'Oumuamua。因此，我们在这里展望未来，旨在提供一个统计框架来解释这些事件，并为未来的观测提供指导，其基本前提是所讨论的现象随机重复以某种未知的恒定速率，$λ$。具体地说，表达式推导出1）的后验分布的$λ$，2）的后验分布的复发时间，和，3）的收益-成本比的进一步观察相对于首个事件。发现这些中的每一个的一些经验法则结果为1）$λ< \{0.7, 2.3, 4.6\}\,t_1^{-1}$到$\{50, 90, 95\}\%$置信度（其中获得第一次检测的$t_1=$时间），2）复发时间是$t_2 < \{1, 9, 99\}\,t_1$至$\{50, 90, 95\}\%$置信度，其中缺少时间$t_2$的重复产生$p$ -值$1/[1+(t_2/t_1)]$，以及，3）在关于该物体内在科学价值的一系列不同假设下，对$\lesssim 10\,t_1$的后续研究预计在科学上是有价值的。我们将这些方法应用于突破听候选1号信号和潮汐中断事件观测TESS。
英文摘要：
Astronomy has always been propelled by the discovery of new phenomena lacking precedent, often followed by new theories to explain their existence and properties. In the modern era of large surveys tiling the sky at ever high precision and sampling rates, these serendipitous discoveries look set to continue, with recent examples including Boyajian's Star, Fast Radio Bursts and `Oumuamua. Accordingly, we here look ahead and aim to provide a statistical framework for interpreting such events and providing guidance to future observations, under the basic premise that the phenomenon in question stochastically repeat at some unknown, constant rate, $λ$. Specifically, expressions are derived for 1) the a-posteriori distribution for $λ$, 2) the a-posteriori distribution for the recurrence time, and, 3) the benefit-to-cost ratio of further observations relative to that of the inaugural event. Some rule-of-thumb results for each of these are found to be 1) $λ< \{0.7, 2.3, 4.6\}\,t_1^{-1}$ to $\{50, 90, 95\}\%$ confidence (where $t_1=$ time to obtain the first detection), 2) the recurrence time is $t_2 < \{1, 9, 99\}\,t_1$ to $\{50, 90, 95\}\%$ confidence, with a lack of repetition by time $t_2$ yielding a $p$-value of $1/[1+(t_2/t_1)]$, and, 3) follow-up for $\lesssim 10\,t_1$ is expected to be scientifically worthwhile under an array of differing assumptions about the object's intrinsic scientific value. We apply these methods to the Breakthrough Listen Candidate 1 signal and tidal disruption events observed by TESS.
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