Black Swans in Astronomical Data

Abstract

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, $\lambda$. Specifically, expressions are derived for 1) the a-posteriori distribution for $\lambda$, 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) $\lambda <\{0.7,2.3,4.6\}{t}_1^{-1}$ 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 $\lesssim 10t_1$ 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.

Accepted to MNRAS

References in corpus (9)

• The Gaia mission
• The Transiting Exoplanet Survey Satellite
• A bright millisecond radio burst of extragalactic origin
• Implications for planetary system formation from interstellar object 1I/2017 U1 (`Oumuamua)
• Systematic Serendipity: A Test of Unsupervised Machine Learning as a Method for Anomaly Detection
• A Machine Learning Classifier for Fast Radio Burst Detection at the VLBA
• The Weird Detector: Flagging periodic, coherent signals of arbitrary shape in time series photometry
• Serendipity in Astronomy
• Anomaly Detection in Astronomical Images with Generative Adversarial Networks

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