The Statistic of One

Prof. David Kipping (Columbia University)
Tuesday, April 27, 2021 - 11:00am

It’s often said that one data point teaches you nothing. In fact, zero data points teaches you nothing, and no magical transition happens from one to two data points. Yet clearly, one data point is the opposite regime to the data-driven enterprise typical of large surveys, where the data is so overwhelming it guides us quite clearly. In this talk, I’ll start by discussing how the Copernican/Mediocrity Principle attempts to exploit one data point with the example concerning the plurality of life, where it flatly fails due to selection bias (and the weak anthropic principle). However, this problem can be recast in terms of timings to make statistical progress, although naturally with a result featuring considerable uncertainty. I will then show how this approach can be extended to the longevity of civilisations. The statistics of one is particularly pertinent for “black swan” events in astronomy, one-offs that often inspire considerable theoretical/observational follow-up - such as Boyajian’s Star or Oumuamua. I’ll present a general Bayesian framework for interpreting such events and demonstrate why black swans require considerable patience to resolve their nature.

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