Bayesian approach to SETI

Significance Ongoing and future initiatives in the search for extraterrestrial intelligence (SETI) will explore the Galaxy on an unprecedented scale to find evidence of communicating civilizations beyond Earth. Here, we construct a Bayesian formulation of SETI to infer the posterior probability of the mean number of radio signals crossing Earth, given a positive or a null outcome of all-sky searches for nonnatural radio emissions. We show that not detecting signals within ∼40 kly from Earth is compatible with the absence in the entire Galaxy of detectable emitters of a wide range of radiated power. The discovery of even a single emission within ∼1 kly implies instead that over 100 signals typically cross our planet from the Milky Way. The search for technosignatures from hypothetical galactic civilizations is going through a new phase of intense activity. For the first time, a significant fraction of the vast search space is expected to be sampled in the foreseeable future, potentially bringing informative data about the abundance of detectable extraterrestrial civilizations or the lack thereof. Starting from the current state of ignorance about the galactic population of nonnatural electromagnetic signals, we formulate a Bayesian statistical model to infer the mean number of radio signals crossing Earth, assuming either nondetection or the detection of signals in future surveys of the Galaxy. Under fairly noninformative priors, we find that not detecting signals within about 1 kly from Earth, while suggesting the lack of galactic emitters or at best the scarcity thereof, is nonetheless still consistent with a probability exceeding 10% that typically over ∼100 signals could be crossing Earth, with radiated power analogous to that of the Arecibo radar, but coming from farther in the Milky Way. The existence in the Galaxy of potentially detectable Arecibo-like emitters can be reasonably ruled out only if all-sky surveys detect no such signals up to a radius of about 40 kly, an endeavor requiring detector sensitivities thousands times higher than those of current telescopes. Conversely, finding even one Arecibo-like signal within ∼1000 light years, a possibility within reach of current detectors, implies almost certainly that typically more than ∼100 signals of comparable radiated power cross the Earth, yet to be discovered.