Bayesian approach to SETI

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 non-natural electromagnetic signals, we formulate a Bayesian statistical model to infer the mean number of radio signals crossing Earth, assuming either non-detection 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 $\sim 100$ 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 $\sim 1000$ light years, a possibility within reach of current detectors, implies almost certainly that typically more than $\sim 100$ signals of comparable radiated power cross the Earth, yet to be discovered.