Bayesian inference from all-sky SETI surveys Claudio Grimaldi C. Grimaldi, Sci. Rep. 7, 46273 (2017) C. Grimaldi, G.W. Marcy, N.K. Tellis, F. Drake, PASP 130, 054101 (2018) C. Grimaldi, G.W. Marcy, PNAS 115 , E9755 (2018)
Bayes rule Bayes’ theorem gives a recipe to update the initial hypothesis Bayes’ theorem gives a recipe to update the initial hypothesis (prior) about the probability of occurrence of an event in response (prior) about the probability of occurrence of an event in response to new evidence (data) to new evidence (data) real-world applications • Alan Turing used a Bayesian system to crack the Enigma Code • Bernard Koopman used Bayes rule to hunt U-boats • used to find missing aircrafts (Air France AF447, Malaysia Airlines MH370) • medicine, weather forecasting, financial risk analysis, cosmology, spam filtering, machine learning, AI, … Bayes rule is a pervasive tool for decision making based on incomplete information
Incomplete information in SETI is an euphemism • no evidence that life exists beyond Earth • the fraction of the SETI search space explored is similar to that of a glass of water to the Earth’s ocean (Tarter - 2010) • UPDATE: The fraction of the SETI search space explored is similar to that of a Jacuzzi to the Earth’s ocean (Wright, Kanodia, Lubar - 2018) • less than 0.1% of stars within 160 ly harbor detectable trasmitters as powerful as the Arecibo radar (or more) in the frequency range 1.1-1.9 GHz (Enriquez et al. 2017) suggesting that the number of Arecibo-like emitters in the Milky Way is between 0 and 10 7 . The present state of SETI is better described by almost complete ignorance rather than incomplete information. … but the data gathered by large-scale SETI projects can potentially enable us to infer the population of ET emitters by Bayesian analysis
Necessary conditions for signal detection the Earth must be within the domain covered by • the EM emissions telescopes must be targeting the emitters • the emitted signal strength must be above the • detection threshold
Necessary conditions for signal detection the Earth must be within the domain covered by • the EM emissions telescopes must be targeting the emitters • the emitted signal strength must be above the • detection threshold The thin disk of the Milky Way has a radius of • about 60 kly The Earth lies approximately on the galactic plane, • at 27 kly from the galactic center any radio wavelength photon emitted before • t M =87,000 years ago is absolutely undetectable
Necessary conditions for signal detection • the Earth must be within the domain covered by the EM emissions • telescopes must be targeting the emitters • the emitted signal strength must be above the detection threshold • q = fraction of N s stars in the Galaxy that harbor emitters whose signal is no older than t M = 87,000 yr • L = average lifetime of the emissions mean number of signals crossing Earth emitted mean number of signals crossing Earth emitted from the entire Milky Way from the entire Milky Way
Necessary conditions for signal detection • the Earth must be within the domain covered by the EM emissions • telescopes must be targeting the emitters • the emitted signal strength must be above the detection threshold Emitters may transmit narrow directional q shell : fraction of stars emitting q beam : fraction of stars emitting beams as a more efficient way to isotropic shell signals randomly oriented beams communicate (less power required) for a solid angle covering the size of the solar system at a distance of 10 ly
Necessary conditions for signal detection • the Earth must be within the domain covered by the EM emissions • telescopes must be targeting the emitters R o • the emitted signal strength must be above the detection threshold ATA MeerKAT VLA SKA1, SKA2
Necessary conditions for signal detection • the Earth must be within the domain covered by the EM emissions • telescopes must be targeting the emitters R o • the emitted signal strength must be above the detection threshold effective luminosity of the emitter observational radius: minimum detectable flux fraction of stars within R o : probability density of stars mean number of detectable signals:
Bayesian analysis = prior PDF that there are in average signals from the entire Galaxy that cross = prior PDF that there are in average signals from the entire Galaxy that cross the Earth, regardless of whether we can detect them or not. the Earth, regardless of whether we can detect them or not. = new evidence on the number of detected signals acquired from new data = new evidence on the number of detected signals acquired from new data Posterior PDF of given Posterior PDF of given Likelihood function Likelihood function Prior PDF Prior PDF likelihood function R o R o R o Earth Earth Earth Probability that there are k =0, 1, 2, … signals crossing Earth from emitters within R o = non -detection = at least one = exactly one detection detection
Bayesian analysis = prior PDF that there are in average signals from the entire Galaxy that cross = prior PDF that there are in average signals from the entire Galaxy that cross the Earth, regardless of whether we can detect them or not. the Earth, regardless of whether we can detect them or not. = new evidence on the number of detected signals acquired from new data = new evidence on the number of detected signals acquired from new data Posterior PDF of given Posterior PDF of given Likelihood function Likelihood function Prior PDF Prior PDF Prior PDF We don’t know even the scale of (the average number of signals at Earth) the most noninformative prior is a log-uniform PDF: The detection threshold of previous all-sky surveys is about S min = 10 -23 W/m 2 (within 1-2 GHz) past SETI surveys have detected no signals within 2x10 13 W
Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz σ : signal-to-noise ratio (15) S sys : system equivalent flux density (Jy=10 -26 W/m 2 Hz) t : integration time (10 min) ∆ν : bandwidth (0.5 Hz) disk-like model for the star distribution
Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz Breakthrough Listen goal: 1 million nearby stars (contained within a sphere of radius R o =500 ly) L E =L Arecibo one detection at least one detection non-detection
Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz Breakthrough Listen goal: 1 million nearby stars What if R o extends up to the galactic center? (contained within a sphere of radius R o =500 ly) L E =L Arecibo L E =L Arecibo one detection at least one detection non-detection
Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz at least one one detection detection non-detection
Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz
Conclusions At present there is almost complete ignorance about the possible population of ET • emitters in the Galaxy A statistical Bayesian approach is still possible by considering possible outcomes of future • extensive SETI all-sky surveys It is unlikely that there are Arecibo-like emitters in the Galaxy If no signals are discovered • within about 40 kly from Earth If a signal is discovered within 1000 ly from Earth it is almost certain that there are more • than 100 Arecibo-like emitters in the Galaxy, yet to be discovered Outlook Improved statistical modelling : adding other galactic components (e.g. globular clusters), • periodic signals, distributed emitter luminosities (power law), frequency dependent SEFD, correlation (signal longevity – luminosity), fractal distribution of emitters, local universe beyond the Milky Way, micrometer-submicrometer wavelength emissions Improved Bayesian analysis : model selection, adaptive distribution of emitters, iterative • Bayesian inference, targeted searches, false positive/negative results (e.g. scintillation), wideband emissions
remerciements Geoff Marcy - UC-Berkeley Andrew Siemion- UC-Berkeley Nathaniel Tellis - UC-Berkeley Emilio Enriques- UC-Berkeley Frank Drake - SETI Institute Eric Korpela- UC-Berkeley Amedeo Balbi – Uni Tor Vergata - Rome Jill Tarter– SETI Institute Avik Chatterjee – SUNI Syracuse Dan Werthimer– UC-Berkeley
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