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We develop Bayesian statistical methods for discovering and assigningprobabilities to non-random (e.g., physical) stellar companions. Thesecompanions are either presently bound or were previously bound. Theprobabilities depend on similarities in corrected proper motion parallel andperpendicular to the brighter component's motion, parallax, and the localphase-space density of field stars. Control experiments are conducted tounderstand the behavior of false positives. The technique is applied to theHipparcos Catalogue within 100 pc. This is the first all-sky survey to locateescaped companions still drifting along with each other. In the <100 pcdistance range, ~220 high probability companions with separations between 0.01- 1 pc are found. The first evidence for a population (~300) of companionsseparated by 1 - 8 pc is found. We find these previously unnoticed naked-eyecompanions (both with V<6th mag): Capella & 50 Per, delta Vel & HIP 43797,Alioth (epsilon UMa), Megrez (delta UMa) & Alcor (80 UMA), gamma & tau Cen, phiEri & eta Hor, 62 & 63 Cnc, gamma & tau Per, zeta & delta Hya, beta01, beta02 &beta03 Tuc, N Vel & HIP 47479, HIP 98174 & HIP 97646, 44 & 58 Oph, s Eri & HIP14913, and pi & rho Cep. High probability fainter companions (V > 6th mag) ofprimaries with V < 4th mag are found for: Fomalhaut (alpha PsA), gamma UMa,alpha Lib, Alvahet (iota Cephi), delta Ara, beta Ser, iota Peg, beta Pic, kappaPhe and gamma Tuc.

Very Wide Binaries and Other Comoving Stellar Companions: A Bayesian Analysis of the Hipparcos Catalogue