We present a Bayesian inference on the neutral hydrogen fraction of the intergalactic medium (IGM), {bar}x_hi_, at z~6-8 using the properties of Lyman break galaxies during the Epoch of Reionization.We use large samples of LBG candidates at 5.5<=z<=8.2 with spectroscopy from Keck/DEIMOS and Keck/MOSFIRE. For each galaxy, we incorporate either the Lyman-{alpha} equivalent width (EW) for detections or the EW limit spectrum for nondetections to parameterize the EW distribution at various ultraviolet brightnesses for a given redshift. Using our reference sample of galaxy candidates from the ionized universe at z~6.0, we are able to infer {bar}x_hi_ at two redshifts: z~6.7 and z~7.6. This work includes intrinsically faint, gravitationally lensed galaxies at z~6.0 in order to constrain the intrinsic faint-end Ly{alpha} EW distribution and provide a comparable population of galaxies to counterparts in our sample that are at higher redshift. The inclusion of faint galaxy candidates, in addition to a more sophisticated modelling framework, allows us to better isolate effects of the interstellar medium and circumgalactic medium on the observed Lyman-{alpha} distribution from those of the IGM. We infer an upper limit of {bar}x_hi_<=0.25 at z=6.7+/-0.2 and a neutral fraction of {bar}x_hi_=0.83^+0.08^-0.11 at z=7.6+/-0.6, both within 1{sigma} uncertainty, results which favor a moderately late and rapid reionization.

Cone search capability for table J/MNRAS/517/3263/nondet (*Information on the properties of LBGs without spectroscopic Lyman-alpha from Keck/DEIMOS)