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We present a Bayesian framework to account for the magnification bias fromboth strong and weak gravitational lensing in estimates of high-redshift galaxyluminosity functions. We illustrate our method by estimating the $z\sim8$ UVluminosity function using a sample of 97 Y-band dropouts (Lyman break galaxies)found in the Brightest of Reionizing Galaxies (BoRG) survey and from theliterature. We find the luminosity function is well described by a Schechterfunction with characteristic magnitude of $M^\star = -19.85^{+0.30}_{-0.35}$,faint-end slope of $\alpha = -1.72^{+0.30}_{-0.29}$, and number density of$\log_{10} \Psi^\star [\textrm{Mpc}^{-3}] = -3.00^{+0.23}_{-0.31}$. Theseparameters are consistent within the uncertainties with those inferred from thesame sample without accounting for the magnification bias, demonstrating thatthe effect is small for current surveys at $z\sim8$, and cannot account for theapparent overdensity of bright galaxies compared to a Schechter function foundrecently by Bowler et al. (2014a,b) and Finkelstein et al. (2014). We estimatethat the probability of finding a strongly lensed $z\sim8$ source in our sampleis in the range $\sim 3-15 \%$ depending on limiting magnitude. We identify onestrongly-lensed candidate and three cases of intermediate lensing in BoRG(estimated magnification $\mu>1.4$) in addition to the previously knowncandidate group-scale strong lens. Using a range of theoretical luminosityfunctions we conclude that magnification bias will dominate wide field surveys-- such as those planned for the Euclid and WFIRST missions -- especially at$z>10$. Magnification bias will need to be accounted for in order to deriveaccurate estimates of high-redshift luminosity functions in these surveys andto distinguish between galaxy formation models.

Correcting the z~8 Galaxy Luminosity Function for Gravitational Lensing Magnification Bias