  Measuring the escape fraction, $f_{\rm esc}$, of ionizing, Lyman Continuum
(LyC) radiation is key to our understanding of the process of cosmic
reionization. In this paper we provide a methodology for recovering the
posterior probability distribution of the LyC escape fraction, $f_{\rm
esc}^{\rm PDF}$, considering both the observational uncertainties and ensembles
of simulated transmission functions through the intergalactic medium (IGM). We
present an example of this method applied to a VUDS galaxy at $z=3.64$ and find
$f_{\rm esc}^{\rm PDF}$ = 0.51$^{+0.33}_{-0.34}$ and compare this to the values
computed assuming averaged IGM transmission with and without consideration of
detection bias along average sightlines yielding $f_{\rm esc}^{\langle T
\rangle}$ = 1.40$^{+0.80}_{-0.42}$, and $f_{\rm esc}^{\rm bias}$ =
0.82$^{+0.33}_{-0.16}$. Our results highlight the limitations of methods
assuming average, smooth transmission functions. We also present MOSFIRE data
for a sample of seven LyC candidates selected based on photometric redshifts at
$z > 3.4$, but find that all seven have overestimated photometric redshifts by
$\Delta z \sim 0.2$ making them unsuitable for LyC measurements. This results
likely due to a bias induced by our selection criteria.
