Constraining the microlensing effect on time delays with new time-delay
  prediction model in $H_{0}$ measurements
  Time-delay strong lensing provides a unique way to directly measure the
Hubble constant ($H_{0}$). The precision of the $H_{0}$ measurement depends on
the uncertainties in the time-delay measurements, the mass distribution of the
main deflector(s), and the mass distribution along the line of sight. Tie and
Kochanek (2018) have proposed a new microlensing effect on time delays based on
differential magnification of the coherent accretion disc variability of the
lensed quasar. If real, this effect could significantly broaden the uncertainty
on the time delay measurements by up to $30\%$ for lens systems such as
PG1115+080, which have relatively short time delays and monitoring over several
different epochs. In this paper we develop a new technique that uses the
time-delay ratios and simulated microlensing maps within a Bayesian framework
in order to limit the allowed combinations of microlensing delays and thus to
lessen the uncertainties due to the proposed effect. We show that, under the
assumption of Tie and Kochanek (2018), the uncertainty on the time-delay
distance ($D_{\Delta t}$, which is proportional to 1/$H_{0}$) of short
time-delay ($\sim18$ days) lens, PG1115+080, increases from $\sim7\%$ to
$\sim10\%$ by simultaneously fitting the three time-delay measurements from the
three different datasets across twenty years, while in the case of long
time-delay ($\sim90$ days) lens, the microlensing effect on time delays is
negligible as the uncertainty on $D_{\Delta t}$ of RXJ1131-1231 only increases
from $\sim2.5\%$ to $\sim2.6\%$.
