  We describe a tool we improved to detect excess noise in the gravitational
wave (GW) channel arising from its bilinear or nonlinear coupling with
fluctuations of various components of a GW interferometer and its environment.
We also describe a higher-order statistics tool we developed to characterize
these couplings, e.g., by unraveling the frequencies of the fluctuations
contributing to such noise, and demonstrate its utility by applying it to
understand nonlinear couplings in Advanced LIGO engineering data. Once such
noise is detected, it is highly desirable to remove it or correct for it. Such
action in the past has been shown to improve the sensitivity of the instrument
in searches of astrophysical signals. If this is not possible, then steps must
be taken to mitigate its influence, e.g., by characterizing its effect on
astrophysical searches. We illustrate this through a study of the effect of
transient sine-Gaussian noise artifacts on a compact binary coalescence
template bank.
