  Our ability to calibrate current kilometer-scale interferometers can
potentially confound the inference of astrophysical signals. Current
calibration uncertainties are well described by a Gaussian process. I exploit
this description to analytically examine the impact of calibration uncertainty.
I derive closed-form expressions for the conditioned likelihood of the
calibration error given the observed data and an astrophysical signal
(astrophysical calibration) as well as for the marginal likelihood for the data
given a signal (integrated over the calibration uncertainty). I show that
calibration uncertainty always reduces search sensitivity and the amount of
information available about astrophysical signals. Additionally, calibration
uncertainty will fundamentally limit the precision to which loud signals can be
constrained, a crucial factor when considering the scientific potential of
proposed third-generation interferometers. For example, I estimate that with
$1\%$ uncertainty in the detector response's amplitude and phase, one will only
be able to measure the leading-order tidal parameter ($\tilde\Lambda$) for a
1.4+1.4$\,M_\odot$ system to better than $\pm 1$ ($\sim 0.2\%$ relative
uncertainty) for signals with signal-to-noise ratios $\gtrsim 10^4$. At this
signal-to-noise ratio, calibration uncertainty increases
$\sigma_{\tilde\Lambda}$ by a factor of $2$ compared to stationary Gaussian
noise alone. Furthermore, 1\% calibration uncertainty limits the precision to
always be $\sigma_{\tilde\Lambda} \gtrsim 0.5$. I also show how to best select
the frequencies at which calibration should be precisely constrained in order
to minimize the information lost about astrophysical parameters. It is not
necessary to constrain the calibration errors to be small at all frequencies to
perform precise astrophysical inference for individual signals.
