  Planetary systems with mean-motion resonances (MMRs) hold special value in
terms of their dynamical complexity and their capacity to constrain planet
formation and migration histories. The key towards making these connections,
however, is to have a reliable characterization of the resonant dynamics,
especially the so-called "libration amplitude", which qualitatively measures
how deep the system is into the resonance. In this work, we identify an
important complication with the interpretation of libration amplitude estimates
from observational data of resonant systems. Specifically, we show that
measurement noise causes inferences of the libration amplitude to be
systematically biased to larger values, with noisier data yielding a larger
bias. We demonstrated this through multiple approaches, including using
dynamical fits of synthetic radial velocity data to explore how the the
libration amplitude distribution inferred from the posterior parameter
distribution varies with the degree of measurement noise. We find that even
modest levels of noise still result in a slight bias. The origin of the bias
stems from the topology of the resonant phase space and the fact that the
available phase space volume increases non-uniformly with increasing libration
amplitude. We highlight strategies for mitigating the bias through the usage of
particular priors. Our results imply that many known resonant systems are
likely deeper in resonance than previously appreciated.
