  Understanding and dealing with inference biases in gravitational-wave (GW)
parameter estimation when a plethora of signals are present in the data is one
of the key challenges for the analysis of data from future GW detectors.
Working within the linear signal approximation, we describe generic metrics to
predict inference biases on GW source parameters in the presence of confusion
noise from unfitted foregrounds, from overlapping signals that coalesce close
in time to one another, and from residuals of other signals that have been
incorrectly fitted out. We illustrate the formalism with simplified, yet
realistic, scenarios appropriate to third-generation ground-based (Einstein
Telescope) and space-based (LISA) detectors, and demonstrate its validity
against Monte-Carlo simulations. We find it to be a reliable tool to cheaply
predict the extent and direction of the biases. Finally, we show how this
formalism can be used to correct for biases that arise in the sequential
characterisation of multiple sources in a single data set, improving the
accuracy of the global-fit without the need for expensive joint-fitting of the
sources.
