  The space-based gravitational-wave observatory LISA relies on a form of
synthetic interferometry (time-delay interferometry, or TDI) where the
otherwise overwhelming laser phase noise is canceled by linear combinations of
appropriately delayed phase measurements. These observables grow in length and
complexity as the realistic features of the LISA orbits are taken into account.
In this paper we outline an implicit formulation of TDI where we write the LISA
likelihood directly in terms of the basic phase measurements, and we
marginalize over the laser phase noises in the limit of infinite laser-noise
variance. Equivalently, we rely on TDI observables that are defined numerically
(rather than algebraically) from a discrete-filter representation of the laser
propagation delays. Our method generalizes to any time dependence of the
armlengths; it simplifies the modeling of gravitational-wave signals; and it
allows a straightforward treatment of data gaps and missing measurements.
