  Data from the Laser Interferometer Space Antenna (LISA) is expected to be
dominated by frequency noise from its lasers. However the noise from any one
laser appears more than once in the data and there are combinations of the data
that are insensitive to this noise. These combinations, called time delay
interferometry (TDI) variables, have received careful study, and point the way
to how LISA data analysis may be performed. Here we approach the problem from
the direction of statistical inference, and show that these variables are a
direct consequence of a principal component analysis of the problem. We present
a formal analysis for a simple LISA model and show that there are eigenvectors
of the noise covariance matrix that do not depend on laser frequency noise.
Importantly, these orthogonal basis vectors correspond to linear combinations
of TDI variables. As a result we show that the likelihood function for source
parameters using LISA data can be based on TDI combinations of the data without
loss of information.
