  An astrophysical population of supermassive black hole binaries is thought to
be the strongest source of gravitational waves in the frequency range covered
by Pulsar Timing Arrays (PTAs). A potential cause for concern is that the
standard cross-correlation method used in PTA data analysis assumes that the
signals are isotropically distributed and Gaussian random, while the signals
from a black hole population are likely to be anisotropic and deterministic.
Here we argue that while the conventional analysis is not optimal, it is not
hopeless either, as the standard Hellings-Downs correlation curve turns out to
hold for point sources, and the small effective number of signal samples blurs
the distinction between Gaussian and deterministic signals. Possible
improvements to the standard cross-correlation analysis that account for the
anisotropy of the signal are discussed.
