  Detecting a stochastic gravitational wave background, particularly radiation
from individually unresolvable super-massive black hole binary systems, is one
of the primary targets for Pulsar Timing Arrays. Increasingly more stringent
upper limits are being set on these signals under the assumption that the
background radiation is isotropic. However, some level of anisotropy may be
present and the characterisation of the power at different angular scales
carries important information. We show that the standard analysis for isotropic
backgrounds can be generalised in a conceptually straightforward way to the
case of generic anisotropic background radiation by decomposing the angular
distribution of the gravitational wave power on the sky into multipole moments.
We introduce the concept of generalised overlap reduction functions which
characterise the effect of the anisotropy multipoles on the correlation of the
timing residuals from the pulsars timed by a Pulsar Timing Array. In a search
for a signal characterised by a generic anisotropy, the generalised overlap
reduction functions play the role of the so-called Hellings and Downs curve
used for isotropic radiation. We compute the generalised overlap reduction
functions for a generic level of anisotropy and Pulsar Timing Array
configuration. We also provide an order of magnitude estimate of the level of
anisotropy that can be expected in the background generated by super-massive
black hole binary systems.
