  Gravitational wave background results from the superposition of gravitational
waves generated from all sources across the Universe. Previous efforts on
detecting such a background with pulsar timing arrays assume it is an isotropic
Gaussian background with a power law spectrum. However, when the number of
sources is limited, the background might be non-Gaussian or the spectrum might
not be a power law. Correspondingly previous analysis may not work effectively.
Here we use a method --- Bayesian Nonparametric Analysis --- to try to detect a
generic gravitational wave background, which directly sets constraints on the
feasible shapes of the pulsar timing signals induced by a gravitational wave
background and allows more flexible forms of the background. Our Bayesian
nonparametric analysis will infer if a gravitational wave background is present
in the data, and also estimate the parameters that characterize the background.
This method will be much more effective than the conventional one assuming the
background spectrum follows a power law in general cases. While the context of
our discussion focuses on pulsar timing arrays, the analysis itself is directly
applicable to detect and characterize any signals that arise from the
superposition of a large number of astrophysical events.
