  The modeling of intrinsic noise in pulsar timing residual data is of crucial
importance for Gravitational Wave (GW) detection and pulsar timing
(astro)physics in general. The noise budget in pulsars is a collection of
several well studied effects including radiometer noise, pulse-phase jitter
noise, dispersion measure (DM) variations, and low frequency spin noise.
However, as pulsar timing data continues to improve, non-stationary and
non-powerlaw noise terms are beginning to manifest which are not well modeled
by current noise analysis techniques. In this work we use a trans-dimensional
approach to model these non-stationary and non-powerlaw effects through the use
of a wavelet basis and an interpolation based adaptive spectral modeling. In
both cases, the number of wavelets and the number of control points in the
interpolated spectrum are free parameters that are constrained by the data and
then marginalized over in the final inferences, thus fully incorporating our
ignorance of the noise model. We show that these new methods outperform
standard techniques when non-stationary and non-powerlaw noise is present. We
also show that these methods return results consistent with the standard
analyses when no such signals are present.
