TempoNest: A Bayesian approach to pulsar timing analysis
  A new Bayesian software package for the analysis of pulsar timing data is
presented in the form of TempoNest which allows for the robust determination of
the non-linear pulsar timing solution simultaneously with a range of additional
stochastic parameters. This includes both red spin noise and dispersion measure
variations using either power law descriptions of the noise, or through a
model-independent method that parameterises the power at individual frequencies
in the signal. We use TempoNest to show that at noise levels representative of
current datasets in the European Pulsar Timing Array (EPTA) and International
Pulsar Timing Array (IPTA) the linear timing model can underestimate the
uncertainties of the timing solution by up to an order of magnitude. We also
show how to perform Bayesian model selection between different sets of timing
model and stochastic parameters, for example, by demonstrating that in the
pulsar B1937+21 both the dispersion measure variations and spin noise in the
data are optimally modelled by simple power laws. Finally we show that not
including the stochastic parameters simultaneously with the timing model can
lead to unpredictable variation in the estimated uncertainties, compromising
the robustness of the scientific results extracted from such analysis.
