Bayesian estimation of non-Gaussianity in pulsar timing analysis

We introduce a method for performing a robust Bayesian analysis of non-Gaussianity present in pulsar timing data, simultaneously with the pulsar timing model, and additional stochastic parameters such as those describing red spin noise and dispersion measure variations. The parameters used to define the presence of non-Gaussianity are zero for Gaussian processes, giving a simple method of defining the strength of non-Gaussian behaviour. We use simulations to show that assuming Gaussian statistics when the noise in the data is drawn from a non-Gaussian distribution can significantly increase the uncertainties associated with the pulsar timing model parameters. We then apply the method to the publicly available 15 year Parkes Pulsar Timing Array data release 1 dataset for the binary pulsar J0437$-$4715. In this analysis we present a significant detection of non-Gaussianity in the uncorrelated non-thermal noise, but we find that it does not yet impact the timing model or stochastic parameter estimates significantly compared to analysis performed assuming Gaussian statistics. The methods presented are, however, shown to be of immediate practical use for current European Pulsar Timing Array (EPTA) and International Pulsar Timing Array (IPTA) datasets.

How to take the interstellar weather with you in pulsar timing analysis

Here we present a Bayesian method of including discrete measurements of dispersion measure due to the interstellar medium in the direction of a pulsar as prior information in the analysis of that pulsar. We use a simple simulation to show the efficacy of this method, where the inclusion of the additional measurements results in both a significant increase in the precision with which the timing model parameters can be obtained, and an improved upper limit on the amplitude of any red noise in the dataset. We show that this method can be applied where no multi-frequency data exists across much of the dataset, and where there is no simultaneous multi-frequency data for any given observing epoch. Including such information in the analysis of upcoming International Pulsar Timing Array (IPTA) and European Pulsar Timing Array (EPTA) data releases could therefore prove invaluable in obtaining the most constraining limits on gravitational wave signals within those datasets.

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.