temponest: a Bayesian approach to pulsar timing analysis

Abstract

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