temponest: a Bayesian approach to pulsar timing analysis

Abstract

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.

The NANOGrav Nine-year Data Set: Measurement and Analysis of Variations in Dispersion Measures

“…There is also the possibility that the DMs measured for the observed epochs do not agree between the sites due to the difference in observing frequencies used and spatial location; the two data sets may essentially be sampling a different ISM due to multipath scattering . Lentati et al (2016) apply a Fourier-based method of DM estimation (see also Lentati et al 2014) that allows for robust correction of DM variations during epochs without multifrequency data in the International Pulsar Timing Array (IPTA) data release (Verbiest et al 2016). The DM noise model used by Lentati et al (2016) assumes the power spectrum of the variations is in the form of a frequency-dependent power law.…”

Limitations in timing precision due to single-pulse shape variability in millisecond pulsars

“…The most common method is to adjust the values until the reduced-χ 2 of the fitted model reaches unity. Bayesian and other maximum likelihood methods have also recently been developed and applied to precision pulsar timing datasets (van Haasteren et al 2009;Lentati et al 2014). In these methods, EFAC and EQUAD are included as nuisance parameters and marginalised when calculating the posterior distributions of parameters of interest or comparing models.…”

Proper motions of 15 pulsars: a comparison between Bayesian and frequentist algorithms

“…This method has now been used to determine the proper motion of millisecond pulsars (Reardon et al 2016). Lentati (2014) demonstrated a similar method in which the noise properties of the data and the pulsar parameters were simultaneously determined using a Bayesian methodology (Desvignes et al 2016). Recently Babak (2016) described the comparison of noise models from Bayesian and frequentist methods and got the consistent upper limits on continuous gravitational waves depended on the two algorithms.…”