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.

Thirty-three fast radio bursts (FRBs) had been detected by March 2018. Although the sample size is still limited, meaningful statistical studies can already be carried out. The normalised luminosity function places important constraints on the intrinsic power output, sheds light on the origin(s) of FRBs, and can guide future observations. In this paper, we measure the normalised luminosity function of FRBs. Using Bayesian statistics, we can naturally account for a variety of factors such as receiver noise temperature, bandwidth, and source selection criteria. We can also include astronomical systematics, such as host galaxy dispersion measure, FRB local dispersion measure, galaxy evolution, geometric projection effects, and Galactic halo contribution. Assuming a Schechter luminosity function, we show that the isotropic luminosities of FRBs have a power-law distribution that covers approximately three orders of magnitude, with a power-law index ranging from −1.8 to −1.2 and a cut off ∼ 2 × 10 44 erg s −1 . By using different galaxy models and well-established Bayesian marginalisation techniques, we show that our conclusions are robust against unknowns, such as the electron densities in the Milky Way halo and the FRB environment, host galaxy morphology, and telescope beam response.