Accelerating pulsar timing data analysis

The analysis of pulsar timing data, especially in pulsar timing array (PTA) projects, has encountered practical difficulties: evaluating the likelihood and/or correlation-based statistics can become prohibitively computationally expensive for large datasets. In situations where a stochastic signal of interest has a power spectral density that dominates the noise in a limited bandwidth of the total frequency domain (e.g. the isotropic background of gravitational waves), a linear transformation exists that transforms the timing residuals to a basis in which virtually all the information about the stochastic signal of interest is contained in a small fraction of basis vectors. By only considering such a small subset of these "generalised residuals", the dimensionality of the data analysis problem is greatly reduced, which can cause a large speedup in the evaluation of the likelihood: the ABC-method (Acceleration By Compression). The compression fidelity, calculable with crude estimates of the signal and noise, can be used to determine how far a dataset can be compressed without significant loss of information. Both direct tests on the likelihood, and Bayesian analysis of mock data, show that the signal can be recovered as well as with an analysis of uncompressed data. In the analysis of IPTA Mock Data Challenge datasets, speedups of a factor of three orders of magnitude are demonstrated. For realistic PTA datasets the acceleration may become greater than six orders of magnitude due to the low signal to noise ratio.