Accelerating pulsar timing data analysis

Abstract

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 data sets. 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 gravitationalwaves), 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 'generalized 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 data set 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 International PTA Mock Data Challenge data sets, speedups of a factor of 3 orders of magnitude are demonstrated. For realistic PTA data sets the acceleration may become greater than six orders of magnitude due to the low signal-to-noise ratio ©2012 The Author.