hide
Free keywords:
Astrophysics, Instrumentation and Methods for Astrophysics, astro-ph.IM,General Relativity and Quantum Cosmology, gr-qc
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 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.
