New advances in the Gaussian-process approach to pulsar-timing data analysis

TL;DR

This paper reviews Gaussian process applications in pulsar-timing noise modeling and introduces two efficient sampling schemes that significantly accelerate Bayesian inference for large datasets.

Contribution

It develops optimized likelihood representations and two novel Gibbs-inspired sampling schemes that reduce autocorrelation and computational time in pulsar-timing data analysis.

Findings

New sampling schemes have lower autocorrelation than MCMC.

Methods enable full-noise-model analysis of large datasets.

Potential to speed up Bayesian inference by orders of magnitude.

Abstract

In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in Bayesian inference on pulsar-timing-array datasets. The resulting viewpoint and formalism lead us to two improved parameter-sampling schemes inspired by Gibbs sampling. The new schemes have vastly lower chain autocorrelation lengths than the Markov Chain Monte Carlo methods currently used in pulsar-timing data analysis, potentially speeding up Bayesian inference by orders of magnitude. The new schemes can be used for a full-noise-model analysis of the large datasets assembled by the International Pulsar Timing Array collaboration, which present a serious computational challenge to existing methods.