Nested sampling as a tool for LISA data analysis

Abstract

Nested sampling is a technique for efficiently computing the probability of a data set under a particular hypothesis, also called the Bayesian Evidence or Marginal Likelihood, and for evaluating the posterior. MULTINEST is a multi-modal nested sampling algorithm which has been designed to efficiently explore and characterize posterior probability surfaces containing multiple secondary solutions. We have applied the MULTINEST algorithm to a number of problems in gravitational wave data analysis. In this article, we describe the algorithm and present results for several applications of the algorithm to analysis of mock LISA data. We summarise recently published results for a test case in which we searched for two non-spinning black hole binary merger signals in simulated LISA data. We also describe results obtained with MULTINEST in the most recent round of the Mock LISA Data Challenge (MLDC), in which the algorithm was used to search for and characterise both spinning supermassive black hole binary inspirals and bursts from cosmic string cusps. In all these applications, the algorithm found the correct number of signals and efficiently recovered the posterior probability distribution. Moreover, in most cases the waveform corresponding to the best a-posteriori parameters had an overlap in excess of 99% with the true signal.