MatBYIB: A Matlab-based code for Bayesian inference of extreme mass-ratio inspiral binary with arbitrary eccentricity

TL;DR

MatBYIB is a MATLAB software package that enables Bayesian parameter estimation of gravitational waves from EMRI systems with arbitrary eccentricity, using efficient waveform generation and convergence-guaranteed sampling methods.

Contribution

This work introduces MatBYIB, a novel MATLAB-based tool that performs Bayesian inference for GW parameters including eccentricity, filling a gap in existing software.

Findings

Strong agreement between FIM and MCMC results.

Efficient convergence with adaptive sampling until R < 1.05.

User-friendly implementation for standard PCs.

Abstract

Accurate parameter estimation(PE) of gravitational waves(GW) is essential for GW data analysis. In extreme mass-ratio inspiral binary(EMRI) systems, orbital eccentricity is a critical parameter for PE. However, current software for for PE of GW often neglects the direct estimation of orbital eccentricity. To fill this gap, we have developed the MatBYIB, a MATLAB-based software package for PE of GW with arbitrary eccentricity. The MatBYIB employs the Analytical Kludge (AK) waveform as a computationally efficient signal generator and computes parameter uncertainties via the Fisher Information Matrix (FIM) and the Markov Chain Monte Carlo (MCMC). For Bayesian inference, we implement the Metropolis-Hastings (M-H) algorithm to derive posterior distributions. To guarantee convergence, the Gelman-Rubin convergence criterion (the Potential Scale Reduction Factor R) is used to determine sampling adequacy, with MatBYIB dynamically increasing the sample size until R < 1.05 for all parameters. Our results demonstrate strong agreement between FIM- based predictions and full MCMC sampling. This program is user-friendly and allows for estimation of gravitational wave parameters with arbitrary eccentricity on standard personal computers. Code availability:The implementation is open-source at https://github.com/GenliangLi/MatBYIB.