Bayesian Inference for LISA Pathfinder using Markov Chain Monte Carlo Methods

TL;DR

This paper develops a Bayesian parameter estimation method using Markov Chain Monte Carlo techniques for calibrating a space-based gravitational wave detector, demonstrating improved convergence and accuracy in LISA Pathfinder data analysis.

Contribution

It introduces a two-stage annealing MCMC approach with two proposal strategies, showing the eigen-space proposal yields better convergence for LISA Pathfinder calibration.

Findings

Eigen-space proposal has higher acceptance rate.

Parameter estimates are within ~1σ of true values.

Errors in force noise estimation are negligible compared to experimental uncertainty.

Abstract

We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of a space based gravitational wave detector. The method is based on the Metropolis-Hastings algorithm and a two-stage annealing treatment in order to ensure an effective exploration of the parameter space at the beginning of the chain. We compare two versions of the algorithm with an application to a LISA Pathfinder data analysis problem. The two algorithms share the same heating strategy but with one moving in coordinate directions using proposals from a multivariate Gaussian distribution, while the other uses the natural logarithm of some parameters and proposes jumps in the eigen-space of the Fisher Information matrix. The algorithm proposing jumps in the eigen-space of the Fisher Information matrix demonstrates a higher acceptance rate and a slightly better convergence towards the equilibrium parameter distributions in the application to LISA Pathfinder data . For this experiment, we return parameter values that are all within $\sim1\sigma$ of the injected values. When we analyse the accuracy of our parameter estimation in terms of the effect they have on the force-per-unit test mass noise estimate, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density.