Bayesian Model Selection for LISA Pathfinder

TL;DR

This paper applies Bayesian model selection techniques to analyze LISA Pathfinder data, aiming to identify the most relevant physical effects in the instrument noise for future gravitational-wave observatories.

Contribution

It compares three Bayesian methods for model selection in the context of LISA Pathfinder, demonstrating their effectiveness in simulated experiments and guiding future flight data analysis.

Findings

Reversible Jump MCMC effectively recovers the best model.

Schwarz criterion provides reliable model comparison.

Laplace approximation offers computational efficiency.

Abstract

The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the eLISA concept. The data analysis team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment on-board LPF. These models are used for simulations, but more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the data analysis team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching this problem is to recover the essential parameters of a LTP model fitting the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes Factor between two competing models. In our analysis, we use three main different methods to estimate it: The Reversible Jump Markov Chain Monte Carlo method, the Schwarz criterion, and the Laplace approximation. They are applied to simulated LPF experiments where the most probable LTP model that explains the observations is recovered. The same type of analysis presented in this paper is expected to be followed during flight operations. Moreover, the correlation of the output of the aforementioned methods with the design of the experiment is explored.