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Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method |
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| Authors: | Luigi Ferraioli Edward K Porter Michele Armano Heather Audley Giuseppe Congedo Ingo Diepholz Ferran Gibert Martin Hewitson Mauro Hueller Nikolaos Karnesis Natalia Korsakova Miquel Nofrarias Eric Plagnol Stefano Vitale |
| Institution: | 1. APC, Université Paris Diderot, CNRS/IN2P3, CEA/Ifru, Observatoire de Paris, Sorbonne Paris Cité, 10 Rue A. Domon et L. Duquet, 75205, Paris Cedex 13, France 2. SRE-OD ESAC, European Space Agency, Camino bajo del Castillo s/n, Urbanización Villafranca del Castillo, Villanueva de la Ca?ada, 28692, Madrid, Spain 3. Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik und Universit?t Hannover, Callinstr. 38, 30167, Hannover, Germany 4. University of Trento and INFN, via Sommarive 14, 38123, Povo (Trento), Italy 5. Institut de Ciències de l’Espai, (CSIC-IEEC), Facultat de Ciències, Campus UAB, Torre C-5, 08193, Bellaterra, Spain |
| 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 the LISA Pathfinder satellite. 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 ～1σ 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 of mass noise, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density. |
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