Bayesian model selection for LISA pathfinder

Karnesis, Nikolaos; Nofrarias, M.; Sopuerta, Carlos F.; Gibert, F.; Armano, M.; Audley, H.; Congedo, G.; Diepholz, I.; Ferraioli, L.; Hewitson, M.; Hueller, M.; Korsakova, Natalia; McNamara, P. W.; Plagnol, E.; Vitale, S.

doi:10.1103/physrevd.89.062001

Cited by 11 publications

(10 citation statements)

References 26 publications

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“…In order to calibrate the dynamics of LPF described in the previous section, the so-called system identification experiments [16][17][18] were regularly performed during the mission. Repeated experiments were necessary both to measure the long term stability of the system, and also because different working configurations of the system and/or potentially different environmental conditions could yield different calibration parameters.…”

Section: System Identification and Parameter Estimationmentioning

confidence: 99%

Calibrating the system dynamics of LISA Pathfinder

Armano¹,

Audley²,

Baird³

et al. 2018

Phys. Rev. D

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LISA Pathfinder (LPF) was a European Space Agency mission with the aim to test key technologies for future space-borne gravitational-wave observatories like LISA. The main scientific goal of LPF was to demonstrate measurements of differential acceleration between free-falling test masses at the sub-femto-g level, and to understand the residual acceleration in terms of a physical model of stray forces, and displacement readout noise. A key step towards reaching the LPF goals was the correct calibration of the dynamics of LPF, which was a three-body system composed by two testmasses enclosed in a single spacecraft, and subject to control laws for system stability. In this work, we report on the calibration procedures adopted to calculate the residual differential stray force per unit mass acting on the two test-masses in their nominal positions. The physical parameters of the adopted dynamical model are presented, together with their role on LPF performance. The analysis and results of these experiments show that the dynamics of the system was accurately modeled and the dynamical parameters were stationary throughout the mission. Finally, the impact and importance of calibrating system dynamics for future space-based gravitational wave observatories is discussed.

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Section: System Identification and Parameter Estimationmentioning

confidence: 99%

Calibrating the system dynamics of LISA Pathfinder

Armano¹,

Audley²,

Baird³

et al. 2018

Phys. Rev. D

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“…It is in fact well-known that the dimensionality can become an issue for MCMC sampling techniques (an application of which to LPF data can be found, for instance, in Ref. [40]): the marginalisation over many linear parameters can be the turning point toward an accurate noise measurement in a large-dimensional problem.…”

Section: Discussionmentioning

confidence: 99%

Measuring test mass acceleration noise in space-based gravitational wave astronomy

Congedo

2015

Phys. Rev. D

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The basic constituent of interferometric gravitational wave detectors -the test mass to test mass interferometric link -behaves as a differential dynamometer measuring effective differential forces, comprising an integrated measure of gravity curvature, inertial effects, as well as non-gravitational spurious forces. This last contribution is going to be characterised by the LISA Pathfinder mission, a technology precursor of future space-borne detectors like eLISA. Changing the perspective from displacement to acceleration can benefit the data analysis of LISA Pathfinder and future detectors. The response in differential acceleration to gravitational waves is derived for a space-based detector's interferometric link. The acceleration formalism can also be integrated into time delay interferometry by building up the unequal-arm Michelson differential acceleration combination. The differential acceleration is nominally insensitive to the system free evolution dominating the slow displacement dynamics of low-frequency detectors. Working with acceleration also provides an effective way to subtract measured signals acting as systematics, including the actuation forces. Because of the strong similarity with the equations of motion, the optimal subtraction of systematic signals, known within some amplitude and time shift, with the focus on measuring the noise provides an effective way to solve the problem and marginalise over nuisance parameters. The F-statistic, in widespread use throughout the gravitation waves community, is included in the method and suitably generalised to marginalise over linear parameters and noise at the same time. The method is applied to LPF simulator data and, thanks to its generality, can also be applied to the data reduction and analysis of future gravitational wave detectors.

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“…In order to ensure that the Markov chain converges to the correct stationary distribution, transdimensional MCMC methods such as reversible jump MCMC (Green, 1995) or the product space approach (Carlin and Chib, 1995) match the dimensionality of parameter spaces across different models (e.g., by adding parameters and link functions). Transdimensional MCMC methods have proven to be very useful for the analysis of many statistical models including capture-recapture models (Arnold et al, 2010), generalized linear models (Forster et al, 2012), factor models (Lopes and West, 2004), and mixture models (Frühwirth-Schnatter, 2001), and are widely used in substantive applications such as selection of phylogenetic trees (Opgen-Rhein et al, 2005), gravitational wave detection in physics (Karnesis, 2014), or cognitive models in psychology (Lodewyckx et al, 2011;Heck et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Quantifying uncertainty in transdimensional Markov chain Monte Carlo using discrete Markov models

et al. 2018

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Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC) relies on sampling a discrete indexing variable to estimate the posterior model probabilities. However, little attention has been paid to the precision of these estimates. If only few switches occur between the models in the transdimensional MCMC output, precision may be low and assessment based on the assumption of independent samples misleading. Here, we propose a new method to estimate the precision based on the observed transition matrix of the model-indexing variable. Assuming a first order Markov model, the method samples from the posterior of the stationary distribution. This allows assessment of the uncertainty in the estimated posterior model probabilities, model ranks, and Bayes factors. Moreover, the method provides an estimate for the effective sample size of the MCMC output. In two model-selection examples, we show that the proposed approach provides a good assessment of the uncertainty associated with the estimated posterior model probabilities. I j=1 p ij = 1. According to the discrete Markov model, the probability distribution of the indexing variable z (t) at iteration t is given by multiplying the transposed initial distribution π 0 by the transition matrix t times, P (z (t) = i) = [π 0 P t ] i . The proposed method estimates the transition matrix P as a free parameter based on the sufficient statistic N , the matrix of frequencies n ij counting the observed transitions from z (t) = i to z (t+1) = j (Anderson and Goodman, 1957).

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Bayesian model selection for LISA pathfinder

Cited by 11 publications

References 26 publications

Calibrating the system dynamics of LISA Pathfinder

Calibrating the system dynamics of LISA Pathfinder

Measuring test mass acceleration noise in space-based gravitational wave astronomy

Quantifying uncertainty in transdimensional Markov chain Monte Carlo using discrete Markov models

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