Skip to main content
Log in

Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method

Experimental Astronomy Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Notes

  1. Once a chain has been run long enough and it begins to settle down to an equilibrium distribution, each point in the chain should reach a state where it is only dependent on the previous point.

  2. The update of the Fisher Information Matrix is performed in order to update the proposal distribution that is a multivariate Gaussian which covariance matrix is provided by the inverse of the Fisher Information Matrix.

  3. We are in log space in order to have the parameters of the same order of magnitude. In the case of S Δ , since it can go negative, we can not use the logarithm and the parameter keeps its standard value of the order 10−5 that is considered small when compared with 1.

References

  1. Armano, M., et al.: Class. Quantum Gravity 26(9), 094001 (2009)

    Article  ADS  Google Scholar 

  2. Antonucci, F., et al.: Class. Quantum Gravity 28(9), 094001 (2011)

    Article  ADS  Google Scholar 

  3. McNamara, P., Vitale, S., Danzmann, K.: On behalf of the LISA Pathfinder science working team. Class. Quantum Gravity 25(11), 114034 (2008)

    Article  ADS  Google Scholar 

  4. Amaro-Seoane, P., et al.: arXiv: 1201.3621 (2012)

  5. Antonucci, F., et al.: Class. Quantum Gravity 28(9), 094006 (2011)

    Article  ADS  Google Scholar 

  6. Congedo, G., Ferraioli, L., Hueller, M., De Marchi, F., Vitale, S., Armano, M., Hewitson, M., Nofrarias, M.: Phys. Rev. D 85(12), 122004 (2012)

    Article  ADS  Google Scholar 

  7. Nofrarias, M., Röver, C., Hewitson, M., Monsky, A., Heinzel, G., Danzmann, K., Ferraioli, L., Hueller, M., Vitale, S.: Phys. Rev. D 82(12), 122002 (2010)

    Article  ADS  Google Scholar 

  8. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: J. Chem. Phys. 21(6), 1087 (1953)

    Article  ADS  Google Scholar 

  9. Hastings, W.K.: Biometrika 57(1), 97 (1970)

    Article  MATH  Google Scholar 

  10. Hitchcock, D.B.: Am. Stat. 57(4), 254 (2003)

    Article  MathSciNet  Google Scholar 

  11. Porter, E.K.: Gravitational Wave Notes (Online Journal) 01 (2009)

  12. Babak, S., Baker, J.G., Benacquista, M.J., Cornish, N.J., Crowder, J., et al.: Class. Quantum Gravity 25, 184026 (2008)

    Article  ADS  Google Scholar 

  13. Ferraioli, L., Hueller, M., Vitale, S., Heinzel, G., Hewitson, M., Monsky, A., Nofrarias, M.: Phys. Rev. D 82(4), 042001 (2010)

    Article  ADS  Google Scholar 

  14. Antonucci, F., et al.: Class. Quantum Gravity 28(9), 094002 (2011)

    Article  ADS  Google Scholar 

  15. Cornish, N.J., Porter, E.K.: Phys. Rev. D 75(2), 021301 (2007)

    Article  ADS  Google Scholar 

  16. Cornish, N.J., Porter, E.K.: Class. Quantum Gravity 24(23), 5729 (2007)

    Article  ADS  MATH  Google Scholar 

  17. Gair, J.R., Porter, E.K.: Class. Quantum Gravity 26, 225004 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  18. Feroz, F., Gair, J.R., Hobson, M.P., Porter, E.K.: Class. Quantum Gravity 26, 215003 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  19. Babak, S., Gair, J.R., Porter, E.K.: Class. Quantum Gravity 26, 135004 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  20. Cornish, N.J., Porter, E.K.: Class. Quantum Gravity 23, 761 (2006)

    Article  ADS  Google Scholar 

  21. Cornish, N.J.: Class. Quantum Gravity 28, 094016 (2011)

    Article  ADS  Google Scholar 

  22. Littenberg, T.B., Cornish, N.J.: Phys. Rev. D 80, 063007 (2009)

    Article  ADS  Google Scholar 

  23. Cornish, N.J., Littenberg, T.B.: Phys. Rev. D 76, 083006 (2007)

    Article  ADS  Google Scholar 

  24. Crowder, J., Cornish, N.J.: Phys. Rev. D 75, 043008 (2007)

    Article  ADS  Google Scholar 

  25. Del Pozzo, W., Veitch, J., Vecchio, A.: Phys. Rev. D 83, 082002 (2011)

    Article  ADS  Google Scholar 

  26. Van der Sluys, M., et al.: Bull. Am. Astron. Soc. 38, 992 (2006)

    ADS  Google Scholar 

  27. Petiteau, A., et al.Phys. Rev. D 81, 104016 (2010)

    Article  ADS  Google Scholar 

  28. Harris, F.: Proc. IEEE 66(1), 51 (1978)

    Article  ADS  Google Scholar 

Download references

Acknowledgment

This research was supported by the Centre National d’Études Spatiales (CNES).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luigi Ferraioli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ferraioli, L., Porter, E.K., Armano, M. et al. Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method. Exp Astron 37, 109–125 (2014). https://doi.org/10.1007/s10686-014-9372-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10686-014-9372-7

Keywords

Navigation