Estimating the parameters of gravitational waves from neutron stars using an adaptive MCMC method

We present a Bayesian Markov chain Monte Carlo technique for estimating the astrophysical parameters of gravitational radiation signals from a neutron star in laser interferometer data. This computational algorithm can estimate up to six unknown parameters of the target, including the rotation frequency and frequency derivative, using reparametrization, delayed rejection and simulated annealing. We highlight how a simple extension of the method, distributed over multiple computer processors, will allow for a search over a narrow frequency band. The ultimate goal of this research is to search for sources at known locations, but uncertain spin parameters; an example would be SN1987A.

[1]  M. M. Casey,et al.  Setting upper limits on the strength of periodic gravitational waves from PSR J1939+2134 using the first science data from the GEO 600 and LIGO detectors , 2004 .

[2]  C. Cutler.  Gravitational Waves from Neutron Stars with Large Toroidal B-fields , 2002, gr-qc/0206051.

[3]  P. Green,et al.  Delayed rejection in reversible jump Metropolis–Hastings , 2001 .

[4]  Bernard F. Schutz,et al.  The GEO 600 gravitational wave detector , 2002 .

[5]  T. Steiman-Cameron,et al.  Rapid photometry of supernova 1987A: a 2.14 ms pulsar? , 2000 .

[6]  P. Brady,et al.  Searching for periodic sources with LIGO. II. Hierarchical searches , 1998, gr-qc/9812014.

[7]  L Tierney,et al.  Some adaptive monte carlo methods for Bayesian inference. , 1999, Statistics in medicine.

[8]  Lars Bildsten,et al.  Gravitational Radiation and Rotation of Accreting Neutron Stars , 1998, astro-ph/9804325.

[9]  B. Schutz,et al.  Data analysis of gravitational-wave signals from spinning neutron stars. I. The signal and its detection , 1998, gr-qc/9804014.

[10]  Antonietta Mira,et al.  Ordering, Slicing And Splitting Monte Carlo Markov Chains , 1998 .

[11]  J. Q. Smith,et al.  1. Bayesian Statistics 4 , 1993 .

[12]  Charles J. Geyer,et al.  Practical Markov Chain Monte Carlo , 1992 .

[13]  Joshua R. Smith,et al.  LIGO: the Laser Interferometer Gravitational-Wave Observatory , 1992, Science.

[14]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[15]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[16]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[17]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.