arXiv subjects
Publications and source records attributed to Nelson Christensen.
LIGO recently conducted its third scientific data run, S3. Here we summarize the veto and data quality studies conducted by the LIGO Scientific Collaboration in connection with the search for binary inspiral signals in the S3 data. LIGO's interferometer channels and physical environmental monitors were monitored, and events in these channels coincident with inspiral triggers were examined.
It is computationally expensive to search the large parameter space associated with a gravitational wave signal of uncertain frequency, such as might be expected from the possible pulsar generated by SN1987A. To address this difficulty we have developed a Markov Chain Monte Carlo method that performs a time-domain Bayesian search for a signal over a 4 Hz frequency band and a spindown of magnitude of up to $1\ee{-9}$ Hz/s. We use Monte Carlo simulations to set upper limits on signal amplitude with this technique, which we intend to apply to a gravitational wave search.
The Laser Interferometer Space Antenna (LISA) is expected to detect gravitational radiation from a large number of compact binary systems. We present a method by which these signals can be identified and have their parameters estimated. Our approach uses Bayesian inference, specifically the application of a Markov chain Monte Carlo method. The simulation study that we present here considers a large number of sinusoidal signals in noise, and our method estimates the number of periodic signals present in the data, the parameters for these signals and the noise level. The method is significantly better than classical spectral techniques at performing these tasks and does not use stopping criteria for estimating the number of signals present.
We present a Markov chain Monte Carlo technique for detecting gravitational radiation from a neutron star in laser interferometer data. The 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 a known locations, but uncertain spin parameters, such as may be found in SN1987A.
Presented is a summary of studies by the LIGO Scientific Collaboration's Inspiral Analysis Group on the development of possible vetoes to be used in evaluation of data from the first two LIGO science data runs. Numerous environmental monitor signals and interferometer control channels have been analyzed in order to characterize the interferometers' performance. The results of studies on selected data segments are provided in this paper. The vetoes used in the compact binary inspiral analyses of LIGO's S1 and S2 science data runs are presented and discussed.
The Markov chain Monte Carlo methods offer practical procedures for detecting signals characterized by a large number of parameters and under conditions of low signal-to-noise ratio. We present a Metropolis-Hastings algorithm capable of inferring the spin and orientation parameters of a neutron star from its periodic gravitational wave signature seen by laser interferometric detectors
We present a strategy for a statistically rigorous Bayesian approach to the problem of determining cosmological parameters from the results of observations of anisotropies in the cosmic microwave background. Our strategy relies on Markov chain Monte Carlo methods, specifically the Metropolis-Hastings algorithm, to perform the necessary high-dimensional integrals. We describe the Metropolis-Hastings algorithm in detail and discuss the results of our test on simulated data.
We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we demonstrate the potential that MCMC techniques may hold for the computation of posterior distributions of parameters of the binary system that created the gravity radiation signal. We describe the use of the Gibbs sampler method, and present examples whereby signals are detected and analyzed from within noisy data.
We discuss entanglement of multiparticle quantum systems. We propose a potential measure of a type of entanglement of pure states of n qubits, the n-tangle. For a system of two qubits the n-tangle is equal to the square of the concurrence, and for systems of three qubits it is equal to the ''residual entanglement''. We show that the n -tangle, is also equal to the generalization of concurrence squared for even n, and use this fact to prove that the n-tangle is an entanglement monotone. However, the n-tangle is undefined for odd n>3. Finally we propose a measure related to the n-tangle for mixed state systems of n qubits, and find an analytical formula for this measure for even n.
We present a strategy for a statistically rigorous Bayesian approach to the problem of determining cosmological parameters from the results of observations of anisotropies in the cosmic microwave radiation background. We propose the application of Markov chain Monte Carlo methods, specifically the Metropolis-Hastings algorithm, to estimate the parameters. A complete statistical analysis is presented, with the Metropolis-Hastings algorithm described in detail.