A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy

The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some artifact created by instrument noise - is a crucial step in the analysis. The on-going analyses of data from ground based detectors employ a frequentist approach to the detection problem. A detection statistic is chosen, for which background levels and detection efficiencies are estimated from Monte Carlo studies. This approach frames the detection problem in terms of an infinite collection of trials, with the actual measurement corresponding to some realization of this hypothetical set. Here we explore an alternative, Bayesian approach to the detection problem, that considers prior information and the actual data in hand. Our particular focus is on the computational techniques used to implement the Bayesian analysis. We find that the Parallel Tempered Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases of the anaylsis in a coherent framework. The signals are found by locating the posterior modes, the model parameters are characterized by mapping out the joint posterior distribution, and finally, the model evidence is computed by thermodynamic integration. As a demonstration, we consider the detection problem of selecting between models describing the data as instrument noise, or instrument noise plus the signal from a single compact galactic binary. The evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found to be in close agreement with those computed using a Reversible Jump Markov Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment

Detecting gravitational waves from highly eccentric compact binaries

In dense stellar regions, highly eccentric binaries of black holes and neutron stars can form through various n-body interactions. Such a binary could emit a significant fraction of its binding energy in a sequence of largely isolated gravitational wave bursts prior to merger. Given expected black hole and neutron star masses, many such systems will emit these repeated bursts at frequencies within the sensitive band of contemporary ground-based gravitational wave detectors. Unfortunately, existing gravitational wave searches are ill-suited to detect these signals. In this work, we adapt a "power stacking" method to the detection of gravitational wave signals from highly eccentric binaries. We implement this method as an extension of the Q-transform, a projection onto a multiresolution basis of windowed complex exponentials that has previously been used to analyze data from the network of LIGO/Virgo detectors. Our method searches for excess power over an ensemble of time-frequency tiles. We characterize the performance of our method using Monte Carlo experiments with signals injected in simulated detector noise. Our results indicate that the power stacking method achieves substantially better sensitivity to eccentric binary signals than existing localized burst searches.Comment: 17 pages, 20 figure

A method of detecting radio transients

Radio transients are sporadic signals and their detection requires that the backends of radio telescopes be equipped with the appropriate hardware and software to undertake this. Observational programs to detect transients can be dedicated or they can piggy-back on observations made by other programs. It is the single-dish single-transient (non-periodical) mode which is considered in this paper. Because neither the width of a transient nor the time of its arrival is known, a sequential analysis in the form of a cumulative sum (cusum) algorithm is proposed here. Computer simulations and real observation data processing are included to demonstrate the performance of the cusum. The use of the Hough transform is here proposed for the purpose of non-coherent de-dispersion. It is possible that the detected transients could be radio frequency interferences (RFI) and a procedure is proposed here which can distinguish between celestial signals and man-made RFI. This procedure is based on an analysis of the statistical properties of the signals

Random template placement and prior information

In signal detection problems, one is usually faced with the task of searching a parameter space for peaks in the likelihood function which indicate the presence of a signal. Random searches have proven to be very efficient as well as easy to implement, compared e.g. to searches along regular grids in parameter space. Knowledge of the parameterised shape of the signal searched for adds structure to the parameter space, i.e., there are usually regions requiring to be densely searched while in other regions a coarser search is sufficient. On the other hand, prior information identifies the regions in which a search will actually be promising or may likely be in vain. Defining specific figures of merit allows one to combine both template metric and prior distribution and devise optimal sampling schemes over the parameter space. We show an example related to the gravitational wave signal from a binary inspiral event. Here the template metric and prior information are particularly contradictory, since signals from low-mass systems tolerate the least mismatch in parameter space while high-mass systems are far more likely, as they imply a greater signal-to-noise ratio (SNR) and hence are detectable to greater distances. The derived sampling strategy is implemented in a Markov chain Monte Carlo (MCMC) algorithm where it improves convergence.Comment: Proceedings of the 8th Edoardo Amaldi Conference on Gravitational Waves. 7 pages, 4 figure

Prospects for the detection of electromagnetic counterparts to gravitational wave events

Various models for electromagnetic emissions correlated with the gravitational wave signals expected to be detectable by the current and planned gravitational wave detectors are studied. The position error on the location of a gravitational wave source is estimated, and is used to show that it could be possible to observe the electromagnetic counterparts to neutron star-neutron star or neutron star-black hole binary coalescences detected with the Advanced LIGO and the Virgo detectors.Comment: 5 pages, 1 table, 1 figur

Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.Comment: 11 pages, 6 figure

Energy Detection UWB Receiver Design using a Multi-resolution VHDL-AMS Description

Ultra Wide Band (UWB) impulse radio systems are appealing for location-aware applications. There is a growing interest in the design of UWB transceivers with reduced complexity and power consumption. Non-coherent approaches for the design of the receiver based on energy detection schemes seem suitable to this aim and have been adopted in the project the preliminary results of which are reported in this paper. The objective is the design of a UWB receiver with a top-down methodology, starting from Matlab-like models and refining the description down to the final transistor level. This goal will be achieved with an integrated use of VHDL for the digital blocks and VHDL-AMS for the mixed-signal and analog circuits. Coherent results are obtained using VHDL-AMS and Matlab. However, the CPU time cost strongly depends on the description used in the VHDL-AMS models. In order to show the functionality of the UWB architecture, the receiver most critical functions are simulated showing results in good agreement with the expectations