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

Bayesian inference on astrophysical binary inspirals based on gravitational-wave measurements

Gravitational waves are predicted by general relativity theory. Their existence could be confirmed by astronomical observations, but until today they have not yet been measured directly. A measurement would not only confirm general relativity, but also allow for interesting astronomical observations. Great effort is currently being expended to facilitate gravitational radiation measurement, most notably through earth-bound interferometers (such as LIGO and Virgo), and the planned space-based LISA interferometer. Earth-bound interferometers have recently taken up operation, so that a detection might be made at any time, while the space-borne LISA interferometer is scheduled to be launched within the next decade.Among the most promising signals for a detection are the waves emitted by the inspiral of a binary system of stars or black holes. The observable gravitational-wave signature of such an event is determined by properties of the inspiralling system, which may in turn be inferred from theobserved data. A Bayesian inference framework for the estimation of parameters of binary inspiral events as measured by ground- and space-based interferometers is described here. Furthermore, appropriate computational methods are developed that are necessary for its application in practice. Starting with a simplified model considering only 5 parameters and data from a single earth-bound interferometer, the model is subsequently refined by extending it to 9 parameters, measurements from several interferometers, and more accurate signal waveform approximations. A realistic joint prior density for the 9 parameters is set up. For the LISA application the model is generalised so that the noise spectrum is treated as unknown as well and can be inferred along with the signal parameters. Inference through the posterior distribution is facilitated by the implementation of Markov chain Monte Carlo (MCMC) methods. The posterior distribution exhibits many local modes, and there is only a small "attraction region" around the global mode(s), making it hard, if not impossible, for basic MCMC algorithms to find the relevant region in parameter space. This problem is solved by introducing a parallel tempering algorithm. Closer investigation of its internal functionality yields some insight into a proper setup of this algorithm, which in turn also enables the efficient implementation for the LISA problem with its vastly enlarged parameter space. Parallel programming was used to implement this computationally expensive MCMC algorithm, so that the code can be run efficiently on a computer cluster. In this thesis, a Bayesian approach to gravitational wave astronomy is shown to be feasible and promising

Localizing gravitational wave sources with optical telescopes and combining electromagnetic and gravitational wave data

Neutron star binaries, which are among the most promising sources for the direct detection of gravitational waves (GW) by ground based detectors, are also potential electromagnetic (EM) emitters. Gravitational waves will provide a new window to observe these events and hopefully give us glimpses of new astrophysics. In this paper, we discuss how EM information of these events can considerably improve GW parameter estimation both in terms of accuracy and computational power requirement. And then in return how GW sky localization can help EM astronomers in follow-up studies of sources which did not yield any prompt emission. We discuss how both EM source information and GW source localization can be used in a framework of multi-messenger astronomy. We illustrate how the large error regions in GW sky localizations can be handled in conducting optical astronomy in the advance detector era. We show some preliminary results in the context of an array of optical telescopes called BlackGEM, dedicated for optical follow-up of GW triggers, that is being constructed in La Silla, Chile and is expected to operate concurrent to the advanced GW detectors.Comment: 8 pages, 8 figures, Proceeding for Sant Cugat Forum for Astrophysic

Gravitational-Wave Astronomy with Inspiral Signals of Spinning Compact-Object Binaries

Inspiral signals from binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave interferometers (LIGO, Virgo, GEO-600 and TAMA-300). We present parameter-estimation simulations for inspirals of black-hole--neutron-star binaries using Markov-chain Monte-Carlo methods. For the first time, we have both estimated the parameters of a binary inspiral source with a spinning component and determined the accuracy of the parameter estimation, for simulated observations with ground-based gravitational-wave detectors. We demonstrate that we can obtain the distance, sky position, and binary orientation at a higher accuracy than previously suggested in the literature. For an observation of an inspiral with sufficient spin and two or three detectors we find an accuracy in the determination of the sky position of typically a few tens of square degrees.Comment: v2: major conceptual changes, 4 pages, 1 figure, 1 table, submitted to ApJ

The effects of LIGO detector noise on a 15-dimensional Markov-chain Monte-Carlo analysis of gravitational-wave signals

Gravitational-wave signals from inspirals of binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave (GW) interferometers (LIGO, Virgo, and GEO-600). We present parameter-estimation results from our Markov-chain Monte-Carlo code SPINspiral on signals from binaries with precessing spins. Two data sets are created by injecting simulated GW signals into either synthetic Gaussian noise or into LIGO detector data. We compute the 15-dimensional probability-density functions (PDFs) for both data sets, as well as for a data set containing LIGO data with a known, loud artefact ("glitch"). We show that the analysis of the signal in detector noise yields accuracies similar to those obtained using simulated Gaussian noise. We also find that while the Markov chains from the glitch do not converge, the PDFs would look consistent with a GW signal present in the data. While our parameter-estimation results are encouraging, further investigations into how to differentiate an actual GW signal from noise are necessary.Comment: 11 pages, 2 figures, NRDA09 proceeding

Bayesian parameter estimation in the second LISA Pathfinder Mock Data Challenge

A main scientific output of the LISA Pathfinder mission is to provide a noise model that can be extended to the future gravitational wave observatory, LISA. The success of the mission depends thus upon a deep understanding of the instrument, especially the ability to correctly determine the parameters of the underlying noise model. In this work we estimate the parameters of a simplified model of the LISA Technology Package (LTP) instrument. We describe the LTP by means of a closed-loop model that is used to generate the data, both injected signals and noise. Then, parameters are estimated using a Bayesian framework and it is shown that this method reaches the optimal attainable error, the Cramer-Rao bound. We also address an important issue for the mission: how to efficiently combine the results of different experiments to obtain a unique set of parameters describing the instrument.Comment: 14 pages, 4 figures, submitted to PR

Analyse und Bewertung zu Stand und Entwicklungsmöglichkeiten von Futterbau und Tierernährung im ökologischen Landbau - Themenbezogenes Netzwerk Tierernährung im Ökologischen Landbau

Das Ziel des Vorhabens war es, ein Netzwerk zum Thema „Futterbau und Tierernährung im Ökologischen Landbau“ zu etablieren. Es soll dazu dienen, Fachleute aus der landwirtschaftlichen Praxis, der Beratung und der Forschung zu verbinden, um einen Wissensaustausch zu ermöglichen und durch inter- und transdisziplinäre Diskussionen Entwicklungsperspektiven aufzuzeigen. Zur detaillierten Analyse und Bewertung der Problematik wurden Arbeitsgruppen gebildet, die für die Bereiche Rinder-, Schweine- und Geflügelfütterung jeweils den Handlungsbedarf aufzeigen und Lösungsansätze für die bedarfsgerechte Versorgung dieser Nutztiere insbesondere im Hinblick auf die Umsetzung der 100 % Biofütterung erarbeiten sollten. Ergänzend dazu wurde eine umfangreiche Literaturrecherche und Schwachstellenanalyse durchgeführt. Die Steuerungsgruppe als zentrales Organ legte die Arbeitsweise des Netzwerks fest und gab die Inhalte vor, die als Grundlage für Diskussionen und wissenschaftliche Auseinandersetzungen dienen sollten. Sie wirkte beratend bei der Ausarbeitung der Schwachstellenanalyse mit und formulierte die Ziele des im Rahmen des Projektes durchgeführten Workshops. Die Koordination des gesamten Vorhabens oblag dem Zentrum Landwirtschaft und Umwelt der Universität Göttingen. Auf einem Workshop im März 2007 wurden die Ergebnisse der Netzwerkarbeit vorgestellt und mit Experten aus Wissenschaft, Beratung und Praxis diskutiert und bewertet. Empfehlungen für Futterbau und Tierernährung im ökologischen Landbau wurden differenziert nach Umsetzungs- und Forschungsbedarf formuliert. Zusätzlich wurden die Ergebnisse in der Zeitschrift „Ökologie und Landbau“ in Form eines Sonderheftes publiziert und so einer breiten landwirtschaftlichen Fachöffentlichkeit zugänglich gemacht. Die Arbeit im Netzwerk hat sich als effiziente Methode erwiesen, vorhandenes Wissen zwischen und innerhalb der einzelnen Disziplinen und Institutionen zu transferieren und zu bündeln. Sie sollte im Interesse aller Beteiligten weitergeführt werden, um den wissenschaftlichen Austausch weiter zu entwickeln und für Kooperationen in der Forschung, aber auch zwischen Praxis und Forschung zu nutzen

Parameter estimation of spinning binary inspirals using Markov-chain Monte Carlo

We present a Markov-chain Monte-Carlo (MCMC) technique to study the source parameters of gravitational-wave signals from the inspirals of stellar-mass compact binaries detected with ground-based gravitational-wave detectors such as LIGO and Virgo, for the case where spin is present in the more massive compact object in the binary. We discuss aspects of the MCMC algorithm that allow us to sample the parameter space in an efficient way. We show sample runs that illustrate the possibilities of our MCMC code and the difficulties that we encounter.Comment: 10 pages, 2 figures, submitted to Classical and Quantum Gravit

Inference on inspiral signals using LISA MLDC data

In this paper we describe a Bayesian inference framework for analysis of data obtained by LISA. We set up a model for binary inspiral signals as defined for the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte Carlo (MCMC) algorithm to facilitate exploration and integration of the posterior distribution over the 9-dimensional parameter space. Here we present intermediate results showing how, using this method, information about the 9 parameters can be extracted from the data.Comment: Accepted for publication in Classical and Quantum Gravity, GWDAW-11 special issu