Gravitational-Wave Detection using Multivariate Analysis

Searches for gravitational-wave bursts (transient signals, typically of unknown waveform) require identification of weak signals in background detector noise. The sensitivity of such searches is often critically limited by non-Gaussian noise fluctuations which are difficult to distinguish from real signals, posing a key problem for transient gravitational-wave astronomy. Current noise rejection tests are based on the analysis of a relatively small number of measured properties of the candidate signal, typically correlations between detectors. Multivariate analysis (MVA) techniques probe the full space of measured properties of events in an attempt to maximise the power to accurately classify events as signal or background. This is done by taking samples of known background events and (simulated) signal events to train the MVA classifier, which can then be applied to classify events of unknown type. We apply the boosted decision tree (BDT) MVA technique to the problem of detecting gravitational-wave bursts associated with gamma-ray bursts. We find that BDTs are able to increase the sensitive distance reach of the search by as much as 50%, corresponding to a factor of ~3 increase in sensitive volume. This improvement is robust against trigger sky position, large sky localisation error, poor data quality, and the simulated signal waveforms that are used. Critically, we find that the BDT analysis is able to detect signals that have different morphologies to those used in the classifier training and that this improvement extends to false alarm probabilities beyond the 3{\sigma} significance level. These findings indicate that MVA techniques may be used for the robust detection of gravitational-wave bursts with a priori unknown waveform.Comment: 14 pages, 12 figure

Special section on modern multivariate analysis

A critically challenging problem facing statisticians is the identification of a suitable framework which consolidates data of various types, from different sources, and across different time frames or scales (many of which can be missing), and from which appropriate analysis and subsequent inference can proceed.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS529 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimization of multivariate analysis for IACT stereoscopic systems

Multivariate methods have been recently introduced and successfully applied for the discrimination of signal from background in the selection of genuine very-high energy gamma-ray events with the H.E.S.S. Imaging Atmospheric Cerenkov Telescope. The complementary performance of three independent reconstruction methods developed for the H.E.S.S. data analysis, namely Hillas, model and 3D-model suggests the optimization of their combination through the application of a resulting efficient multivariate estimator. In this work the boosted decision tree method is proposed leading to a significant increase in the signal over background ratio compared to the standard approaches. The improved sensitivity is also demonstrated through a comparative analysis of a set of benchmark astrophysical sources.Comment: 10 pages, 8 figures, 3 tables, accepted for publication in Astroparticle Physic

MULTIVARIATE ANALYSIS IN VECTOR TIME SERIES

This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Peña and Box (1987) and Peña and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed.

Multivariate analysis of the globular clusters in M87

An objective classification of 147 globular clusters in the inner region of the giant elliptical galaxy M87 is carried out with the help of two methods of multivariate analysis. First independent component analysis is used to determine a set of independent variables that are linear combinations of various observed parameters (mostly Lick indices) of the globular clusters. Next K-means cluster analysis is applied on the independent components, to find the optimum number of homogeneous groups having an underlying structure. The properties of the four groups of globular clusters thus uncovered are used to explain the formation mechanism of the host galaxy. It is suggested that M87 formed in two successive phases. First a monolithic collapse, which gave rise to an inner group of metal-rich clusters with little systematic rotation and an outer group of metal-poor clusters in eccentric orbits. In a second phase, the galaxy accreted low-mass satellites in a dissipationless fashion, from the gas of which the two other groups of globular clusters formed. Evidence is given {\bf for a blue stellar population in the more metal rich clusters, which we interpret by Helium enrichment.} Finally, it is found that the clusters of M87 differ in some of their chemical properties (NaD, TiO1, light element abundances) from globular clusters in our Galaxy and M31.Comment: 19 pages, 10 figures,Accepted in Publications of The Astronomical Society of Australi

Multivariate Analysis from a Statistical Point of View

Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, many of the common approaches were borrowed from other fields. We clarify what the goal of a multivariate algorithm should be for the search for a new particle and compare different approaches. We also translate the Neyman-Pearson theory into the language of statistical learning theory.Comment: Talk from PhyStat2003, Stanford, Ca, USA, September 2003, 4 pages, LaTeX, 1 eps figures. PSN WEJT00

Multivariate analysis of morphological variation in enset (Ensete ventricosum (Welw.) Cheesman) reveals regional and clinal variation in germplasm from south and south western Ethiopia

Enset (Ensete ventricosum (Welw.) Cheesman) is cultivated by millions of people across Ethiopia in diverse agro-ecological and cultural settings, selecting for various agronomic traits. However, as for other underutilized crops, our understanding of the diversity and utilization of enset remains limited. This work sought to redress this limitation by estimating morphological diversity among enset accessions collected from major enset growing regions, including across altitudinal gradients. In total, landraces comprising 387 accessions originating from nine regions of Ethiopia were characterized using multivariate analysis of 15 quantitative traits. Cluster analysis grouped accessions in to five distinct classes with maximum number of accessions 338 in cluster (I) and minimum 1 in cluster (V). The clustering of accessions did not show grouping on the basis of region of origin. The first four principal components accounted for ~74% of the total variance. Linear discriminant analysis indicated that around 40.8% (160 accessions) and 45.2% (175 accession) of the studied accessions were correctly classified to their respective regions of origin altitude groups, respectively. The breadth of phenotypic differences in these 15 traits suggests significant degrees of genetic variation. These traits will be exploited to identify potential donors for future enset improvement efforts