Analysis of Modulated Multivariate Oscillations

The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is proposed, and the time-varying bias properties of the recovery method are derived. The method, an extension of wavelet ridge analysis to the multivariate case, identifies the common oscillation by seeking, at each point in time, a frequency for which a bandpassed version of the signal obtains a local maximum in power. The lowest-order bias is shown to involve a quantity, termed the instantaneous curvature, which measures the strength of local quadratic modulation of the signal after demodulation by the common oscillation frequency. The bias can be made to be small if the analysis filter, or wavelet, can be chosen such that the signal's instantaneous curvature changes little over the filter time scale. An application is presented to the detection of vortex motions in a set of freely-drifting oceanographic instruments tracking the ocean currents

Astrocladistics: Multivariate Evolutionary Analysis in Astrophysics

The Hubble tuning fork diagram, based on morphology and established in the 1930s, has always been the preferred scheme for classification of galaxies. However, the current large amount of data up to higher and higher redshifts asks for more sophisticated statistical approaches like multivariate analyses. Clustering analyses are still very confidential, and do not take into account the unavoidable characteristics in our Universe: evolution. Assuming branching evolution of galaxies as a 'transmission with modification', we have shown that the concepts and tools of phylogenetic systematics (cladistics) can be heuristically transposed to the case of galaxies. This approach that we call "astrocladistics", has now successfully been applied on several samples of galaxies and globular clusters. Maximum parsimony and distance-based approaches are the most popular methods to produce phylogenetic trees and, like most other studies, we had to discretize our variables. However, since astrophysical data are intrinsically continuous, we are contributing to the growing need for applying phylogenetic methods to continuous characters.Comment: Invited talk at the session: Astrostatistics (Statistical analysis of data related to Astronomy and Astrophysics

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

Permutation inference methods for multivariate meta-analysis

Multivariate meta-analysis is gaining prominence in evidence synthesis research because it enables simultaneous synthesis of multiple correlated outcome data, and random-effects models have generally been used for addressing between-studies heterogeneities. However, coverage probabilities of confidence regions or intervals for standard inference methods for random-effects models (e.g., restricted maximum likelihood estimation) cannot retain their nominal confidence levels in general, especially when the number of synthesized studies is small because their validities depend on large sample approximations. In this article, we provide permutation-based inference methods that enable exact joint inferences for average outcome measures without large sample approximations. We also provide accurate marginal inference methods under general settings of multivariate meta-analyses. We propose effective approaches for permutation inferences using optimal weighting based on the efficient score statistic. The effectiveness of the proposed methods is illustrated via applications to bivariate meta-analyses of diagnostic accuracy studies for airway eosinophilia in asthma and a network meta-analysis for antihypertensive drugs on incident diabetes, as well as through simulation experiments. In numerical evaluations performed via simulations, our methods generally provided accurate confidence regions or intervals under a broad range of settings, whereas the current standard inference methods exhibited serious undercoverage properties.Comment: 20 pages, 2 figures, 2 tabl

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 meta-analysis of QTL mapping studies

A large number of quantitative trait loci (QTLs) for milk production and quality traits in dairy cattle has been reported in literature. The large amount of information available could be exploited by meta-analyses to draw more general conclusions from results obtained in different experimental conditions (animals, statistical methodologies). QTL meta-analyses have been carried out to estimate the distribution of QTL effects in livestock and to find consensus on QTL position. In this study, multivariate dimension reduction techniques are used to analyse a database of dairy cattle QTL published results, in order to extract latent variables able to characterise the research. A total of 92 papers by 72 authors were found on 25 scientific Journals for the period January 1995-February 2008. More than thirty parameters were picked up from the articles. To overcome the problem of different map location, the flanking markers were mapped on release 4.1 of the Bos taurus genome sequence (www.ensembl. org). Their position was retrieved from public databases and, when absent, was calculated in silico by blasting (http://blast.wustl.edu/) the markers’ nucleotide sequence against the genomic sequence. Records were discarded if flanking markers or P-values were not available. After these edits, the final archive consisted of 1,162 records. Seven selected variables were analysed both with the Factor Analysis (FA), combined with the varimax rotation technique, and Principal Component Analysis (PCA). FA was able to explain 68% of the original variability with 3 latent factors: the first factor extracted was highly associated (factor loading of 0.98) to marker location along the chromosome and could be considered as a marker map index; the second factor showed factor loadings of 0.74 and 0.84 related to the variable number of animals involved and year of the experiment, respectively, and it can be regarded as an indicator of the dimension of the study; the third factor was correlated to the significance level of the statistical test (0.78), number of families (0.63), and, negatively, to the marker density (-0.43). It can be named as index of power of the experiment. Same patterns can be observed in the eigenvectors of PCA. Four PCs were able to explain about 80% of the original variance. The first two PCs basically underlined accurately the same structure found with the first two factors in FA, whereas PC3 and PC4 summarized the structure of F3. The score that each QTL gets on each Factor or PC could be useful to classify the original QTL records and make them more comparable once that the redundancy of information has been removed