A Case Study of On-the-Fly Wide-Field Radio Imaging Applied to the Gravitational-wave Event GW 151226

We apply a newly-developed On-the-Fly mosaicing technique on the NSF's Karl G. Jansky Very Large Array (VLA) at 3 GHz in order to carry out a sensitive search for an afterglow from the Advanced LIGO binary black hole merger event GW 151226. In three epochs between 1.5 and 6 months post-merger we observed a 100 sq. deg region, with more than 80% of the survey region having a RMS sensitivity of better than 150 uJy/beam, in the northern hemisphere having a merger containment probability of 10%. The data were processed in near-real-time, and analyzed to search for transients and variables. No transients were found but we have demonstrated the ability to conduct blind searches in a time-frequency phase space where the predicted afterglow signals are strongest. If the gravitational wave event is contained within our survey region, the upper limit on any late-time radio afterglow from the merger event at an assumed mean distance of 440 Mpc is about 1e29 erg/s/Hz. Approximately 1.5% of the radio sources in the field showed variability at a level of 30%, and can be attributed to normal activity from active galactic nuclei. The low rate of false positives in the radio sky suggests that wide-field imaging searches at a few Gigahertz can be an efficient and competitive search strategy. We discuss our search method in the context of the recent afterglow detection from GW 170817 and radio follow-up in future gravitational wave observing runs.Comment: 11 pages. 6 figures. 1 table. Accepted for publication in ApJ Letter

Detection of a sparse submatrix of a high-dimensional noisy matrix

We observe a $N\times M$ matrix $Y_{ij}=s_{ij}+\xi_{ij}$ with $\xi_{ij}\sim {\mathcal {N}}(0,1)$ i.i.d. in $i,j$, and $s_{ij}\in \mathbb {R}$. We test the null hypothesis $s_{ij}=0$ for all $i,j$ against the alternative that there exists some submatrix of size $n\times m$ with significant elements in the sense that $s_{ij}\ge a>0$. We propose a test procedure and compute the asymptotical detection boundary $a$ so that the maximal testing risk tends to 0 as $M\to\infty$, $N\to\infty$, $p=n/N\to0$, $q=m/M\to0$. We prove that this boundary is asymptotically sharp minimax under some additional constraints. Relations with other testing problems are discussed. We propose a testing procedure which adapts to unknown $(n,m)$ within some given set and compute the adaptive sharp rates. The implementation of our test procedure on synthetic data shows excellent behavior for sparse, not necessarily squared matrices. We extend our sharp minimax results in different directions: first, to Gaussian matrices with unknown variance, next, to matrices of random variables having a distribution from an exponential family (non-Gaussian) and, finally, to a two-sided alternative for matrices with Gaussian elements.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ470 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Revisiting Multi-Subject Random Effects in fMRI: Advocating Prevalence Estimation

Random Effects analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation in the study group since in order to be significant, an activation has to be larger than the inter-subject variability. Indeed, detected regions are smaller when using random effect analysis versus fixed effects. The statistical assumptions behind the classic random effects model are that the effect in each location is normally distributed over subjects, and "activation" refers to a non-null mean effect. We argue this model is unrealistic compared to the true population variability, where, due to functional plasticity and registration anomalies, at each brain location some of the subjects are active and some are not. We propose a finite-Gaussian--mixture--random-effect. A model that amortizes between-subject spatial disagreement and quantifies it using the "prevalence" of activation at each location. This measure has several desirable properties: (a) It is more informative than the typical active/inactive paradigm. (b) In contrast to the hypothesis testing approach (thus t-maps) which are trivially rejected for large sample sizes, the larger the sample size, the more informative the prevalence statistic becomes. In this work we present a formal definition and an estimation procedure of this prevalence. The end result of the proposed analysis is a map of the prevalence at locations with significant activation, highlighting activations regions that are common over many brains

Graph-Based Change-Point Detection

We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations, is proposed. The graph-based approach is non-parametric, and can be applied to any data set as long as an informative similarity measure on the sample space can be defined. Accurate analytic approximations to the significance of graph-based scan statistics for both the single change-point and the changed interval alternatives are provided. Simulations reveal that the new approach has better power than existing approaches when the dimension of the data is moderate to high. The new approach is illustrated on two applications: The determination of authorship of a classic novel, and the detection of change in a network over time

Identification of activity peaks in time-tagged data with a scan-statistics driven clustering method and its application to gamma-ray data samples

The investigation of activity periods in time-tagged data-samples is a topic of large interest. Among Astrophysical samples, gamma-ray sources are widely studied, due to the huge quasi-continuum data set available today from the FERMI-LAT and AGILE-GRID gamma-ray telescopes. To reveal flaring episodes of a given gamma-ray source, researchers make use of binned light-curves. This method suffers several drawbacks: the results depends on time-binning, the identification of activity periods is difficult for bins with low signal to noise ratio. I developed a general temporal-unbinned method to identify flaring periods in time-tagged data and discriminate statistically-significant flares: I propose an event clustering method in one-dimension to identify flaring episodes, and Scan-statistics to evaluate the flare significance within the whole data sample. This is a photometric algorithm. The comparison of the photometric results (e.g., photometric flux, gamma-ray spatial distribution) for the identified peaks with the standard likelihood analysis for the same period is mandatory to establish if source-confusion is spoiling results. The procedure can be applied to reveal flares in any time-tagged data sample. The study of the gamma ray activity of 3C 454.3 and of the fast variability of the Crab Nebula are shown as examples. The result of the proposed method is similar to a photometric light curve, but peaks are resolved, they are statistically significant within the whole period of investigation, and peak detection capability does not suffer time-binning related issues. The method can be applied for gamma-ray sources of known celestial position. Furthermore the method can be used when it is necessary to assess the statistical significance within the whole period of investigation of a flare from an unknown gamma-ray source.Comment: 17 pages, 10 figures Accepted for publication in A&

Optimal analysis of azimuthal features in the CMB

We present algorithms for searching for azimuthally symmetric features in CMB data. Our algorithms are fully optimal for masked all-sky data with inhomogeneous noise, computationally fast, simple to implement, and make no approximations. We show how to implement the optimal analysis in both Bayesian and frequentist cases. In the Bayesian case, our algorithm for evaluating the posterior likelihood is so fast that we can do a brute-force search over parameter space, rather than using a Monte Carlo Markov chain. Our motivating example is searching for bubble collisions, a pre-inflationary signal which can be generated if multiple tunneling events occur in an eternally inflating spacetime, but our algorithms are general and should be useful in other contexts.Comment: 30 pages, 5 figure