3,540 research outputs found
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
A change-point problem and inference for segment signals
We address the problem of detection and estimation of one or two
change-points in the mean of a series of random variables. We use the formalism
of set estimation in regression: To each point of a design is attached a binary
label that indicates whether that point belongs to an unknown segment and this
label is contaminated with noise. The endpoints of the unknown segment are the
change-points. We study the minimal size of the segment which allows
statistical detection in different scenarios, including when the endpoints are
separated from the boundary of the domain of the design, or when they are
separated from one another. We compare this minimal size with the minimax rates
of convergence for estimation of the segment under the same scenarios. The aim
of this extensive study of a simple yet fundamental version of the change-point
problem is twofold: Understanding the impact of the location and the separation
of the change points on detection and estimation and bringing insights about
the estimation and detection of convex bodies in higher dimensions.Comment: arXiv admin note: substantial text overlap with arXiv:1404.622
Convex set detection
We address the problem of one dimensional segment detection and estimation,
in a regression setup. At each point of a fixed or random design, one observes
whether that point belongs to the unknown segment or not, up to some additional
noise. We try to understand what the minimal size of the segment is so it can
be accurately seen by some statistical procedure, and how this minimal size
depends on some a priori knowledge about the location of the unknown segment
Matched Filtering of Numerical Relativity Templates of Spinning Binary Black Holes
Tremendous progress has been made towards the solution of the
binary-black-hole problem in numerical relativity. The waveforms produced by
numerical relativity will play a role in gravitational wave detection as either
test-beds for analytic template banks or as template banks themselves. As the
parameter space explored by numerical relativity expands, the importance of
quantifying the effect that each parameter has on first the detection of
gravitational waves and then the parameter estimation of their sources
increases. In light of this, we present a study of equal-mass, spinning
binary-black-hole evolutions through matched filtering techniques commonly used
in data analysis. We study how the match between two numerical waveforms varies
with numerical resolution, initial angular momentum of the black holes and the
inclination angle between the source and the detector. This study is limited by
the fact that the spinning black-hole-binaries are oriented axially and the
waveforms only contain approximately two and a half orbits before merger. We
find that for detection purposes, spinning black holes require the inclusion of
the higher harmonics in addition to the dominant mode, a condition that becomes
more important as the black-hole-spins increase. In addition, we conduct a
preliminary investigation of how well a template of fixed spin and inclination
angle can detect target templates of arbitrary spin and inclination for the
axial case considered here
Minimax rank estimation for subspace tracking
Rank estimation is a classical model order selection problem that arises in a
variety of important statistical signal and array processing systems, yet is
addressed relatively infrequently in the extant literature. Here we present
sample covariance asymptotics stemming from random matrix theory, and bring
them to bear on the problem of optimal rank estimation in the context of the
standard array observation model with additive white Gaussian noise. The most
significant of these results demonstrates the existence of a phase transition
threshold, below which eigenvalues and associated eigenvectors of the sample
covariance fail to provide any information on population eigenvalues. We then
develop a decision-theoretic rank estimation framework that leads to a simple
ordered selection rule based on thresholding; in contrast to competing
approaches, however, it admits asymptotic minimax optimality and is free of
tuning parameters. We analyze the asymptotic performance of our rank selection
procedure and conclude with a brief simulation study demonstrating its
practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio
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