54,345 research outputs found
The adaptive patched cubature filter and its implementation
There are numerous contexts where one wishes to describe the state of a
randomly evolving system. Effective solutions combine models that quantify the
underlying uncertainty with available observational data to form scientifically
reasonable estimates for the uncertainty in the system state. Stochastic
differential equations are often used to mathematically model the underlying
system.
The Kusuoka-Lyons-Victoir (KLV) approach is a higher order particle method
for approximating the weak solution of a stochastic differential equation that
uses a weighted set of scenarios to approximate the evolving probability
distribution to a high order of accuracy. The algorithm can be performed by
integrating along a number of carefully selected bounded variation paths. The
iterated application of the KLV method has a tendency for the number of
particles to increase. This can be addressed and, together with local dynamic
recombination, which simplifies the support of discrete measure without harming
the accuracy of the approximation, the KLV method becomes eligible to solve the
filtering problem in contexts where one desires to maintain an accurate
description of the ever-evolving conditioned measure.
In addition to the alternate application of the KLV method and recombination,
we make use of the smooth nature of the likelihood function and high order
accuracy of the approximations to lead some of the particles immediately to the
next observation time and to build into the algorithm a form of automatic high
order adaptive importance sampling.Comment: to appear in Communications in Mathematical Sciences. arXiv admin
note: substantial text overlap with arXiv:1311.675
Correlated noise in networks of gravitational-wave detectors: subtraction and mitigation
One of the key science goals of advanced gravitational-wave detectors is to
observe a stochastic gravitational-wave background. However, recent work
demonstrates that correlated magnetic fields from Schumann resonances can
produce correlated strain noise over global distances, potentially limiting the
sensitivity of stochastic background searches with advanced detectors. In this
paper, we estimate the correlated noise budget for the worldwide Advanced LIGO
network and conclude that correlated noise may affect upcoming measurements. We
investigate the possibility of a Wiener filtering scheme to subtract correlated
noise from Advanced LIGO searches, and estimate the required specifications. We
also consider the possibility that residual correlated noise remains following
subtraction, and we devise an optimal strategy for measuring astronomical
parameters in the presence of correlated noise. Using this new formalism, we
estimate the loss of sensitivity for a broadband, isotropic stochastic
background search using 1 yr of LIGO data at design sensitivity. Given our
current noise budget, the uncertainty with which LIGO can estimate energy
density will likely increase by a factor of ~4--if it is impossible to achieve
significant subtraction. Additionally, narrowband cross-correlation searches
may be severely affected at low frequencies f < 45 Hz without effective
subtraction.Comment: 16 pages, 8 figure
The Neural Particle Filter
The robust estimation of dynamically changing features, such as the position
of prey, is one of the hallmarks of perception. On an abstract, algorithmic
level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing
signals based on the history of observations, provides a mathematical framework
for dynamic perception in real time. Since the general, nonlinear filtering
problem is analytically intractable, particle filters are considered among the
most powerful approaches to approximating the solution numerically. Yet, these
algorithms prevalently rely on importance weights, and thus it remains an
unresolved question how the brain could implement such an inference strategy
with a neuronal population. Here, we propose the Neural Particle Filter (NPF),
a weight-less particle filter that can be interpreted as the neuronal dynamics
of a recurrently connected neural network that receives feed-forward input from
sensory neurons and represents the posterior probability distribution in terms
of samples. Specifically, this algorithm bridges the gap between the
computational task of online state estimation and an implementation that allows
networks of neurons in the brain to perform nonlinear Bayesian filtering. The
model captures not only the properties of temporal and multisensory integration
according to Bayesian statistics, but also allows online learning with a
maximum likelihood approach. With an example from multisensory integration, we
demonstrate that the numerical performance of the model is adequate to account
for both filtering and identification problems. Due to the weightless approach,
our algorithm alleviates the 'curse of dimensionality' and thus outperforms
conventional, weighted particle filters in higher dimensions for a limited
number of particles
A stochastic template placement algorithm for gravitational wave data analysis
This paper presents an algorithm for constructing matched-filter template
banks in an arbitrary parameter space. The method places templates at random,
then removes those which are "too close" together. The properties and
optimality of stochastic template banks generated in this manner are
investigated for some simple models. The effectiveness of these template banks
for gravitational wave searches for binary inspiral waveforms is also examined.
The properties of a stochastic template bank are then compared to the
deterministically placed template banks that are currently used in
gravitational wave data analysis.Comment: 14 pages, 11 figure
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