13,171 research outputs found
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
Selection of proposal distributions for generalized importance sampling estimators
The standard importance sampling (IS) estimator, generally does not work well
in examples involving simultaneous inference on several targets as the
importance weights can take arbitrarily large values making the estimator
highly unstable. In such situations, alternative generalized IS estimators
involving samples from multiple proposal distributions are preferred. Just like
the standard IS, the success of these multiple IS estimators crucially depends
on the choice of the proposal distributions. The selection of these proposal
distributions is the focus of this article. We propose three methods based on
(i) a geometric space filling coverage criterion, (ii) a minimax variance
approach, and (iii) a maximum entropy approach. The first two methods are
applicable to any multi-proposal IS estimator, whereas the third approach is
described in the context of Doss's (2010) two-stage IS estimator. For the first
method we propose a suitable measure of coverage based on the symmetric
Kullback-Leibler divergence, while the second and third approaches use
estimates of asymptotic variances of Doss's (2010) IS estimator and Geyer's
(1994) reverse logistic estimator, respectively. Thus, we provide consistent
spectral variance estimators for these asymptotic variances. The proposed
methods for selecting proposal densities are illustrated using various detailed
examples
Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data
In this paper, I propose a technique for recovering quantum dynamical
information from imaginary-time data via the resolution of a one-dimensional
Hamburger moment problem. It is shown that the quantum autocorrelation
functions are uniquely determined by and can be reconstructed from their
sequence of derivatives at origin. A general class of reconstruction algorithms
is then identified, according to Theorem 3. The technique is advocated as
especially effective for a certain class of quantum problems in continuum
space, for which only a few moments are necessary. For such problems, it is
argued that the derivatives at origin can be evaluated by Monte Carlo
simulations via estimators of finite variances in the limit of an infinite
number of path variables. Finally, a maximum entropy inversion algorithm for
the Hamburger moment problem is utilized to compute the quantum rate of
reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.
An invitation to quantum tomography
We describe quantum tomography as an inverse statistical problem and show how
entropy methods can be used to study the behaviour of sieved maximum likelihood
estimators. There remain many open problems, and a main purpose of the paper is
to bring these to the attention of the statistical community.Comment: 19 pages, submitted to J. Royal Stat. Soc. B. Note added 31/05/04: a
revised version with further statistical results but less mathematical
details, and with co-author Luis Artiles, has been posted on arXiv as
math.ST/040559
Neural networks and separation of Cosmic Microwave Background and astrophysical signals in sky maps
The Independent Component Analysis (ICA) algorithm is implemented as a neural
network for separating signals of different origin in astrophysical sky maps.
Due to its self-organizing capability, it works without prior assumptions on
the signals, neither on their frequency scaling, nor on the signal maps
themselves; instead, it learns directly from the input data how to separate the
physical components, making use of their statistical independence. To test the
capabilities of this approach, we apply the ICA algorithm on sky patches, taken
from simulations and observations, at the microwave frequencies, that are going
to be deeply explored in a few years on the whole sky, by the Microwave
Anisotropy Probe (MAP) and by the {\sc Planck} Surveyor Satellite. The maps are
at the frequencies of the Low Frequency Instrument (LFI) aboard the {\sc
Planck} satellite (30, 44, 70 and 100 GHz), and contain simulated astrophysical
radio sources, Cosmic Microwave Background (CMB) radiation, and Galactic
diffuse emissions from thermal dust and synchrotron. We show that the ICA
algorithm is able to recover each signal, with precision going from 10% for the
Galactic components to percent for CMB; radio sources are almost completely
recovered down to a flux limit corresponding to , where
is the rms level of CMB fluctuations. The signal recovering
possesses equal quality on all the scales larger then the pixel size. In
addition, we show that the frequency scalings of the input signals can be
partially inferred from the ICA outputs, at the percent precision for the
dominant components, radio sources and CMB.Comment: 15 pages; 6 jpg and 1 ps figures. Final version to be published in
MNRA
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