14,018 research outputs found
Moment Estimation Using a Marginalized Transform
We present a method for estimating mean and covariance of a transformed Gaussian random variable. The method is based on evaluations of the transforming function and resembles the unscented transform and Gauss-Hermite integration in that respect. The information provided by the evaluations is used in a Bayesian framework to form a posterior description of the parameters in a model of the transforming function. Estimates are then derived by marginalizing these parameters from the analytical expression of the mean and covariance. An estimation algorithm, based on the assumption that the transforming function can be described using Hermite polynomials, is presented and applied to the non-linear filtering problem. The resulting marginalized transform (MT) estimator is compared to the cubature rule, the unscented transform and the divided difference estimator. The evaluations show that the presented method performs better than these methods, more specifically in estimating the covariance matrix. Contrary to the unscented transform, the resulting approximation of the covariance matrix is guaranteed to be positive-semidefinite
Towards optimal quantum tomography with unbalanced homodyning
Balanced homodyning, heterodyning and unbalanced homodyning are the three
well-known sampling techniques used in quantum optics to characterize all
possible photonic sources in continuous-variable quantum information theory. We
show that for all quantum states and all observable-parameter tomography
schemes, which includes the reconstructions of arbitrary operator moments and
phase-space quasi-distributions, localized sampling with unbalanced homodyning
is always tomographically more powerful (gives more accurate estimators) than
delocalized sampling with heterodyning. The latter is recently known to often
give more accurate parameter reconstructions than conventional marginalized
sampling with balanced homodyning. This result also holds for realistic
photodetectors with subunit efficiency. With examples from first- through
fourth-moment tomography, we demonstrate that unbalanced homodyning can
outperform balanced homodyning when heterodyning fails to do so. This new
benchmark takes us one step towards optimal continuous-variable tomography with
conventional photodetectors and minimal experimental components.Comment: 9 pages, 4 figure
Surrogate model for an aligned-spin effective one body waveform model of binary neutron star inspirals using Gaussian process regression
Fast and accurate waveform models are necessary for measuring the properties
of inspiraling binary neutron star systems such as GW170817. We present a
frequency-domain surrogate version of the aligned-spin binary neutron star
waveform model using the effective one body formalism known as SEOBNRv4T. This
model includes the quadrupolar and octopolar adiabatic and dynamical tides. The
version presented here is improved by the inclusion of the spin-induced
quadrupole moment effect, and completed by a prescription for tapering the end
of the waveform to qualitatively reproduce numerical relativity simulations.
The resulting model has 14 intrinsic parameters. We reduce its dimensionality
by using universal relations that approximate all matter effects in terms of
the leading quadrupolar tidal parameters. The implementation of the time-domain
model can take up to an hour to evaluate using a starting frequency of 20Hz,
and this is too slow for many parameter estimation codes that require
sequential waveform evaluations. We therefore construct a fast and faithful
frequency-domain surrogate of this model using Gaussian process regression. The
resulting surrogate has a maximum mismatch of for the
Advanced LIGO detector, and requires 0.13s to evaluate for a waveform with a
starting frequency of 20Hz. Finally, we perform an end-to-end test of the
surrogate with a set of parameter estimation runs, and find that the surrogate
accurately recovers the parameters of injected waveforms.Comment: 19 pages, 10 figures, submitted to PR
Cosmological parameters from CMB and other data: a Monte-Carlo approach
We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters
Power spectrum of the SDSS luminous red galaxies: constraints on cosmological parameters
In this paper we determine the constraints on cosmological parameters using
the CMB data from the WMAP experiment together with the recent power spectrum
measurement of the SDSS Luminous Red Galaxies (LRGs). Specifically, we focus on
spatially flat, low matter density models with adiabatic Gaussian initial
conditions. The spatial flatness is achieved with an additional quintessence
component whose equation of state parameter w_eff is taken to be independent of
redshift. Throughout most of the paper we do not allow any massive neutrino
contribution and also the influence of the gravitational waves on the CMB is
taken to be negligible. The analysis is carried out separately for two cases:
(i) using the acoustic scale measurements as presented in H\"utsi (2006), (ii)
using the full SDSS LRG power spectrum and its covariance matrix. We are able
to obtain a very tight constraint on the Hubble constant: H_0 = 70.8
^{+2.1}_{-2.0} km/s/Mpc, which helps in breaking several degeneracies between
the parameters and allows us to determine the low redshift expansion law with
much higher accuracy than available from the WMAP + HST data alone. The
positive deceleration parameter q_0 is found to be ruled out at 5.5 \sigma
confidence level. Finally, we extend our analysis by investigating the effects
of relaxing the assumption of spatial flatness and also allow for a
contribution from massive neutrinos.Comment: Final version accepted in A&A, added analysis for the models with
massive neutrinos and non-flat spatial geometrie
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