6,978 research outputs found
Parametrizations, fixed and random effects
International audienceWe consider the problem of estimating the random element s of a finite dimensional vector space S from the continuous data corrupted by noise with unknown variance σ 2 w. The mean E(s) (the fixed effect) of s belongs to a known vector subspace F of S, and the likelihood of the centred component s − E(s) (the random effect) belongs to an unknown supplementary space E of F relative to S and has the PDF proportional to exp{−q(s)/2σ 2 s }, where σ 2 s is some unknown positive parameter. We introduce the notion of bases separating the fixed and random effects and define comparison criteria between two separating bases using the partition functions and the maximum likelihood method. We illustrate our results for climate change detection using the set S of cubic splines. We show the influence of the choice of separating basis on the estimation of the linear tendency of the temperature and the signal-to-noise ratio σ 2 w /σ 2 s
Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations
The effects of different parametrizations on the convergence of Bayesian
computational algorithms for hierarchical models are well explored. Techniques
such as centering, noncentering and partial noncentering can be used to
accelerate convergence in MCMC and EM algorithms but are still not well studied
for variational Bayes (VB) methods. As a fast deterministic approach to
posterior approximation, VB is attracting increasing interest due to its
suitability for large high-dimensional data. Use of different parametrizations
for VB has not only computational but also statistical implications, as
different parametrizations are associated with different factorized posterior
approximations. We examine the use of partially noncentered parametrizations in
VB for generalized linear mixed models (GLMMs). Our paper makes four
contributions. First, we show how to implement an algorithm called nonconjugate
variational message passing for GLMMs. Second, we show that the partially
noncentered parametrization can adapt to the quantity of information in the
data and determine a parametrization close to optimal. Third, we show that
partial noncentering can accelerate convergence and produce more accurate
posterior approximations than centering or noncentering. Finally, we
demonstrate how the variational lower bound, produced as part of the
computation, can be useful for model selection.Comment: Published in at http://dx.doi.org/10.1214/13-STS418 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Parametrizing modified gravity for cosmological surveys
One of the challenges in testing gravity with cosmology is the vast freedom
opened when extending General Relativity. For linear perturbations, one
solution consists in using the Effective Field Theory of Dark Energy (EFT of
DE). Even then, the theory space is described in terms of a handful of free
functions of time. This needs to be reduced to a finite number of parameters to
be practical for cosmological surveys. We explore in this article how well
simple parametrizations, with a small number of parameters, can fit observables
computed from complex theories. Imposing the stability of linear perturbations
appreciably reduces the theory space we explore. We find that observables are
not extremely sensitive to short time-scale variations and that simple, smooth
parametrizations are usually sufficient to describe this theory space. Using
the Bayesian Information Criterion, we find that using two parameters for each
function (an amplitude and a power law index) is preferred over complex models
for 86% of our theory space.Comment: 10 pages, 5 figure
Climate dynamics and fluid mechanics: Natural variability and related uncertainties
The purpose of this review-and-research paper is twofold: (i) to review the
role played in climate dynamics by fluid-dynamical models; and (ii) to
contribute to the understanding and reduction of the uncertainties in future
climate-change projections. To illustrate the first point, we focus on the
large-scale, wind-driven flow of the mid-latitude oceans which contribute in a
crucial way to Earth's climate, and to changes therein. We study the
low-frequency variability (LFV) of the wind-driven, double-gyre circulation in
mid-latitude ocean basins, via the bifurcation sequence that leads from steady
states through periodic solutions and on to the chaotic, irregular flows
documented in the observations. This sequence involves local, pitchfork and
Hopf bifurcations, as well as global, homoclinic ones. The natural climate
variability induced by the LFV of the ocean circulation is but one of the
causes of uncertainties in climate projections. Another major cause of such
uncertainties could reside in the structural instability in the topological
sense, of the equations governing climate dynamics, including but not
restricted to those of atmospheric and ocean dynamics. We propose a novel
approach to understand, and possibly reduce, these uncertainties, based on the
concepts and methods of random dynamical systems theory. As a very first step,
we study the effect of noise on the topological classes of the Arnol'd family
of circle maps, a paradigmatic model of frequency locking as occurring in the
nonlinear interactions between the El Nino-Southern Oscillations (ENSO) and the
seasonal cycle. It is shown that the maps' fine-grained resonant landscape is
smoothed by the noise, thus permitting their coarse-grained classification.
This result is consistent with stabilizing effects of stochastic
parametrization obtained in modeling of ENSO phenomenon via some general
circulation models.Comment: Invited survey paper for Special Issue on The Euler Equations: 250
Years On, in Physica D: Nonlinear phenomen
Study of noise effects in electrical impedance tomography with resistor networks
We present a study of the numerical solution of the two dimensional
electrical impedance tomography problem, with noisy measurements of the
Dirichlet to Neumann map. The inversion uses parametrizations of the
conductivity on optimal grids. The grids are optimal in the sense that finite
volume discretizations on them give spectrally accurate approximations of the
Dirichlet to Neumann map. The approximations are Dirichlet to Neumann maps of
special resistor networks, that are uniquely recoverable from the measurements.
Inversion on optimal grids has been proposed and analyzed recently, but the
study of noise effects on the inversion has not been carried out. In this paper
we present a numerical study of both the linearized and the nonlinear inverse
problem. We take three different parametrizations of the unknown conductivity,
with the same number of degrees of freedom. We obtain that the parametrization
induced by the inversion on optimal grids is the most efficient of the three,
because it gives the smallest standard deviation of the maximum a posteriori
estimates of the conductivity, uniformly in the domain. For the nonlinear
problem we compute the mean and variance of the maximum a posteriori estimates
of the conductivity, on optimal grids. For small noise, we obtain that the
estimates are unbiased and their variance is very close to the optimal one,
given by the Cramer-Rao bound. For larger noise we use regularization and
quantify the trade-off between reducing the variance and introducing bias in
the solution. Both the full and partial measurement setups are considered.Comment: submitted to Inverse Problems and Imagin
Bose-Einstein Correlations from Random Walk Models
We argue that strong final state rescattering among the secondary particles
created in relativistic heavy ion collisions is essential to understand the
measured Bose-Einstein correlations. The recently suggested ``random walk
models'' which contain only initial state scattering are unable to reproduce
the measured magnitude and K_\perp-dependence of R_\perp in Pb+Pb collisions
and the increase of R_l with increasing size of the collision system.Comment: 5 pages, REVTEX, 1 figure included with epsf.sty, revised version to
be published in Phys.Lett.
Neutrino scattering rates in the presence of hyperons from a Skyrme model in the RPA approximation
The contribution of Lambda hyperons to neutrino scattering rates is
calculated in the random phase approximation in a model where the interaction
is described by a Skyrme potential. Finite temperature and neutrino trapping
are taken into account in view of applications to the deleptonization stage of
protoneutron star cooling. The hyperons can remove the problem of ferromagnetic
instability common to (nearly) all Skyrme parametrizations of the
nucleon-nucleon interaction. As a consequence, there is not any longer a pole
at the transition in the neutrino-baryon cross section. However there still
remains an enhancement in this region. In the absence of ferromagnetism the
mean free path in npLambda matter is reduced compared to its value in np matter
as consequence of the presence of this additional degree of freedom. At high
density the results are very sensitive to the choice of the Lambda-Lambda
interaction.Comment: 21 pages, 13 figure
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