142,541 research outputs found
Progressive construction of a parametric reduced-order model for PDE-constrained optimization
An adaptive approach to using reduced-order models as surrogates in
PDE-constrained optimization is introduced that breaks the traditional
offline-online framework of model order reduction. A sequence of optimization
problems constrained by a given Reduced-Order Model (ROM) is defined with the
goal of converging to the solution of a given PDE-constrained optimization
problem. For each reduced optimization problem, the constraining ROM is trained
from sampling the High-Dimensional Model (HDM) at the solution of some of the
previous problems in the sequence. The reduced optimization problems are
equipped with a nonlinear trust-region based on a residual error indicator to
keep the optimization trajectory in a region of the parameter space where the
ROM is accurate. A technique for incorporating sensitivities into a
Reduced-Order Basis (ROB) is also presented, along with a methodology for
computing sensitivities of the reduced-order model that minimizes the distance
to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced
optimization framework is applied to subsonic aerodynamic shape optimization
and shown to reduce the number of queries to the HDM by a factor of 4-5,
compared to the optimization problem solved using only the HDM, with errors in
the optimal solution far less than 0.1%
Non-parametric deprojection of NIKA SZ observations: Pressure distribution in the Planck-discovered cluster PSZ1 G045.85+57.71
The determination of the thermodynamic properties of clusters of galaxies at
intermediate and high redshift can bring new insights into the formation of
large-scale structures. It is essential for a robust calibration of the
mass-observable scaling relations and their scatter, which are key ingredients
for precise cosmology using cluster statistics. Here we illustrate an
application of high resolution arcsec) thermal Sunyaev-Zel'dovich (tSZ)
observations by probing the intracluster medium (ICM) of the \planck-discovered
galaxy cluster \psz\ at redshift , using tSZ data obtained with the
NIKA camera, which is a dual-band (150 and 260~GHz) instrument operated at the
IRAM 30-meter telescope. We deproject jointly NIKA and \planck\ data to extract
the electronic pressure distribution from the cluster core () to its outskirts () non-parametrically for the
first time at intermediate redshift. The constraints on the resulting pressure
profile allow us to reduce the relative uncertainty on the integrated Compton
parameter by a factor of two compared to the \planck\ value. Combining the tSZ
data and the deprojected electronic density profile from \xmm\ allows us to
undertake a hydrostatic mass analysis, for which we study the impact of a
spherical model assumption on the total mass estimate. We also investigate the
radial temperature and entropy distributions. These data indicate that \psz\ is
a massive ( M) cool-core cluster.
This work is part of a pilot study aiming at optimizing the treatment of the
NIKA2 tSZ large program dedicated to the follow-up of SZ-discovered clusters at
intermediate and high redshifts. (abridged)Comment: 16 pages, 10 figure
Beyond first-order asymptotics for Cox regression
To go beyond standard first-order asymptotics for Cox regression, we develop
parametric bootstrap and second-order methods. In general, computation of
-values beyond first order requires more model specification than is
required for the likelihood function. It is problematic to specify a censoring
mechanism to be taken very seriously in detail, and it appears that
conditioning on censoring is not a viable alternative to that. We circumvent
this matter by employing a reference censoring model, matching the extent and
timing of observed censoring. Our primary proposal is a parametric bootstrap
method utilizing this reference censoring model to simulate inferential
repetitions of the experiment. It is shown that the most important part of
improvement on first-order methods - that pertaining to fitting nuisance
parameters - is insensitive to the assumed censoring model. This is supported
by numerical comparisons of our proposal to parametric bootstrap methods based
on usual random censoring models, which are far more unattractive to implement.
As an alternative to our primary proposal, we provide a second-order method
requiring less computing effort while providing more insight into the nature of
improvement on first-order methods. However, the parametric bootstrap method is
more transparent, and hence is our primary proposal. Indications are that
first-order partial likelihood methods are usually adequate in practice, so we
are not advocating routine use of the proposed methods. It is however useful to
see how best to check on first-order approximations, or improve on them, when
this is expressly desired.Comment: Published at http://dx.doi.org/10.3150/13-BEJ572 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
A Kolmogorov-Smirnov test for the molecular clock on Bayesian ensembles of phylogenies
Divergence date estimates are central to understand evolutionary processes
and depend, in the case of molecular phylogenies, on tests of molecular clocks.
Here we propose two non-parametric tests of strict and relaxed molecular clocks
built upon a framework that uses the empirical cumulative distribution (ECD) of
branch lengths obtained from an ensemble of Bayesian trees and well known
non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS)
goodness-of-fit test. In the strict clock case, the method consists in using
the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny
is clock-like, in other words, if it follows a Poisson law. The ECD is computed
from the discretized branch lengths and the parameter of the expected
Poisson distribution is calculated as the average branch length over the
ensemble of trees. To compensate for the auto-correlation in the ensemble of
trees and pseudo-replication we take advantage of thinning and effective sample
size, two features provided by Bayesian inference MCMC samplers. Finally, it is
observed that tree topologies with very long or very short branches lead to
Poisson mixtures and in this case we propose the use of the two-sample KS test
with samples from two continuous branch length distributions, one obtained from
an ensemble of clock-constrained trees and the other from an ensemble of
unconstrained trees. Moreover, in this second form the test can also be applied
to test for relaxed clock models. The use of a statistically equivalent
ensemble of phylogenies to obtain the branch lengths ECD, instead of one
consensus tree, yields considerable reduction of the effects of small sample
size and provides again of power.Comment: 14 pages, 9 figures, 8 tables. Minor revision, additin of a new
example and new title. Software:
https://github.com/FernandoMarcon/PKS_Test.gi
Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions
This paper has a twofold goal. The first aim is to provide a deeper
understanding of the family of the Real Elliptically Symmetric (RES)
distributions by investigating their intrinsic semiparametric nature. The
second aim is to derive a semiparametric lower bound for the estimation of the
parametric component of the model. The RES distributions represent a
semiparametric model where the parametric part is given by the mean vector and
by the scatter matrix while the non-parametric, infinite-dimensional, part is
represented by the density generator. Since, in practical applications, we are
often interested only in the estimation of the parametric component, the
density generator can be considered as nuisance. The first part of the paper is
dedicated to conveniently place the RES distributions in the framework of the
semiparametric group models. The second part of the paper, building on the
mathematical tools previously introduced, the Constrained Semiparametric
Cram\'{e}r-Rao Bound (CSCRB) for the estimation of the mean vector and of the
constrained scatter matrix of a RES distributed random vector is introduced.
The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust
-estimator of mean vector and scatter matrix when no a-priori information on
the density generator is available. A closed form expression for the CSCRB is
derived. Finally, in simulations, we assess the statistical efficiency of the
Tyler's and Huber's scatter matrix -estimators with respect to the CSCRB.Comment: This paper has been accepted for publication in IEEE Transactions on
Signal Processin
Short and long-term wind turbine power output prediction
In the wind energy industry, it is of great importance to develop models that
accurately forecast the power output of a wind turbine, as such predictions are
used for wind farm location assessment or power pricing and bidding,
monitoring, and preventive maintenance. As a first step, and following the
guidelines of the existing literature, we use the supervisory control and data
acquisition (SCADA) data to model the wind turbine power curve (WTPC). We
explore various parametric and non-parametric approaches for the modeling of
the WTPC, such as parametric logistic functions, and non-parametric piecewise
linear, polynomial, or cubic spline interpolation functions. We demonstrate
that all aforementioned classes of models are rich enough (with respect to
their relative complexity) to accurately model the WTPC, as their mean squared
error (MSE) is close to the MSE lower bound calculated from the historical
data. We further enhance the accuracy of our proposed model, by incorporating
additional environmental factors that affect the power output, such as the
ambient temperature, and the wind direction. However, all aforementioned
models, when it comes to forecasting, seem to have an intrinsic limitation, due
to their inability to capture the inherent auto-correlation of the data. To
avoid this conundrum, we show that adding a properly scaled ARMA modeling layer
increases short-term prediction performance, while keeping the long-term
prediction capability of the model
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