2,223 research outputs found
Monte Carlo techniques for filtering and prediction of nonlinear stochastic processes
Imperial Users onl
A spatial analysis of multivariate output from regional climate models
Climate models have become an important tool in the study of climate and
climate change, and ensemble experiments consisting of multiple climate-model
runs are used in studying and quantifying the uncertainty in climate-model
output. However, there are often only a limited number of model runs available
for a particular experiment, and one of the statistical challenges is to
characterize the distribution of the model output. To that end, we have
developed a multivariate hierarchical approach, at the heart of which is a new
representation of a multivariate Markov random field. This approach allows for
flexible modeling of the multivariate spatial dependencies, including the
cross-dependencies between variables. We demonstrate this statistical model on
an ensemble arising from a regional-climate-model experiment over the western
United States, and we focus on the projected change in seasonal temperature and
precipitation over the next 50 years.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS369 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Does waste-recycling really improve Metropolis-Hastings Monte Carlo algorithm?
The Metropolis Hastings algorithm and its multi-proposal extensions are aimed
at the computation of the expectation of a function $f$ under a
probability measure $\pi$ difficult to simulate. They consist in constructing
by an appropriate acceptation/rejection procedure a Markov chain $(X_k,k\geq
0)$ with transition matrix $P$ such that $\pi$ is reversible with respect to
$P$ and in estimating by the empirical mean
I_n(f)=\inv{n}\sum_{k=1}^n f(X_k). The waste-recycling Monte Carlo (WR)
algorithm introduced by physicists is a modification of the Metropolis-Hastings
algorithm, which makes use of all the proposals in the empirical mean, whereas
the standard Metropolis-Hastings algorithm only uses the accepted proposals. In
this paper, we extend the WR algorithm into a general control variate technique
and exhibit the optimal choice of the control variate in terms of asymptotic
variance. We also give an example which shows that in contradiction to the
intuition of physicists, the WR algorithm can have an asymptotic variance
larger than the one of the Metropolis-Hastings algorithm. However, in the
particular case of the Metropolis-Hastings algorithm called Boltzmann
algorithm, we prove that the WR algorithm is asymptotically better than the
Metropolis-Hastings algorithm
Multilevel Markov Chain Monte Carlo Method for High-Contrast Single-Phase Flow Problems
In this paper we propose a general framework for the uncertainty
quantification of quantities of interest for high-contrast single-phase flow
problems. It is based on the generalized multiscale finite element method
(GMsFEM) and multilevel Monte Carlo (MLMC) methods. The former provides a
hierarchy of approximations of different resolution, whereas the latter gives
an efficient way to estimate quantities of interest using samples on different
levels. The number of basis functions in the online GMsFEM stage can be varied
to determine the solution resolution and the computational cost, and to
efficiently generate samples at different levels. In particular, it is cheap to
generate samples on coarse grids but with low resolution, and it is expensive
to generate samples on fine grids with high accuracy. By suitably choosing the
number of samples at different levels, one can leverage the expensive
computation in larger fine-grid spaces toward smaller coarse-grid spaces, while
retaining the accuracy of the final Monte Carlo estimate. Further, we describe
a multilevel Markov chain Monte Carlo method, which sequentially screens the
proposal with different levels of approximations and reduces the number of
evaluations required on fine grids, while combining the samples at different
levels to arrive at an accurate estimate. The framework seamlessly integrates
the multiscale features of the GMsFEM with the multilevel feature of the MLMC
methods following the work in \cite{ketelson2013}, and our numerical
experiments illustrate its efficiency and accuracy in comparison with standard
Monte Carlo estimates.Comment: 29 pages, 6 figure
Improving the precision matrix for precision cosmology
The estimation of cosmological constraints from observations of the large
scale structure of the Universe, such as the power spectrum or the correlation
function, requires the knowledge of the inverse of the associated covariance
matrix, namely the precision matrix, . In most analyses,
is estimated from a limited set of mock catalogues. Depending
on how many mocks are used, this estimation has an associated error which must
be propagated into the final cosmological constraints. For future surveys such
as Euclid and DESI, the control of this additional uncertainty requires a
prohibitively large number of mock catalogues. In this work we test a novel
technique for the estimation of the precision matrix, the covariance tapering
method, in the context of baryon acoustic oscillation measurements. Even though
this technique was originally devised as a way to speed up maximum likelihood
estimations, our results show that it also reduces the impact of noisy
precision matrix estimates on the derived confidence intervals, without
introducing biases on the target parameters. The application of this technique
can help future surveys to reach their true constraining power using a
significantly smaller number of mock catalogues.Comment: 9 pages, 7 figures, minor changes to match version accepted by MNRA
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