19,550 research outputs found
Hastings-Metropolis algorithm on Markov chains for small-probability estimation
Shielding studies in neutron transport, with Monte Carlo codes, yield
challenging problems of small-probability estimation. The particularity of
these studies is that the small probability to estimate is formulated in terms
of the distribution of a Markov chain, instead of that of a random vector in
more classical cases. Thus, it is not straightforward to adapt classical
statistical methods, for estimating small probabilities involving random
vectors, to these neutron-transport problems. A recent interacting-particle
method for small-probability estimation, relying on the Hastings-Metropolis
algorithm, is presented. It is shown how to adapt the Hastings-Metropolis
algorithm when dealing with Markov chains. A convergence result is also shown.
Then, the practical implementation of the resulting method for
small-probability estimation is treated in details, for a Monte Carlo shielding
study. Finally, it is shown, for this study, that the proposed
interacting-particle method considerably outperforms a simple-Monte Carlo
method, when the probability to estimate is small.Comment: 33 page
Path-tracing Monte Carlo Library for 3D Radiative Transfer in Highly Resolved Cloudy Atmospheres
Interactions between clouds and radiation are at the root of many
difficulties in numerically predicting future weather and climate and in
retrieving the state of the atmosphere from remote sensing observations. The
large range of issues related to these interactions, and in particular to
three-dimensional interactions, motivated the development of accurate radiative
tools able to compute all types of radiative metrics, from monochromatic, local
and directional observables, to integrated energetic quantities. In the
continuity of this community effort, we propose here an open-source library for
general use in Monte Carlo algorithms. This library is devoted to the
acceleration of path-tracing in complex data, typically high-resolution
large-domain grounds and clouds. The main algorithmic advances embedded in the
library are those related to the construction and traversal of hierarchical
grids accelerating the tracing of paths through heterogeneous fields in
null-collision (maximum cross-section) algorithms. We show that with these
hierarchical grids, the computing time is only weakly sensitivive to the
refinement of the volumetric data. The library is tested with a rendering
algorithm that produces synthetic images of cloud radiances. Two other examples
are given as illustrations, that are respectively used to analyse the
transmission of solar radiation under a cloud together with its sensitivity to
an optical parameter, and to assess a parametrization of 3D radiative effects
of clouds.Comment: Submitted to JAMES, revised and submitted again (this is v2
Bounding rare event probabilities in computer experiments
We are interested in bounding probabilities of rare events in the context of
computer experiments. These rare events depend on the output of a physical
model with random input variables. Since the model is only known through an
expensive black box function, standard efficient Monte Carlo methods designed
for rare events cannot be used. We then propose a strategy to deal with this
difficulty based on importance sampling methods. This proposal relies on
Kriging metamodeling and is able to achieve sharp upper confidence bounds on
the rare event probabilities. The variability due to the Kriging metamodeling
step is properly taken into account. The proposed methodology is applied to a
toy example and compared to more standard Bayesian bounds. Finally, a
challenging real case study is analyzed. It consists of finding an upper bound
of the probability that the trajectory of an airborne load will collide with
the aircraft that has released it.Comment: 21 pages, 6 figure
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