5,800 research outputs found
Efficient rare-event simulation for the maximum of heavy-tailed random walks
Let be a sequence of i.i.d. r.v.'s with negative mean. Set
and define . We propose an importance sampling
algorithm to estimate the tail of that is strongly
efficient for both light and heavy-tailed increment distributions. Moreover, in
the case of heavy-tailed increments and under additional technical assumptions,
our estimator can be shown to have asymptotically vanishing relative variance
in the sense that its coefficient of variation vanishes as the tail parameter
increases. A key feature of our algorithm is that it is state-dependent. In the
presence of light tails, our procedure leads to Siegmund's (1979) algorithm.
The rigorous analysis of efficiency requires new Lyapunov-type inequalities
that can be useful in the study of more general importance sampling algorithms.Comment: Published in at http://dx.doi.org/10.1214/07-AAP485 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Numerical approximation of statistical solutions of scalar conservation laws
We propose efficient numerical algorithms for approximating statistical
solutions of scalar conservation laws. The proposed algorithms combine finite
volume spatio-temporal approximations with Monte Carlo and multi-level Monte
Carlo discretizations of the probability space. Both sets of methods are proved
to converge to the entropy statistical solution. We also prove that there is a
considerable gain in efficiency resulting from the multi-level Monte Carlo
method over the standard Monte Carlo method. Numerical experiments illustrating
the ability of both methods to accurately compute multi-point statistical
quantities of interest are also presented
Numerical approximation of statistical solutions of scalar conservation laws
We propose efficient numerical algorithms for approximating statistical
solutions of scalar conservation laws. The proposed algorithms combine finite
volume spatio-temporal approximations with Monte Carlo and multi-level Monte
Carlo discretizations of the probability space. Both sets of methods are proved
to converge to the entropy statistical solution. We also prove that there is a
considerable gain in efficiency resulting from the multi-level Monte Carlo
method over the standard Monte Carlo method. Numerical experiments illustrating
the ability of both methods to accurately compute multi-point statistical
quantities of interest are also presented
Parallelizing the QUDA Library for Multi-GPU Calculations in Lattice Quantum Chromodynamics
Graphics Processing Units (GPUs) are having a transformational effect on
numerical lattice quantum chromodynamics (LQCD) calculations of importance in
nuclear and particle physics. The QUDA library provides a package of mixed
precision sparse matrix linear solvers for LQCD applications, supporting single
GPUs based on NVIDIA's Compute Unified Device Architecture (CUDA). This
library, interfaced to the QDP++/Chroma framework for LQCD calculations, is
currently in production use on the "9g" cluster at the Jefferson Laboratory,
enabling unprecedented price/performance for a range of problems in LQCD.
Nevertheless, memory constraints on current GPU devices limit the problem sizes
that can be tackled. In this contribution we describe the parallelization of
the QUDA library onto multiple GPUs using MPI, including strategies for the
overlapping of communication and computation. We report on both weak and strong
scaling for up to 32 GPUs interconnected by InfiniBand, on which we sustain in
excess of 4 Tflops.Comment: 11 pages, 7 figures, to appear in the Proceedings of Supercomputing
2010 (submitted April 12, 2010
sPLINK : a hybrid federated tool as a robust alternative to meta-analysis in genome-wide association studies
Meta-analysis has been established as an effective approach to combining summary statistics of several genome-wide association studies (GWAS). However, the accuracy of meta-analysis can be attenuated in the presence of cross-study heterogeneity. We present sPLINK, a hybrid federated and user-friendly tool, which performs privacy-aware GWAS on distributed datasets while preserving the accuracy of the results. sPLINK is robust against heterogeneous distributions of data across cohorts while meta-analysis considerably loses accuracy in such scenarios. sPLINK achieves practical runtime and acceptable network usage for chi-square and linear/logistic regression tests.Peer reviewe
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