1,246 research outputs found
Multiprocess parallel antithetic coupling for backward and forward Markov Chain Monte Carlo
Antithetic coupling is a general stratification strategy for reducing Monte
Carlo variance without increasing the simulation size. The use of the
antithetic principle in the Monte Carlo literature typically employs two strata
via antithetic quantile coupling. We demonstrate here that further
stratification, obtained by using k>2 (e.g., k=3-10) antithetically coupled
variates, can offer substantial additional gain in Monte Carlo efficiency, in
terms of both variance and bias. The reason for reduced bias is that
antithetically coupled chains can provide a more dispersed search of the state
space than multiple independent chains. The emerging area of perfect simulation
provides a perfect setting for implementing the k-process parallel antithetic
coupling for MCMC because, without antithetic coupling, this class of methods
delivers genuine independent draws. Furthermore, antithetic backward coupling
provides a very convenient theoretical tool for investigating antithetic
forward coupling. However, the generation of k>2 antithetic variates that are
negatively associated, that is, they preserve negative correlation under
monotone transformations, and extremely antithetic, that is, they are as
negatively correlated as possible, is more complicated compared to the case
with k=2. In this paper, we establish a theoretical framework for investigating
such issues. Among the generating methods that we compare, Latin hypercube
sampling and its iterative extension appear to be general-purpose choices,
making another direct link between Monte Carlo and quasi Monte Carlo.Comment: Published at http://dx.doi.org/10.1214/009053604000001075 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Design and Analysis of Monte Carlo Experiments
monte carlo experiments;simulation models;mathematical analysis;sensitivity analysis;experimental design
Quantile-based optimization under uncertainties using adaptive Kriging surrogate models
Uncertainties are inherent to real-world systems. Taking them into account is
crucial in industrial design problems and this might be achieved through
reliability-based design optimization (RBDO) techniques. In this paper, we
propose a quantile-based approach to solve RBDO problems. We first transform
the safety constraints usually formulated as admissible probabilities of
failure into constraints on quantiles of the performance criteria. In this
formulation, the quantile level controls the degree of conservatism of the
design. Starting with the premise that industrial applications often involve
high-fidelity and time-consuming computational models, the proposed approach
makes use of Kriging surrogate models (a.k.a. Gaussian process modeling).
Thanks to the Kriging variance (a measure of the local accuracy of the
surrogate), we derive a procedure with two stages of enrichment of the design
of computer experiments (DoE) used to construct the surrogate model. The first
stage globally reduces the Kriging epistemic uncertainty and adds points in the
vicinity of the limit-state surfaces describing the system performance to be
attained. The second stage locally checks, and if necessary, improves the
accuracy of the quantiles estimated along the optimization iterations.
Applications to three analytical examples and to the optimal design of a car
body subsystem (minimal mass under mechanical safety constraints) show the
accuracy and the remarkable efficiency brought by the proposed procedure
sgsR: a structurally guided sampling toolbox for LiDAR-based forest inventories
Establishing field inventories can be labor intensive, logistically challenging and expensive. Optimizing a sample to derive accurate forest attribute predictions is a key management-level inventory objective. Traditional sampling designs involving pre-defined, interpreted strata could result in poor selection of within-strata sampling intensities, leading to inaccurate estimates of forest structural variables. The use of airborne laser scanning (ALS) data as an applied forest inventory tool continues to improve understanding of the composition and spatial distribution of vegetation structure across forested landscapes. The increased availability of wall-to-wall ALS data is promoting the concept of structurally guided sampling (SGS), where ALS metrics are used as an auxiliary data source driving stratification and sampling within management-level forest inventories. In this manuscript, we present an open-source R package named sgsR that provides a robust toolbox for implementing various SGS approaches. The goal of this package is to provide a toolkit to facilitate better optimized allocation of sample units and sample size, as well as to assess and augment existing plot networks by accounting for current forest structural conditions. Here, we first provide justification for SGS approaches and the creation of the sgsR toolbox. We then briefly describe key functions and workflows the package offers and provide two reproducible examples. Avenues to implement SGS protocols according to auxiliary data needs are presented
The Coyote Universe III: Simulation Suite and Precision Emulator for the Nonlinear Matter Power Spectrum
Many of the most exciting questions in astrophysics and cosmology, including
the majority of observational probes of dark energy, rely on an understanding
of the nonlinear regime of structure formation. In order to fully exploit the
information available from this regime and to extract cosmological constraints,
accurate theoretical predictions are needed. Currently such predictions can
only be obtained from costly, precision numerical simulations. This paper is
the third in a series aimed at constructing an accurate calibration of the
nonlinear mass power spectrum on Mpc scales for a wide range of currently
viable cosmological models, including dark energy. The first two papers
addressed the numerical challenges, and the scheme by which an interpolator was
built from a carefully chosen set of cosmological models. In this paper we
introduce the "Coyote Univers"' simulation suite which comprises nearly 1,000
N-body simulations at different force and mass resolutions, spanning 38 wCDM
cosmologies. This large simulation suite enables us to construct a prediction
scheme, or emulator, for the nonlinear matter power spectrum accurate at the
percent level out to k~1 h/Mpc. We describe the construction of the emulator,
explain the tests performed to ensure its accuracy, and discuss how the central
ideas may be extended to a wider range of cosmological models and applications.
A power spectrum emulator code is released publicly as part of this paper.Comment: 10 pages, 10 figures, minor changes to address referee report,
version v1.1 of the power spectrum emulator code can be downloaded at
http://www.hep.anl.gov/cosmology/CosmicEmu/emu.html, includes now fortran
wrapper and choice of any redshift between z=0 and z=1 (note: webpage now
maintained at Argonne National Laboratory
- …