52 research outputs found
Global sensitivity analysis of computer models with functional inputs
Global sensitivity analysis is used to quantify the influence of uncertain
input parameters on the response variability of a numerical model. The common
quantitative methods are applicable to computer codes with scalar input
variables. This paper aims to illustrate different variance-based sensitivity
analysis techniques, based on the so-called Sobol indices, when some input
variables are functional, such as stochastic processes or random spatial
fields. In this work, we focus on large cpu time computer codes which need a
preliminary meta-modeling step before performing the sensitivity analysis. We
propose the use of the joint modeling approach, i.e., modeling simultaneously
the mean and the dispersion of the code outputs using two interlinked
Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The
``mean'' model allows to estimate the sensitivity indices of each scalar input
variables, while the ``dispersion'' model allows to derive the total
sensitivity index of the functional input variables. The proposed approach is
compared to some classical SA methodologies on an analytical function. Lastly,
the proposed methodology is applied to a concrete industrial computer code that
simulates the nuclear fuel irradiation
Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels
The global sensitivity analysis method, used to quantify the influence of
uncertain input variables on the response variability of a numerical model, is
applicable to deterministic computer code (for which the same set of input
variables gives always the same output value). This paper proposes a global
sensitivity analysis methodology for stochastic computer code (having a
variability induced by some uncontrollable variables). The framework of the
joint modeling of the mean and dispersion of heteroscedastic data is used. To
deal with the complexity of computer experiment outputs, non parametric joint
models (based on Generalized Additive Models and Gaussian processes) are
discussed. The relevance of these new models is analyzed in terms of the
obtained variance-based sensitivity indices with two case studies. Results show
that the joint modeling approach leads accurate sensitivity index estimations
even when clear heteroscedasticity is present
Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes
Composite likelihoods are increasingly used in applications where the full
likelihood is analytically unknown or computationally prohibitive. Although the
maximum composite likelihood estimator has frequentist properties akin to those
of the usual maximum likelihood estimator, Bayesian inference based on
composite likelihoods has yet to be explored. In this paper we investigate the
use of the Metropolis--Hastings algorithm to compute a pseudo-posterior
distribution based on the composite likelihood. Two methodologies for adjusting
the algorithm are presented and their performance on approximating the true
posterior distribution is investigated using simulated data sets and real data
on spatial extremes of rainfall
Likelihood-based inference for max-stable processes
The last decade has seen max-stable processes emerge as a common tool for the
statistical modeling of spatial extremes. However, their application is
complicated due to the unavailability of the multivariate density function, and
so likelihood-based methods remain far from providing a complete and flexible
framework for inference. In this article we develop inferentially practical,
likelihood-based methods for fitting max-stable processes derived from a
composite-likelihood approach. The procedure is sufficiently reliable and
versatile to permit the simultaneous modeling of marginal and dependence
parameters in the spatial context at a moderate computational cost. The utility
of this methodology is examined via simulation, and illustrated by the analysis
of U.S. precipitation extremes
ABC random forests for Bayesian parameter inference
This preprint has been reviewed and recommended by Peer Community In
Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036).
Approximate Bayesian computation (ABC) has grown into a standard methodology
that manages Bayesian inference for models associated with intractable
likelihood functions. Most ABC implementations require the preliminary
selection of a vector of informative statistics summarizing raw data.
Furthermore, in almost all existing implementations, the tolerance level that
separates acceptance from rejection of simulated parameter values needs to be
calibrated. We propose to conduct likelihood-free Bayesian inferences about
parameters with no prior selection of the relevant components of the summary
statistics and bypassing the derivation of the associated tolerance level. The
approach relies on the random forest methodology of Breiman (2001) applied in a
(non parametric) regression setting. We advocate the derivation of a new random
forest for each component of the parameter vector of interest. When compared
with earlier ABC solutions, this method offers significant gains in terms of
robustness to the choice of the summary statistics, does not depend on any type
of tolerance level, and is a good trade-off in term of quality of point
estimator precision and credible interval estimations for a given computing
time. We illustrate the performance of our methodological proposal and compare
it with earlier ABC methods on a Normal toy example and a population genetics
example dealing with human population evolution. All methods designed here have
been incorporated in the R package abcrf (version 1.7) available on CRAN.Comment: Main text: 24 pages, 6 figures Supplementary Information: 14 pages, 5
figure
Extreme events in total ozone over the Northern mid-latitudes: an analysis based on long-term data sets from five European ground-based stations
We apply methods from extreme value theory to identify extreme events in high (termed EHOs) and low (termed ELOs) total ozone and to describe the distribution tails (i.e. very high and very low values) of five long-term European ground-based total ozone time series. The influence of these extreme events on observed mean values, long-term trends and changes is analysed. The results show a decrease in EHOs and an increase in ELOs during the last decades, and establish that the observed downward trend in column ozone during the 1970-1990s is strongly dominated by changes in the frequency of extreme events. Furthermore, it is shown that clear 'fingerprints' of atmospheric dynamics (NAO, ENSO) and chemistry [ozone depleting substances (ODSs), polar vortex ozone loss] can be found in the frequency distribution of ozone extremes, even if no attribution is possible from standard metrics (e.g. annual mean values). The analysis complements earlier analysis for the world's longest total ozone record at Arosa, Switzerland, confirming and revealing the strong influence of atmospheric dynamics on observed ozone changes. The results provide clear evidence that in addition to ODS, volcanic eruptions and strong/moderate ENSO and NAO events had significant influence on column ozone in the European sector
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