Perfect simulation of a coupling achieving the dˉ\bar{d}-distance between ordered pairs of binary chains of infinite order

We explicitly construct a coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of iid sequence of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.Comment: Typos corrected. The final publication is available at http://www.springerlink.co

Parametrized Kantorovich-Rubinstein theorem and application to the coupling of random variables

We prove a version for random measures of the celebrated Kantorovich-Rubinstein duality theorem and we give an application to the coupling of random variables which extends and unifies known results.Comment: date de redaction 22 octobre 200

The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.John Jakeman’s work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program. Joseph Guillaume received funding from an Australian Research Council Discovery Early Career Award (project no. DE190100317). Arnald Puy worked on this paper on a Marie Sklodowska-Curie Global Fellowship, grant number 792178. Takuya Iwanaga is supported through an Australian Government Research Training Program (AGRTP) Scholarship and the ANU Hilda-John Endowment Fun

The future of sensitivity analysis: an essential discipline for systems modeling and policy support

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society

Dataset for: Estimation of the Multivariate Conditional-Tail-Expectation for extreme risk levels: illustration on environmental data-sets

This paper deals with the problem of estimating the Multivariate version of the Conditional-Tail-Expectation introduced by Di Bernardino et al. (2013) and Cousin and Di Bernardino (2014). We propose a new semi-parametric estimator for this risk measure, essentially based on statistical extrapolation techniques, well designed for extreme risk levels. We prove a central limit theorem for the obtained estimator. We illustrate the practical properties of our estimator on simulations. The performances of our new estimator are discussed and compared to the ones of the empirical Kendall's process based estimator, previously proposed in Di Bernardino and Prieur (2014). We conclude with two applications on real data-sets: rainfall measurements recorded at three stations located in the south of Paris (France) and the analysis of strong wind gusts in the north west of France

Gradient-based dimension reduction of multivariate vector-valued functions

International audienceMultivariate functions encountered in high-dimensional uncertainty quantification problems often vary along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these directions and using them to construct ridge approximations of such functions, in a setting where the functions are vector-valued (e.g., taking values in Rn). The methodology consists of minimizing an upper bound on the approximation error, obtained by subspace Poincaré inequalities. We provide a thorough mathematical analysis in the case where theparameter space is equipped with a Gaussian probability measure. The resulting method generalizes the notion of active subspaces associated with scalar-valued functions. A numerical illustration shows that using gradients of the function yields effective dimension reduction. We also show how the choice of norm on the codomain of the function has an impact on the function's low-dimensional approximation

Gradient-based dimension reduction of multivariate vector-valued functions

Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these directions and using them to construct ridge approximations of such functions, in a setting where the functions are vector-valued (e.g., taking values in Rn). The methodology consists of minimizing an upper bound on the approximation error, obtained by subspace Poincaré inequalities. We provide a thorough mathematical analysis in the case where theparameter space is equipped with a Gaussian probability measure. The resulting method generalizes the notion of active subspaces associated with scalar-valued functions. A numerical illustration shows that using gradients of the function yields effective dimension reduction. We also show how the choice of norm on the codomain of the function has an impact on the function's low-dimensional approximation

New dependence coefficient Examples and applications to statistics

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 22522, issue : a.2003 n.8 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Coupling for T-dependent sequences and applications

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 22522, issue : a.2003 n.2 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

The FANCM:p.Arg658* truncating variant is associated with risk of triple-negative breast cancer

Breast cancer is a common disease partially caused by genetic risk factors. Germline pathogenic variants in DNA repair genes BRCA1, BRCA2, PAM, ATM, and CHEK2 are associated with breast cancer risk. FANCM, which encodes for a DNA translocase, has been proposed as a breast cancer predisposition gene, with greater effects for the ER-negative and triple-negative breast cancer (TNBC) subtypes. We tested the three recurrent protein-truncating variants FANCM:p.Arg658*, p.Gln1701*, and pArg1931* for association with breast cancer risk in 67,112 cases, 53,766 controls, and 26,662 carriers of pathogenic variants of BRCA1 or BRCA2. These three variants were also studied functionally by measuring survival and chromosome fragility in FANCM(-/-) patient-derived immortalized fibroblasts treated with diepoxybutane or olaparib. We observed that FANCM:p.Arg658* was associated with increased risk of ER-negative disease and TNBC (OR = 2.44, P = 0.034 and OR = 3.79; P = 0.009, respectively). In a country-restricted analysis, we confirmed the associations detected for FANCM:p.Arg658* and found that also FANCM:p.Arg1931* was associated with ER-negative breast cancer risk (OR = 1.96; P = 0.006). The functional results indicated that all three variants were deleterious affecting cell survival and chromosome stability with FANCM:p.Arg658* causing more severe phenotypes. In conclusion, we confirmed that the two rare FANCM deleterious variants p.Arg658* and p.Arg1931* are risk factors for ER-negative and TNBC subtypes. Overall our data suggest that the effect of truncating variants on breast cancer risk may depend on their position in the gene. Cell sensitivity to olaparib exposure, identifies a possible therapeutic option to treat FANCM-associated tumors