196 research outputs found
The Centrists against the Ideologues: What are the Falsehoods that Divide Americans on the Issue of Comprehensive Immigration Reform
Evaluating Physician Compare: Benefits and Challenges of Scorecards for Individual Physicians
Representation of Gaussian fields in series with independent coefficients
The numerical discretization of problems with stochastic data or stochastic parameters generally involves the introduction of coordinates that describe the stochastic behaviour, such as coefficients in a series expansion or values at discrete points. The series expansion of a Gaussian field with respect to any orthonormal basis of its Cameron-Martin space has independent standard normal coefficients. A standard choice for numerical simulations is the Karhunen-Loève series, which is based on eigenfunctions of the covariance operator. We suggest an alternative, the hierarchic discrete spectral expansion, which can be constructed directly from the covariance kernel. The resulting basis functions are often well localized, and the convergence of the series expansion seems to be comparable to that of the Karhunen-Loève series. We provide explicit formulas for particular cases and general numerical methods for computing exact representations of such bases. Finally, we relate our approach to numerical discretizations based on replacing a random field by its values on a finite se
Letter to the editor: Commentary on “Strategic choice in linear sequential unmasking, Roger Koppl, Science & Justice, https://doi.org/10.1016/j.scijus.2018.10.010”
This letter to the Editor comments on the paper ‘Strategic choice in linear sequential unmasking’ by Roger Koppl (Science & Justice, https://doi.org/10.1016/j.scijus.2018.10.010)
Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs
Partial differential equations (PDEs) with random input data, such as random loadings and coefficients, are reformulated as parametric, deterministic PDEs on parameter spaces of high, possibly infinite dimension. Tensorized operator equations for spatial and temporal k-point correlation functions of their random solutions are derived. Parametric, deterministic PDEs for the laws of the random solutions are derived. Representations of the random solutions' laws on infinite-dimensional parameter spaces in terms of ‘generalized polynomial chaos' (GPC) series are established. Recent results on the regularity of solutions of these parametric PDEs are presented. Convergence rates of best N-term approximations, for adaptive stochastic Galerkin and collocation discretizations of the parametric, deterministic PDEs, are established. Sparse tensor products of hierarchical (multi-level) discretizations in physical space (and time), and GPC expansions in parameter space, are shown to converge at rates which are independent of the dimension of the parameter space. A convergence analysis of multi-level Monte Carlo (MLMC) discretizations of PDEs with random coefficients is presented. Sufficient conditions on the random inputs for superiority of sparse tensor discretizations over MLMC discretizations are established for linear elliptic, parabolic and hyperbolic PDEs with random coefficient
Adaptive wavelet methods for elliptic partial differential equations with random operators
We apply adaptive wavelet methods to boundary value problems with random coefficients, discretized by wavelets in the spatial domain and tensorized polynomials in the parameter domain. Greedy algorithms control the approximate application of the fully discretized random operator, and the construction of sparse approximations to this operator. We suggest a power iteration for estimating errors induced by sparse approximations of linear operators
Modeling the forensic two-trace problem with Bayesian networks
The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375-381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727-732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this proble
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