The AEP algorithm for the fast computation of the distribution of the sum of dependent random variables

We propose a new algorithm to compute numerically the distribution function of the sum of $d$ dependent, non-negative random variables with given joint distribution.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ284 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Computable Finite Element Error Bounds for Poisson's Equation

New explicit finite element error bounds are presented for approximation by (1) piecewise linear elements over triangles and (2) piecewise bilinear elements over squares and rectangles. By this the error bounds given in Bamhill, Brown & Mitchell (1981) are improve

Bayesian Copulae Distributions, with Application to Operational Risk Management—Some Comments

This paper points out mistakes in some results given in the paper "Bayesian Copulae Distributions, with Application to Operational Risk Management” by Luciana Dalla Valle, published in 2009 in volume11, number1 of "Methodology and Computing in Applied Probability”. In particular, we explain why the inverse Wishart distribution is not a conjugate prior to the Gaussian copul

Estimating Copulas for Insurance from Scarce Observations, Expert Opinion and Prior Information: A Bayesian Approach

A prudent assessment of dependence is crucial in many stochastic models for insurance risks. Copulas have become popular to model such dependencies. However, estimation procedures for copulas often lead to large parameter uncertainty when observations are scarce. In this paper, we propose a Bayesian method which combines prior information (e.g. from regulators), observations and expert opinion in order to estimate copula parameters and determine the estimation uncertainty. The combination of different sources of information can significantly reduce the parameter uncertainty compared to the use of only one source. The model can also account for uncertainty in the marginal distributions. Furthermore, we describe the methodology for obtaining expert opinion and explain involved psychological effects and popular fallacies. We exemplify the approach in a case stud

Experiments on a Parallel Nonlinear Jacobi–Davidson Algorithm

AbstractThe Jacobi–Davidson (JD) algorithm is very well suited for the computation of a few eigen-pairs of large sparse complex symmetric nonlinear eigenvalue problems. The performance of JD crucially depends on the treatment of the so-called correction equation, in particular the preconditioner, and the initial vector. Depending on the choice of the spectral shift and the accuracy of the solution, the convergence of JD can vary from linear to cubic. We investigate parallel preconditioners for the Krylov space method used to solve the correction equation.We apply our nonlinear Jacobi–Davidson (NLJD) method to quadratic eigenvalue problems that originate from the time-harmonic Maxwell equation for the modeling and simulation of resonating electromagnetic structures

Perfectly Matched Layers in a Divergence Preserving ADI Scheme for Electromagnetics

For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 um the computational domain has dimensions roughly 5 orders of magnitude larger resulting in very large mesh sizes. The particles are confined to a small area of this domain only. To resolve the smallest scales close to the particles subgrids are envisioned. For reasons of stability the alternating direction implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009) pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the domain absorbing boundary conditions have to be employed to prevent reflection of the radiation. In this paper we show how the divergence preserving ADI scheme has to be formulated in perfectly matched layers (PML) and compare the performance in several scenarios.Comment: 8 pages, 6 figure