Recently, the analysis of quasi-Monte Carlo (QMC) sampling of integrands with singularities gained considerable interest. In this setting error bounds for QMC integration, in addition to discrepancy, include a measure how well the singularities are avoided by the utilized sequences. The article aims to generalize results for the corner avoidance of the classical Halton sequence to Halton sequen...

Recently, the analysis of quasi-Monte Carlo (QMC) sampling of integrands with singularities gained considerable interest. In this setting error bounds for QMC integration, in addition to discrepancy, include a measure how well the singularities are avoided by the utilized sequences. The article aims to generalize results for the corner avoidance of the classical Halton sequence to Halton sequen...

We have calculated the ground state energy of the hydrogen molecule using the quantum Monte Carlo (QMC) method of solving the Schrodinger equation, without the use of the Born-Oppenheimer or any other adiabatic approximations. The wave function sampling was carried out in the full 12-dimensional configuration space of the four particles (two electrons and two protons). Two different methods wer...

Bond stretching mimics different levels of electron correlation and provides a challenging test bed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N(2) and in the H(50) chain. To control the sign/phase problem, the phaseless AF QMC method ...

We present a manually-adaptive extension of Quasi Monte Carlo (QMC) integration for approximating marginal densities, moments, and quantiles when the joint density is known up to a normalization constant. Randomization and a batch-wise approach involving (0; s)-sequences are the cornerstones of the technique. By incorporating a variety of graphical diagnostics the method allows the user to adap...

The splitting of Quasi-Monte Carlo (QMC) point sequences into blocks or interleaved substreams has been suggested to raise the speed of distributed numerical integration and to lower to traffic on the network. The usefulness of this approach in GRID environments is discussed. After specifying requirements for using QMC techniques in GRID environments in general we review and evaluate the propos...

We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type, extending both the multi-level first order analysis in [F.Y. Kuo, Ch. Schwab, and I.H. Sloan, Multi-level quasi-Monte Carlo finite element methods for...

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with the system size as a low power. A QMC approach with auxiliary fields, in principle, allows an exact solution of the Schrodinger equation in the chosen basis. However, th...

Summary Maximum simulated likelihood estimation of mixed multinomial logit models requires evaluation a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences and modified Latin hypercube sampling are workhorse for integral approximation. Earlier studies explored the potential sparse grid quadrature (SGQ), but SGQ suffers from negative weights. As an alternative to ...

The conventional control variate method proposed by Kemna and Vorst (1990) to evaluate Asian options under the Black-Scholes model can be interpreted as a particular selection of linear martingale controls. We generalize the constant control parameter into a control process to gain more reduction on variance. By means of an option price approximation, we construct a martingale control variate m...