Many statistical multiple integration problems involve integrands that have a dominant peak. In applying numerical methods to solve these problems, statisticians have paid relatively little attention to existing quadrature methods and available software developed in the numerical analysis literature. One reason these methods have been largely overlooked, even though they are known to be more ef...

A new integration technique based on use of Quasi Monte Carlo Integration (QMCI) technique is proposed for Method of Moments (MoM) solution of Integral equation for capacitance computation. The integral equation for unknown charge distribution over the capacitors is formulated. The solutions are obtained by MoM using the QMCI technique. It is observed that the proposed method is not only capabl...

This paper presents an enhanced transillumination radiosity method that can provide accurate solutions at relatively low computational cost. The proposed algorithm breaks down the double integral of the gathered power to an area integral that is computed analytically and to a directional integral that is evaluated by quasi-Monte Carlo or Monte-Carlo techniques. The paper also analyses the requi...

In this paper, the importance sampling filter proposed by Mariano and Tanizaki (1995), Tanizaki (1996), Tanizaki and Mariano (1994) is extended using the antithetic Monte Carlo method to reduce the simulation errors. By Monte Carlo studies, the importance sampling filter with the antithetic Monte Carlo method is compared with the importance sampling filter without the antithetic Monte Carlo met...

To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators /'j and J'2 based on 2N and 4N observations, respec2 2 » tively, of the function. He also considered estimators Dy and D2 of the variances of/j and J'2, respectively. This paper shows that all these estimators are asymptotically normally distributed as N tends to infinity.

Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or non-Gaussian state estimation problems have been developed. Numerical integration becomes extremely computer-intensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling techniques such as Monte Carlo integrat...