A software package is described for the numerical evaluation of integrals that arise in Bayesian statistical analysis. Diierent types of transformations that can be user selected to precondition the problem are discussed. These all begin with a standardizing transformation, that can be adaptively constructed, and is followed by a multivariate Normal, multivariate Student's t or split-t transfor...

This paper compares fault position and Monte Carlo methods as the most common methods in stochastic assessment of voltage sags. To compare their abilities, symmetrical and unsymmetrical faults with different probability distribution of fault positions along the lines are applied in a test system. The voltage sag magnitude in different nodes of test system is calculated. The problem with the...

Required libraries: The code uses the FF library [3] to calculate scalar one-loop integrals and the dilogarithm. Random numbers for the Monte Carlo integration are generated using the Ranlux library written by Martin Lüscher [4]. Monte Carlo integration is done using an adapted version of Vegas [5, 6]. For convenience Ranlux and the FF library are included in the package. Please cite the aforem...

The n’th point of the Halton sequence in [0, 1]d is shown to have components whose product is larger than Cn−1 where C > 0 depends on d. This property makes the Halton sequence very well suited to quasi-Monte Carlo integration of some singular functions that become unbounded as the argument approaches the origin. The Halton sequence avoids a similarly shaped (though differently sized) region ar...

For Halloween, we come as a math course 1 Monte Carlo Integration Suppose we want to evaluate a definite integral,

For Halloween, we come as a math course 1 Monte Carlo Integration Suppose we want to evaluate a definite integral,

In a recent paper Keister proposed two quadrature rules as alternatives to Monte Carlo for certain multidimensional integrals and reported his test results. In earlier work we had shown that the quasi-Monte Carlo method with generalized Faure points is very effective for a variety of high dimensional integrals occuring in mathematical finance. In this paper we report test results of this method...

This paper proposes a Monte Carlo approach for the evaluation of integrals of smooth functions defined on compact Lie groups. The approach is based on the ergodic property of Brownian processes in compact Lie groups. The paper provides an elementary proof of this property and obtains the following results. It gives the rate of almost sure convergence of time averages along with a “large deviati...

In this manuscript, we establish an integration by parts formula for the quadrature of discontinuous payoffs in a multidimensional Heston model. For its derivation we use Malliavin calculus techniques and work under mild integrability conditions on the payoff and under the assumption of a strictly positive volatility. Since the integration by parts procedure smoothes the original functional, ou...

We present a quasi-Monte Carlo spectral method for a class of elliptic partial differential equations (PDEs) with random coefficients defined on the unit sphere. The random coefficients are parametrised by the Karhunen-Loève expansion, while the exact solution is approximated by the spherical harmonics. The expectation of the solution is approximated by a quasi-Monte Carlo integration rule. A m...