There have been few studies on practical error estimation methods of quasi-Monte Carlo integrations. Recently, some theoretical works were developed by Owen to analyze the quasi-Monte Carlo integration error. However his method given by those works is complicated to be implemented and needs huge computational e orts, so it would be of some interest to investigate into a simple error estimation ...

Traditional Monte Carlo (MC) integration methods use point samples to numerically approximate the underlying integral. This approximation introduces variance in the integrated result, and this error can depend critically on the sampling patterns used during integration. Most of the well known samplers used for MC integration in graphics, e.g. jitter, Latin hypercube (n-rooks), multi-jitter, are...

In this report, we revisit the work of Pilleboue et al. [2015], providing a representation-theoretic derivation of the closed-form expression for the expected value and variance in homogeneous Monte Carlo integration. We show that the results obtained for the variance estimation of Monte Carlo integration on the torus, the sphere, and Euclidean space can be formulated as specific instances of a...

When estimating logistic-normal models, the integral appearing in the marginal likelihood is analytically intractable, so that numerical methods such as GaussHermite quadrature (GH) are needed. When the dimensionality increases, the number of quadrature points becomes too high. A possible solution can be found among the Quasi-Monte Carlo (QMC) methods, because these techniques yield quite good ...

A review of Monte Carlo methods for approximating the high-dimensional integrals that arise in Bayesian statistical analysis. Emphasis is on the features of many Bayesian applications which make Monte Carlo methods especially appropriate, and on Monte Carlo variance-reduction techniques especially well suited to Bayesian applications. A generalized logistic regression example is used to illustr...

Monte Carlo integration is often used for antialiasing in rendering processes. Due to low sampling rates only expected error estimates can be stated, and the variance can be high. In this article quasi-Monte Carlo methods are presented, achieving a guaranteed upper error bound and a convergence rate essentially as fast as usual Monte Carlo.

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Ca...