Hamiltonian Monte Carlo is a Markov chain Monte Carlo method that uses Hamiltonian dynamics to efficiently produce distant samples. It employs geometric numerical integration to simulate Hamiltonian dynamics, which is a key of its high performance. We present a Hamiltonian Monte Carlo method with adaptive step size control to further enhance the efficiency. We propose a new explicit, reversible...

Algorithms for estimating the integral over hyper-rectangular regions are discussed. Solving this problem in high dimensions is usually considered a domain of Monte Carlo and quasi-Monte Carlo methods, because their power degrades little with increasing dimension. These algorithms are compared to integration routines based on interpolatory cubature rules, which are usually only used in low dime...

In the present paper we study quasi-Monte Carlo methods to integrate functions representable by generalized Haar series in high dimensions. Using (t; m; s)-nets to calculate the quasi-Monte Carlo approximation, we get best possible estimates of the integration error for practically relevant classes of functions. The local structure of the Haar functions yields interesting new aspects in proofs ...

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering...

The convergence of Monte Carlo method for numerical integration can often be improved by replacing pseudorandom numbers (PRNs) with more uniformly distributed numbers known as quasirandom numbers(QRNs). Standard Monte Carlo methods use pseudorandom sequences and provide a convergence rate of O(N−1/2) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting converg...

Monte Carlo applications are widely perceived as computationally intensive but naturally parallel. Therefore, they can be effectively executed on the grid using the dynamic bag-of-work model. We improve the efficiency of the subtask-scheduling scheme by using an N-out-of-M strategy, and develop a Monte Carlo-specific lightweight checkpoint technique, which leads to a performance improvement for...

A generative model’s partition function is typically expressed as an intractable multi-dimensional integral, whose approximation presents a challenge to numerical and Monte Carlo integration. In this work, we propose a new estimation method for intractable partition functions, based on distilling an intractable generative model into a tractable approximation thereof, and using the latter for pr...

In a distribution ray tracer, the crucial part of the direct lighting calculation is the sampling strategy for shadow ray testing. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specic probability density functions which are used to generate sample points for the numerical quadrature. Probability densi...