Related papers: Monte Carlo Integration with Subtraction
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with $d$-dimensions and derivatives of order…
The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…
A novel linear integration rule called $\textit{control neighbors}$ is proposed in which nearest neighbor estimates act as control variates to speed up the convergence rate of the Monte Carlo procedure on metric spaces. The main result is…
A Monte-Carlo algorithm for discrete statistical models that combines the full power of the Belief Propagation algorithm with the advantages of a detailed-balanced heat bath approach is presented. A sub-tree inside the factor graph is first…
We propose an improved Path Integral Monte Carlo (PIMC) algorithm called Harmonic PIMC (H-PIMC) and its generalization, Mixed PIMC (M-PIMC). PIMC is a powerful tool for studying quantum condensed phases. However, it often suffers from a low…
We propose a method to efficiently integrate truncated probability densities. The method uses Markov chain Monte Carlo method to sample from a probability density matching the function being integrated. The required normalisation or…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…
In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time…
An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…
Extant "fast" algorithms for Monte Carlo confidence sets are limited to univariate shift parameters for the one-sample and two-sample problems using the sample mean as the test statistic; moreover, some do not converge reliably and most do…
Functional data analysis has been a growing field of study in recent decades, and one fundamental task in functional data analysis is estimating the sample location. A notion called statistical depth has been extended from multivariate data…
This paper surveys in detail the relations between numerical integration and the Hamiltonian (or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in the numerical integrations, these should be performed as…
We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion…
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…
We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by "splitting" the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is…
Monte Carlo radiative transfer, which has been demonstrated as a successful algorithm for modeling radiation transport through the astrophysical medium, relies on sampling of scattering phase functions. We review several classic sampling…
Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in generalized linear models; however, these algorithms are prohibitively slow in massive data…