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This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate…
An introduction to the basics of Monte Carlo is given. The topics covered include, sample space, events, probabilities, random variables, mean, variance, covariance, characteristic function, chebyshev inequality, law of large numbers,…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…
We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with…
This paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a…
Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the…
Nonlinear systems of polynomial equations arise naturally in many applied settings, for example loglinear models on contingency tables and Gaussian graphical models. The solution sets to these systems over the reals are often positive…
I describe the classic circle-packing problem on a sphere, and the analytic and numerical approaches that have been used to study it. I then present a very simple Markov-chain Monte Carlo algorithm, which succeeds in finding the best…
We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…
In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical…
We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…
In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of…