Related papers: Monte Carlo Integration with Subtraction
We discuss modern ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce to the Metropolis and the…
The classical approaches to numerically integrating a function $f$ are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate $f$ and have error $O(\sigma(f)/\sqrt{n})$, where $\sigma(f)$ is the…
Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we use the underlying geometry of Hamiltonian Monte Carlo to…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family…
An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This…
A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalised. The novel…
Monte Carlo (MC) simulations are extensively used for various purposes in modern high-energy physics (HEP) experiments. Precision measurements of established Standard Model processes or searches for new physics often require the collection…
We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira-Leggett formulation, which describes the system in the…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
The paper describes the practical work for students visually clarifying the mechanism of the Monte Carlo method applying to approximating the value of Pi. Considering a traditional quadrant (circular sector) inscribed in a square, here we…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular…
Control variates are a variance-reduction technique for Monte Carlo integration. The principle involves approximating the integrand by a function that can be analytically integrated, and integrating using the Monte Carlo method only the…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
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…
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…
We introduce a Monte Carlo scheme for sampling bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo (BMC) is significantly broader than that…
In high-energy particle physics, complex Monte Carlo (MC) simulations are needed to compare theory predictions to measurable quantities. Many and large MC samples are needed to be generated to take into account all the systematics.…
Due to the complex characteristics of bottle-brush polymers, it became a challenge to develop an efficient algorithm for studying such macromolecules under various solvent conditions or some constraints in the space by using computer…