Related papers: Optimizing The Integrator Step Size for Hamiltonia…
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…
We study a Monte Carlo algorithm that is based on a specific (randomly shifted and dilated) lattice point set. The main result of this paper is that the mean squared error for a given compactly supported, square-integrable function is…
We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance…
The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…
Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian…
Although evaluation of the expectations on the Ising model is essential in various applications, it is mostly infeasible because of intractable multiple summations. Spatial Monte Carlo integration (SMCI) is a sampling-based approximation.…
Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
We compare the integration error of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods for approximating the normalizing constant of posterior distributions and certain marginal likelihoods. In doing so, we characterize the dependency of…
The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct…
We consider two recent suggestions for how to perform an empirically motivated Monte Carlo study to help select a treatment effect estimator under unconfoundedness. We show theoretically that neither is likely to be informative except under…
Generating samples from a continuous probability density is a central algorithmic problem across statistics, engineering, and the sciences. For high-dimensional settings, Hamiltonian Monte Carlo (HMC) is the default algorithm across…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form $H=A+\epsilon B$. We give a constructive proof that for all integer $p$, there exists an integrator with positive steps…