Related papers: A Monte Carlo Algorithm for Sampling Rare Events: …
In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…
The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
We propose a new Monte Carlo algorithm for complex discrete distributions. The algorithm is motivated by the N-Fold Way, which is an ingenious event-driven MCMC sampler that avoids rejection moves at any specific state. The N-Fold Way can…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…
We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each…
In this paper we will give a Monte Carlo algorithm by which the moments of a functions of Dirichlet probability distributions can be estimated. This algorithm is called Inner Nested Sampling and is an implementation of Skilling's general…
High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates…
Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is…
We use importance sampling in a redefined way to highlight and investigate rare events in the form of trajectories trapped inside a target coherent set. We take a transfer operator approach to finding these sets on a reconstructed…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…
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 present a Monte Carlo method to compute efficiently susceptibilites or covariances of two physical variables. The method relies on a generalization of the exchange cluster algorithm to any model of interacting particles with any $2$-body…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…