Related papers: Analysis of a micro-macro acceleration method with…
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139--1160], showing how algorithms which are approximations to an…
We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…
The Metropolis implementation of the Monte Carlo algorithm has been developed to study the equilibrium thermodynamics of many-body systems. Choosing small trial moves, the trajectories obtained applying this algorithm agree with those…
In MCMC methods, such as the Metropolis-Hastings (MH) algorithm, the Gibbs sampler, or recent adaptive methods, many different strategies can be proposed, often associated in practice to unknown rates of convergence. In this paper we…
The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…
We apply the Monte Carlo method to solving the Dirichlet problem of linear parabolic equations with fractional Laplacian. This method exploit- s the idea of weak approximation of related stochastic differential equations driven by the…
Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara…
Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many…
An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive…
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…
The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and…
The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…