Related papers: Variance Reduction via Simultaneous Importance Sam…
An importance sampling approach for sampling copula models is introduced. We propose two algorithms that improve Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at…
Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand,…
In this review, we address the use of Monte Carlo methods for approximating definite integrals of the form $Z = \int L(x) d P(x)$, where $L$ is a target function (often a likelihood) and $P$ a finite measure. We present vertical-likelihood…
Multilevel Monte Carlo (MLMC) is a recently proposed variation of Monte Carlo (MC) simulation that achieves variance reduction by simulating the governing equations on a series of spatial (or temporal) grids with increasing resolution.…
Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling in the framework of diffusion process and consider the change…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the 1D Heisenberg ring…
For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its effectiveness, the performance of IS is…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…
The recent growth in multi-fidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a…
We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of…
Learning strategies for imperfect information games from samples of interaction is a challenging problem. A common method for this setting, Monte Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term convergence rates…
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…
Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…
We present an unbiased numerical integration algorithm that handles both low-frequency regions and high frequency details of multidimensional integrals. It combines quadrature and Monte Carlo integration, by using a quadrature-base…
We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of…
This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [10] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the…