Related papers: Adaptive Reduced Multilevel Splitting
This paper investigates Monte Carlo (MC) methods to estimate probabilities of rare events associated with solutions to the $d$-dimensional McKean-Vlasov stochastic differential equation (MV-SDE). MV-SDEs are usually approximated using a…
The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
Recent success in Deep Reinforcement Learning (DRL) methods has shown that policy optimization with respect to an off-policy distribution via importance sampling is effective for sample reuse. In this paper, we show that the use of…
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the…
The estimation of rare event or failure probabilities in high dimensions is of interest in many areas of science and technology. We consider problems where the rare event is expressed in terms of a computationally costly numerical model.…
We study the multi-terminal remote estimation problem under a rate constraint, in which the goal of the encoder is to help each decoder estimate a function over a certain distribution -- while the distribution is known only to the encoder,…
Approximate Bayesian computation (ABC) is a well-established family of Monte Carlo methods for performing approximate Bayesian inference in the case where an ``implicit'' model is used for the data: when the data model can be simulated, but…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a…
The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given…
This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multilevel Monte Carlo method recently introduced by Giles (Giles 2008) to the framework of stochastic optimization by means of…
Monte Carlo methods can provide accurate p-value estimates of word counting test statistics and are easy to implement. They are especially attractive when an asymptotic theory is absent or when either the search sequence or the word pattern…
Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte…
Large-scale rare events data are commonly encountered in practice. To tackle the massive rare events data, we propose a novel distributed estimation method for logistic regression in a distributed system. For a distributed framework, we…
Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often…
A sampling procedure for the transition matrix Monte Carlo method is introduced that generates the density of states function over a wide parameter range with minimal coding effort.
Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a…