Related papers: Rare event probability estimation for groundwater …

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…

We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected,…

In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its…

We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…

In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…

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…

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…

Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…

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,…

The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…

We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…

We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is…

Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury's orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

This article analyzes and compares two general techniques of rare event simulation for generating paths of Markov processes over fixed time horizons: exponential tilting and stochastic bridge. These two methods allow to accurately compute…

This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces…

We consider the problem of approximate Bayesian parameter inference in non-linear state-space models with intractable likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is one approach to approximate the…

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…

Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we…

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…