Related papers: Complexity of Multilevel Monte Carlo Tau-Leaping
In this work, we consider the problem of estimating summary statistics to characterise biochemical reaction networks of interest. Such networks are often described using the framework of the Chemical Master Equation (CME). For…
We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the…
The Gillespie algorithm and its extensions are commonly used for the simulation of chemical reaction networks. A limitation of these algorithms is that they have to process and update the system after every reaction, requiring significant…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…
We explore the use of Array-RQMC, a randomized quasi-Monte Carlo method designed for the simulation of Markov chains, to reduce the variance when simulating stochastic biological or chemical reaction networks with $\tau$-leaping. The task…
Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
The multilevel Monte Carlo (MLMC) method for continuous-time Markov chains, first introduced by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012), is a highly efficient simulation technique that can be used to estimate various…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of…
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…
We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo…