Related papers: Computational complexity analysis for Monte Carlo …
Tau-leaping is a popular discretization method for generating approximate paths of continuous time, discrete space, Markov chains, notably for biochemical reaction systems. To compute expected values in this context, an appropriate…
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random…
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of…
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
The paper presents an investigation of estimating treatment effect using different matching methods. The study proposed a new method which is computationally efficient and convenient in implication-'largest caliper matching' and compared…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
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…
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the…