Related papers: Robustly simulating biochemical reaction kinetics …
Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…
The stochastic dynamics of biochemical networks are usually modelled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically, and numerical methods typically produce estimates with…
We present a new combinatorial method for the calculation of the nuclear level density. It is based on a Monte Carlo technique, in order to avoid a direct counting procedure which is generally impracticable for high-A nuclei. The Monte…
Modern computational advances have enabled easy parallel implementations of Markov chain Monte Carlo (MCMC). However, almost all work in estimating the variance of Monte Carlo averages, including the efficient batch means (BM) estimator,…
Sequential Monte Carlo (SMC) is a class of algorithms that approximate high-dimensional expectations of a Markov chain. SMC algorithms typically include a resampling step. There are many possible ways to resample, but the relative…
We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte…
Metamodels, or the regression analysis of Monte Carlo simulation results, provide a powerful tool to summarize simulation findings. However, an underutilized approach is the multilevel metamodel (MLMM) that accounts for the dependent data…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
A goal of systems biology is to understand the dynamics of intracellular systems. Stochastic chemical kinetic models are often utilized to accurately capture the stochastic nature of these systems due to low numbers of molecules. Collecting…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to…