Related papers: Multilevel Monte Carlo Method for Statistical Mode…
A grand canonical Monte Carlo (MC) algorithm is presented for studying the lattice gas model (LGM) of multiple protein sequence alignment, which coherently combines long-range interactions and variable-length insertions. MC simulations are…
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…
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…
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…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
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,…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Problems (OCP) where the constraints are described in the form…
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…
We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
Statistical model checking delivers quantitative verification results with statistical guarantees by applying Monte Carlo simulation to formal models. It scales to model sizes and model types that are out of reach for exhaustive, analytical…
Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling of numerical solutions in…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…
This paper develops a novel sequential Monte Carlo (SMC) approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets. The approach…
In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been…
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…
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…
The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we…