Related papers: Parametric multi-fidelity Monte Carlo estimation w…
Multilevel Monte Carlo can efficiently compute statistical estimates of discretized random variables, for a given error tolerance. Traditionally, only a certain statistic is computed from a particular implementation of multilevel Monte…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
We present a Monte Carlo study of the two-component $\phi^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $\lambda$ we eliminate leading order corrections to scaling. High statistics…
Multifidelity approximate Bayesian computation (MF-ABC) is a likelihood-free technique for parameter inference that exploits model approximations to significantly increase the speed of ABC algorithms (Prescott and Baker, 2020). Previous…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions,…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
Any data modeling exercise has two main components: parameter estimation and model selection. The latter will be the topic of this lecture note. More concretely we will introduce several Monte-Carlo sampling-based rules for model selection…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Typically, operational risk losses are reported above a threshold. Fitting data reported above a constant threshold is a well known and studied problem. However, in practice, the losses are scaled for business and other factors before the…
In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
Accurately modelling the Earth's climate has widespread applications ranging from forecasting local weather to understanding global climate change. Low-fidelity simulations of climate phenomena are readily available, but high-fidelity…
Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties…
Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need…
We present a novel method for determining multi-fractal properties from experimental data. It is based on maximising the likelihood that the given finite data set comes from a particular set of parameters in a multi-parameter family of well…
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…