Related papers: Adaptive Monte Carlo applied to uncertainty estima…
We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an $XY$ model into the target model, and we study its mathematical properties for a variety of nonlinear $\sigma$-models. We then apply the method…
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…
In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…
Many sources of errors exist in the manufacturing process of complex shapes. Some approximations occur at each step from the design geometry to the machined part. The aim of the paper is to present a method to evaluate the effect of high…
Convolutional neural networks have shown to achieve superior performance on image segmentation tasks. However, convolutional neural networks, operating as black-box systems, generally do not provide a reliable measure about the confidence…
Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…
It is important to estimate the errors of probabilistic inference algorithms. Existing diagnostics for Markov chain Monte Carlo methods assume inference is asymptotically exact, and are not appropriate for approximate methods like…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…
Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the…
Machine learning models are commonly applied to human brain imaging datasets in an effort to associate function or structure with behaviour, health, or other individual phenotypes. Such models often rely on low-dimensional maps generated by…
Monte Carlo (MC) permutation test is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail. However, in modern data science settings where a large…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
Model uncertainty sets are required in many robust optimization problems, such as robust control and prediction with uncertainty, but there is no definite methodology to generate uncertainty sets for nonlinear dynamical systems. In this…
Deep neural networks have become the gold-standard approach for the automated segmentation of 3D medical images. Their full acceptance by clinicians remains however hampered by the lack of intelligible uncertainty assessment of the provided…
The primary focus of Monte Carlo simulation is to identify and quantify risk related to uncertainty and variability in spreadsheet model inputs. The stress of Monte Carlo simulation often reveals logical errors in the underlying spreadsheet…