Related papers: Multi-level Monte Carlo Dropout for Efficient Unce…

Model uncertainty obtained by variational Bayesian inference with Monte Carlo dropout is prone to miscalibration. The uncertainty does not represent the model error well. In this paper, temperature scaling is extended to dropout variational…

Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo…

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…

The recently developed method Lasso Monte Carlo (LMC) for uncertainty quantification is applied to the characterisation of spent nuclear fuel. The propagation of nuclear data uncertainties to the output of calculations is an often required…

We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…

Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature…

Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…

Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) are closely related. This connection is elaborated by presenting a new general class…

Uncertainty quantification (UQ) is an active area of research, and an essential technique used in all fields of science and engineering. The most common methods for UQ are Monte Carlo and surrogate-modelling. The former method is…

We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…

We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…

In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…

Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…

Due to complex experimental settings, missing values are common in biomedical data. To handle this issue, many methods have been proposed, from ignoring incomplete instances to various data imputation approaches. With the recent rise of…

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…

Neural networks are lately more and more often being used in the context of data-driven control, as an approximate model of the true system dynamics. Model Predictive Control (MPC) adopts this practise leading to neural MPC strategies. This…

Recently, there has been a significant amount of interest in satellite telemetry anomaly detection (AD) using neural networks (NN). For AD purposes, the current approaches focus on either forecasting or reconstruction of the time series,…

Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…