Related papers: A statistical formalism for alignment analysis
The behaviour of the one--dimensional random--forced Burgers equation is investigated in the path integral formalism, using a discrete space--time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
The tolerancing step has a great importance in the design process. It characterises the relationship between the different sectors of the product life cycle: Design, Manufacturing and Control. We can distinguish several methods to assist…
In regimes of low signal strengths and therefore a small signal-to-noise ratio, standard data analysis methods often fail to accurately estimate system properties. We present a method based on Monte Carlo simulations to effectively restore…
Knowledge of a machine tool axis to axis location errors allows compensation and correcting actions to be taken to enhance its volumetric accuracy. Several procedures exist, involving either lengthy individual test for each geometric error…
Random field Monte Carlo (MC) reliability analysis is a robust stochastic method to determine the probability of failure. This method, however, requires a large number of numerical simulations demanding high computational costs. This paper…
It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…
The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a…
A Monte Carlo model was used to study the scattering error of an absorption meter with a divergent light beam and a limited acceptance angle of the receiver. Reflections at both ends of the tube were taken into account. Calculations of the…
Alignments provide sophisticated diagnostics that pinpoint deviations in a trace with respect to a process model and their severity. However, approaches based on trace alignments use crisp process models as reference and recent…
A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
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…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…
In many polarimetry applications, including observations in the X-ray band, the measurement of a polarization signal can be reduced to the detection and quantification of a deviation from uniformity of a distribution of measured angles. We…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based…