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Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

Signal Processing · Electrical Eng. & Systems 2022-02-15 Alice Cicirello , Filippo Giunta

The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…

Probability · Mathematics 2019-02-07 Barbara Pacchiarotti , Alessandro Pigliacelli

Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of analytical tools for computing first-passage time densities (FPTDs) for complex…

Statistical Mechanics · Physics 2016-02-18 Markus Nyberg , Tobias Ambjörnsson , Ludvig Lizana

We investigate the asymptotic distribution of the maximum of a frequency smoothed estimate of the spectral coherence of a M-variate complex Gaussian time series with mutually independent components when the dimension M and the number of…

Statistics Theory · Mathematics 2021-07-08 Alexis Rosuel , Philippe Loubaton , Pascal Vallet

This paper considers a distributed interference avoidance problem employing frequency assignment in the Gaussian interference channel (IC). We divide the common channel into several subchannels and each user chooses the subchannel with less…

Information Theory · Computer Science 2010-03-23 Zhenhai Jing , Baoming Bai , Xiao Ma , Ying Li

In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…

Computation · Statistics 2016-04-01 Xiaoyu Xiong , Václav Šmídl , Maurizio Filippone

In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…

Statistics Theory · Mathematics 2017-11-01 Zuofeng Shang , Guang Cheng

The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…

Statistics Theory · Mathematics 2019-11-27 François Bachoc , José Bétancourt , Reinhard Furrer , Thierry Klein

Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional…

Probability · Mathematics 2024-06-06 Yuan Fang , Zhongquan Tan

This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a…

Statistics Theory · Mathematics 2012-07-12 Romain Azaïs , François Dufour , Anne Gégout-Petit

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

Computation · Statistics 2016-08-16 A. Garbuno-Inigo , F. A. DiazDelaO , K. M. Zuev

In substations, the presence of random transient impulsive interference sources makes noise highly non-Gaussian. In this paper, the primary interest is to provide a general model for wireless channel in presence of these transient impulsive…

Methodology · Statistics 2015-04-28 Minh Au , Basile L. Agba , François Gagnon

The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an…

Methodology · Statistics 2024-03-26 Emma S. Simpson , Thomas Opitz , Jennifer L. Wadsworth

For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a double exponential (Gumbel) distribution.

Probability · Mathematics 2020-12-08 Nikita Karagodin , Mikhail Lifshits

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…

Machine Learning · Statistics 2013-12-18 Roger Frigola , Fredrik Lindsten , Thomas B. Schön , Carl E. Rasmussen

In this short note we study the asymptotic behaviour of the minima over compact intervals of Gaussian processes, whose paths are not necessarily smooth. We show that, beyond the logarithmic large deviation Gaussian estimates, this problem…

Probability · Mathematics 2019-08-27 Zhixin Wu , Arijit Chakrabarty , Gennady Samorodnitsky

We consider weighted graphs satisfying sub-Gaussian estimate for the natural random walk. On such graphs, we study symmetric Markov chains with heavy tailed jumps. We establish a threshold behavior of such Markov chains when the index…

Probability · Mathematics 2015-09-03 Mathav Murugan , Laurent Saloff-Coste

This paper investigates the problem of Gaussian approximation for the wireless multi-access interference distribution in large spatial wireless networks. First, a principled methodology is presented to establish rates of convergence of the…

Probability · Mathematics 2015-06-04 Hazer Inaltekin

We prove the asymptotic normality of the standardized number of crossings of a centered stationary mixing Gaussian process when both the level and the time horizon go to infinity in such a way that the expected number of crossings also goes…

Probability · Mathematics 2018-02-23 Federico Dalmao , José Rafael León , Ernesto Mordecki , Stéphane Mourareau

We develop a Bayesian non-parametric framework based on multi-task Gaussian processes, appropriate for temporal shrinkage. We focus on a particular class of dynamic hierarchical models to obtain evidence-based knowledge of infectious…