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A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical…

Statistics Theory · Mathematics 2026-03-30 Lujia Bai , Holger Dette , Zihao Yuan

We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…

Pattern Formation and Solitons · Physics 2012-05-15 Zachary P. Kilpatrick , Bard Ermentrout

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…

Statistics Theory · Mathematics 2015-12-29 Teppei Ogihara

Scientists are often interested in estimating an association between a covariate and a binary- or count-valued response. For instance, public health officials are interested in how much disease presence (a binary response per individual)…

Methodology · Statistics 2025-09-03 David R. Burt , Renato Berlinghieri , Tamara Broderick

On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the…

Pattern Formation and Solitons · Physics 2008-04-24 Maxim A. Molchan

We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…

Probability · Mathematics 2024-09-04 Enrico Bernardi , Leonardo Marconi

We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…

Machine Learning · Statistics 2015-07-03 Cuong Tran , Vladimir Pavlovic , Robert Kopp

In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…

Methodology · Statistics 2015-06-30 Daniel Cervone , Natesh S. Pillai

Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…

Statistics Theory · Mathematics 2026-01-06 Didong Li , Aritra Halder , Sudipto Banerjee

Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an…

Statistics Theory · Mathematics 2014-12-02 Johannes Schmidt-Hieber

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…

Methodology · Statistics 2021-05-20 Henry Lam , Huajie Qian

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Machine Learning · Statistics 2020-02-26 Ivan Ustyuzhaninov , Ieva Kazlauskaite , Carl Henrik Ek , Neill D. F. Campbell

The problem of estimating the slope parameter in regression between two spatial processes under confounding by an unmeasured spatial process has received widespread attention in the recent statistical literature. Yet, a fundamental question…

Statistics Theory · Mathematics 2026-03-04 Abhirup Datta , Michael L. Stein

We study the asymptotic behaviour of both spherical $t$-designs and random uniform designs as the set of sampling points in non-parametric regression with spherical regressors of arbitrary dimension. We show that the corresponding…

Statistics Theory · Mathematics 2026-05-05 Martin Kroll

Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…

Machine Learning · Statistics 2023-06-21 Pratik Nag , Yiping Hong , Sameh Abdulah , Ghulam A. Qadir , Marc G. Genton , Ying Sun

Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geostatistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the…

Statistics Theory · Mathematics 2020-07-30 François Bachoc , Emilio Porcu , Moreno Bevilacqua , Reinhard Furrer , Tarik Faouzi

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…

Machine Learning · Statistics 2017-03-31 Maziar Raissi , Paris Perdikaris , George Em Karniadakis

Motivated by estimating the lead-lag relationships in high-frequency financial data, we propose noisy bivariate Neyman-Scott point processes with gamma kernels (NBNSP-G). NBNSP-G tolerates noises that are not necessarily Poissonian and has…

Statistics Theory · Mathematics 2026-01-06 Takaaki Shiotani , Nakahiro Yoshida

The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and…

Probability · Mathematics 2016-07-15 Xia Chen , Yaozhong Hu , David Nualart , Samy Tindel

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…

Econometrics · Economics 2022-08-30 Abhimanyu Gupta , Xi Qu