Related papers: Nonstationary covariance models for global data
Aiming to generate realistic synthetic times series of the bivariate process of daily mean temperature and precipitations, we introduce a non-homogeneous hidden Markov model. The non-homogeneity lies in periodic transition probabilities…
Nonstationary and non-Gaussian spatial data are common in various fields, including ecology (e.g., counts of animal species), epidemiology (e.g., disease incidence counts in susceptible regions), and environmental science (e.g.,…
We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics…
Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…
Environmental phenomena are influenced by complex interactions among various factors. For instance, the amount of rainfall measured at different stations within a given area is shaped by atmospheric conditions, orography, and physics of…
Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties. For general distributions, the covariance and precision…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Quantifying uncertainty in future climate projections is hindered by the prohibitive computational cost of running physical climate models, which severely limits the availability of training data. We propose a data-efficient framework for…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
It is increasingly understood that the assumption of stationarity is unrealistic for many spatial processes. In this article, we combine dimension expansion with a spectral method to model big non-stationary spatial fields in a…
We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such that the algorithm can be efficiently implemented in…
We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on…
We consider a stationary spatio-temporal random process and assume that we have a sample. By defining a sequence of discrete Fourier transforms at canonical frequencies at each location, and using these complex valued random varables as…
Generating high quality uncertainty estimates for sequential regression, particularly deep recurrent networks, remains a challenging and open problem. Existing approaches often make restrictive assumptions (such as stationarity) yet still…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that…