scholarly journals Reduction problems and deformation approaches to nonstationary covariance functions over spheres

2020 ◽  
Vol 14 (1) ◽  
pp. 890-916
Author(s):  
Emilio Porcu ◽  
Rachid Senoussi ◽  
Enner Mendoza ◽  
Moreno Bevilacqua
Keyword(s):  
Covariance Functions ◽  
Nonstationary Covariance

scholarly journals ACE of space: estimating genetic components of high-dimensional imaging data

Biostatistics ◽  
2019 ◽  
Author(s):  
Benjamin B Risk ◽  
Hongtu Zhu
Keyword(s):  
Cortical Thickness ◽  
Twin Studies ◽  
High Dimensional ◽  
Imaging Data ◽  
Covariance Functions ◽  
Genetic Components ◽  
Human Connectome Project ◽  
Nonstationary Covariance ◽  
Brain Structure And Function ◽  
And Function

SUMMARY It is of great interest to quantify the contributions of genetic variation to brain structure and function, which are usually measured by high-dimensional imaging data (e.g., magnetic resonance imaging). In addition to the variance, the covariance patterns in the genetic effects of a functional phenotype are of biological importance, and covariance patterns have been linked to psychiatric disorders. The aim of this article is to develop a scalable method to estimate heritability and the nonstationary covariance components in high-dimensional imaging data from twin studies. Our motivating example is from the Human Connectome Project (HCP). Several major big-data challenges arise from estimating the genetic and environmental covariance functions of functional phenotypes extracted from imaging data, such as cortical thickness with 60 000 vertices. Notably, truncating to positive eigenvalues and their eigenfunctions from unconstrained estimators can result in large bias. This motivated our development of a novel estimator ensuring positive semidefiniteness. Simulation studies demonstrate large improvements over existing approaches, both with respect to heritability estimates and covariance estimation. We applied the proposed method to cortical thickness data from the HCP. Our analysis suggests fine-scale differences in covariance patterns, identifying locations in which genetic control is correlated with large areas of the brain and locations where it is highly localized.

scholarly journals Spatial modelling using a new class of nonstationary covariance functions

2006 ◽  
Vol 17 (5) ◽  
pp. 483-506 ◽  
Author(s):  
Christopher J. Paciorek ◽  
Mark J. Schervish
Keyword(s):  
Spatial Modelling ◽  
New Class ◽  
Covariance Functions ◽  
Nonstationary Covariance

Implementation of geostatistical models for large spatiotemporal datasets using multi-resolution approximations

2021 ◽  
Author(s):  
Marius Appel ◽  
Edzer Pebesma
Keyword(s):  
Computation Time ◽  
Spatiotemporal Analysis ◽  
R Package ◽  
American Statistical Association ◽  
Environmental Data ◽  
Covariance Functions ◽  
Nonstationary Covariance ◽  
Geostatistical Models ◽  
Convolution Approach ◽  
Selection Of

<p>The multi-resolution approximation approach (MRA) [1] provides an efficient representation of Gaussian processes that scales beyond millions of observations. MRA leaves flexibility in the selection of covariance functions and allows to trade off computation time against prediction performance, depending on the selection of parameters. Recent work [2] has shown how MRA can be used for global spatiotemporal processes by integrating nonstationary covariance functions, where parameters vary over space and/or time following a kernel convolution approach. As such, MRA turns out to be a promising approach for geostatistical modelling of global spatiotemporal datasets, such as those coming from Earth observation satellites.</p><p>In this work, we show how MRA can be used for spatiotemporal analysis from a practical perspective. In the first part, we will discuss the influence of parameters (spatiotemporal shape of partitioning regions, the number of basis functions, and the number of partitioning levels) by analyzing a real world dataset. In the second part, we will present and discuss our implementation as an R package stmra[3]. We will demonstrate how traditional models as from the gstat package can be implemented efficiently with MRA, and how non-stationary models can be defined by users in a relatively simple way. </p><p>[1] Katzfuss, M. (2017). A multi-resolution approximation for massive spatial datasets. Journal of the American Statistical Association, 112(517), 201-214</p><p>[2] Appel, M., & Pebesma, E. (2020). Spatiotemporal multi-resolution approximations for analyzing global environmental data. Spatial Statistics, 38, 100465.</p><p>[3] https://github.com/appelmar/stmra</p>

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

Matérn Cross-Covariance Functions for Multivariate Random Fields

2010 ◽  
Vol 105 (491) ◽  
pp. 1167-1177 ◽  
Author(s):  
Tilmann Gneiting ◽  
William Kleiber ◽  
Martin Schlather
Keyword(s):  
Random Fields ◽  
Covariance Functions ◽  
Cross Covariance

Investigating Local Dependence with Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Local Dependence ◽  
Conditional Covariance ◽  
Covariance Functions
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