# A linear mixed model formulation for spatio-temporal random processes with computational advances for the product, sum, and product–sum covariance functions

@article{Dumelle2020ALM, title={A linear mixed model formulation for spatio-temporal random processes with computational advances for the product, sum, and product–sum covariance functions}, author={Michael Dumelle and Jay M. Ver Hoef and Claudio Fuentes and Alix I. Gitelman}, journal={arXiv: Methodology}, year={2020} }

## Figures and Tables from this paper

## One Citation

Separable spatio-temporal kriging for fast virtual sensing

- Computer Science
- 2022

It is shown that this perspective on kriging allows to perform virtual sensing even in the case of tall datasets, and the use of convenient spatial and temporal models eases up computation.

## References

SHOWING 1-10 OF 63 REFERENCES

30 Years of space–time covariance functions

- MathematicsWIREs Computational Statistics
- 2020

While this article focuses primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships.

Spatio-temporal kriging based on the product-sum model: some computational aspects

- Computer ScienceEarth Science Informatics
- 2014

An R routine for “spatio-temporal kriging” with hole effects, and appropriate space-time search neighborhoods is described, and the experimental results show that the spatio-tem temporal random field provides more information than the purely spatial random field, because the accuracy of interpolation has been improved.

Fast computing of some generalized linear mixed pseudo-models with temporal autocorrelation

- Computer ScienceComput. Stat.
- 2010

This paper obtain linearly increasing computing time with number of observations, as opposed to O(n3) increasing computingTime using numerical optimization, and finds a surprising result; that incomplete optimization for covariance parameters within the larger parameter estimation algorithm actually decreases time to convergence.

Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach

- Computer Science
- 2012

Two methods for estimating space and space-time covariance functions from a Gaussian random field based on the composite likelihood idea are proposed, which are useful for practitioners looking for a good balance between computational complexity and statistical efficiency.

Statistical Methods for Spatial Data Analysis

- Mathematics
- 2004

INTRODUCTION The Need for Spatial Analysis Types of Spatial Data Autocorrelation-Concept and Elementary Measures Autocorrelation Functions The Effects of Autocorrelation on Statistical Inference…

Classes of nonseparable, spatio-temporal stationary covariance functions

- Mathematics, Environmental Science
- 1999

Abstract Suppose that a random process Z(s;t), indexed in space and time, has spatio-temporal stationary covariance C(h;u), where h ∈ ℝd (d ≥ 1) is a spatial lag and u ∈ ℝ is a temporal lag.…

Fixed rank kriging for very large spatial data sets

- Mathematics
- 2008

Summary. Spatial statistics for very large spatial data sets is challenging. The size of the data set, n, causes problems in computing optimal spatial predictors such as kriging, since its…

Methods for Analyzing Large Spatial Data: A Review and Comparison

- Computer Science
- 2017

This study provides an introductory overview of several methods for analyzing large spatial data and describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology.