Approximating likelihoods for large spatial data sets

By Michael L. Stein, Zhiyi Chi, Leah J. Welty. 2004

500 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/523ff8e17e4ac642015ce9c3f56ae7fb10e19ebe

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets (2008, background): “Stein et al. (2004) extended Vecchia’s idea to RMLEs and examined more ﬂexible choices of conditioning sets.”
Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models (2007, background): “[23] developed a similar “information sandwich’’ approximation for the spatial covariance matrix of the resulting estimator to the one we propose here.”
Likelihood approximation with hierarchical matrices for large spatial datasets (2017, background): “During the past two decades, a large amount of research has been devoted to tackling the aforementioned computational challenge of developing scalable methods: for example, covariance tapering [21, 36, 60], likelihood approximations in both the spatial [64] and spectral [19] domains, latent processe”
Matérn Cross-Covariance Functions for Multivariate Random Fields (2010, methodology): “Alternative approaches to estimation are of interest, such as likelihood approximations for large spatial datasets (Stein, Chi, and Welty 2004; Fuentes 2007), and some of the recent developments for the linear model of coregionalization (LMC), namely GLS and the EM algorithm (Pelletier et al. 2004;…”
Joint composite estimating functions in spatiotemporal models (2012, methodology): “In contrast, conditional CL approaches (e.g. Vecchia (1988) and Stein et al. (2004)) are usually vulnerable to model misspecification, because they require the formulation of higher dimensional distributions.”
Non‐stationary Cross‐Covariance Models for Multivariate Processes on a Globe (2011, methodology): “In that circumstance, we may resort to covariance tapering (Kaufman et al., 2008; Furrer & Sain, 2009) or other likelihood approximation methods such as Stein et al. (2004) and Fuentes (2007).”
A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data (2013, methodology): “The likelihood approximation methods seek to approximate the likelihood function in the spectral domain of the spatial process (Stein 1999; Fuentes 2007; Matsuda and Yajima 2009) or by a product of conditional densities (Vecchia 1988; Jones and Zhang 1997; Stein et al. 2004).”
Space–Time Covariance Functions (2005, methodology): “This approximation ignores the dependence between the Yj ’s, but does yield an unbiased estimating equation for θ (Stein et al. 2004).”
Gaussian predictive process models for large spatial data sets (2008, background): “A second approach seeks, instead, to approximate the likelihood either by working in the spectral domain of the spatial process and avoiding the matrix computations (Stein, 1999; Fuentes, 2007; Paciorek, 2007) or by forming a product of appropriate conditional distributions to approximate the likeli”
Statistical Properties of Covariance Tapers (2013, methodology): “The block taper is itself a crude approximation method and can sometimes be substantially improved upon using the approach in Vecchia (1988), further developed in Stein, Chi, and Welty (2004).”
On fixed-domain asymptotics and covariance tapering in Gaussian random field models (2011, background): “It is generally acknowledged (e.g., Stein, Chi and Welty [13], Furrer, Genton and Nychka [6], Kaufman, Schervish and Nychka [10] and Du, Zhang and Mandrekar [5]) that in practice, the data set in (3) is usually very large and is irregularly spaced.”
A full scale approximation of covariance functions for large spatial data sets (2012, background): “Various approximations of the covariance functions have been introduced to reduce the computational cost.”
Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain (2015, methodology): “Conditional approaches construct the composite likelihood as a product of conditional likelihoods for each observation given neighboring observations [Vecchia, 1988; Stein et al., 2004].”
A General Framework for Vecchia Approximations of Gaussian Processes (2017, methodology): “Stein et al. (2004) showed that maximizing (2) corresponds to solving a set of unbiased estimating equations, and they proposed a residual maximum likelihood (REML) method for estimating covariance parameters.”