Fast sampling of Gaussian Markov random fields

By Håvard Rue. 2000

430 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fa2970cab78537bddc679372c1fe0ec0ac29cc48

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

A Bayesian Semiparametric Latent Variable Model for Mixed Responses (2007, positive): “More information about Markov random fields is given in Rue (2005).”
The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling (2017, methodology): “Recent articles using the former approach include Rue (2001) for linear Gaussian Markov random fields; Chan and Jeliazkov (2009) and McCausland, Miller, and Pelletier (2011) for linear Gaussian state–space models; Rue, Martino, and Chopin (2009) for nonlinear Markov random fields; McCausland…”
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, neutral): “See Rue and Held (2005) for more details on both issues.”
A latent Gaussian Markov random‐field model for spatiotemporal rainfall disaggregation (2003, methodology): “If the transformation (1) was linear, it would be easy to sample yA conditionally on its sum being a constant (see, for example Rue (2001)).”
Non-Centered Parameterisations for Hierarchical Models and Data Augmentation (2003, background): “Note that this depends on the marginal likelihood of the dataL(θ;Y ), but this is usually tractable whenever sampling X | θ, Y in a single block is possible (Rue 2001, Wilkinson and Yeung 2002b).”
Bayesian P-Splines (2004, methodology): “Following Rue (2001), drawing random numbers from p(¯j j¢) is as follows: We rst compute the Cholesky decompositionPj = LL0.”
Geoadditive Survival Models (2006, methodology): “be efficiently drawn using an algorithm by Rue (2001). The ac-”
Bayesian Geostatistical Design (2006, positive): “However, work by Rue (2001) and Rue & Tjelmeland (2002) is leading to very substantial gains in the speed of computation for geostatistical analysis of much larger data sets.”
Gaussian Markov Random Fields: Theory and Applications (2006, background): “In the statistics literature, Rue (2001) comprehensively discusses fast unconditional and conditional sampling from GMRFs and approximation techniques for more complicated GMRF applications, taking advantage of sparse matrix operations developed in the computer science literature.”
A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion (2013, positive): “Even if a Gaussian Markov random field is not based on an elliptic differential operator, this Markov property permits the use of fast, sparsity-exploiting algorithms, for instance, for taking samples from the distribution [40].”
Smooth skyride through a rough skyline: Bayesian coalescent-based inference of population dynamics. (2008, background): “Such a special form of density (A2) allows one to generate samples from its Gaussian approximation using computationally efficient algorithms for sparse matrix computations (Rue 2001).”
Non-Denoising Forward-Time Diffusions (2023, background): “Alternative scalable approaches abound, from Gaussian Markov Random Fields (Rue & Tjelmeland, 2002; Rue, 2001) to Karhunen–Loève expansions (Betz et al., 2014).”
Monotonic Regression Based on Bayesian P–Splines (2008, positive): “This involves a Cholesky decomposition and avoids expensive matrix inversions (compare Rue 2001).”
Modelling spatially correlated data via mixtures: a Bayesian approach (2002, methodology): “Thus, instead of a standard algorithm for multivariate normal random generation, we used the algorithm developed by Rue (2001) for fast sampling of Gaussian Markov random fields.”