TY - JOUR
T1 - A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models
AU - Guan, Yawen
AU - Haran, Murali
N1 - Publisher Copyright:
© 2018, © 2018 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
PY - 2018/10/2
Y1 - 2018/10/2
N2 - Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduced-dimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction; our methods also compare favorably to existing “reduced-rank” approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types. Supplementary material for this article is available online.
AB - Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduced-dimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction; our methods also compare favorably to existing “reduced-rank” approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types. Supplementary material for this article is available online.
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U2 - 10.1080/10618600.2018.1425625
DO - 10.1080/10618600.2018.1425625
M3 - Article
AN - SCOPUS:85052374561
SN - 1061-8600
VL - 27
SP - 701
EP - 714
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
IS - 4
ER -