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Title: Scalable Predictions for Spatial Probit Linear Mixed Models Using Nearest Neighbor Gaussian Processes
Spatial probit generalized linear mixed models (spGLMM) with a linear fixed effect and a spatial random effect, endowed with a Gaussian Process prior, are widely used for analysis of binary spatial data. However, the canonical Bayesian implementation of this hierarchical mixed model can involve protracted Markov Chain Monte Carlo sampling. Alternate approaches have been proposed that circumvent this by directly representing the marginal likelihood from spGLMM in terms of multivariate normal cummulative distribution functions (cdf). We present a direct and fast rendition of this latter approach for predictions from a spatial probit linear mixed model. We show that the covariance matrix of the cdf characterizing the marginal cdf of binary spatial data from spGLMM is amenable to approximation using Nearest Neighbor Gaussian Processes (NNGP). This facilitates a scalable prediction algorithm for spGLMM using NNGP that only involves sparse or small matrix computations and can be deployed in an embarrassingly parallel manner. We demonstrate the accuracy and scalability of the algorithm via numerous simulation experiments and an analysis of species presence-absence data.  more » « less
Award ID(s):
1915803
NSF-PAR ID:
10447670
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Data Science
ISSN:
1680-743X
Page Range / eLocation ID:
533 to 544
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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