Scalable Predictions for Spatial Probit Linear Mixed Models Using Nearest Neighbor Gaussian Processes.

Area of Science:

• Statistics
• Spatial statistics
• Computational statistics

Background:

• Spatial probit generalized linear mixed models (spGLMM) are standard for binary spatial data.
• Bayesian spGLMM implementations often require lengthy Markov Chain Monte Carlo (MCMC) sampling.
• Existing alternatives approximate marginal likelihoods using multivariate normal cumulative distribution functions (cdf).

Purpose of the Study:

• To develop a fast and direct prediction algorithm for spatial probit linear mixed models.
• To leverage Nearest Neighbor Gaussian Processes (NNGP) for approximating complex covariance matrices.
• To enable scalable and efficient analysis of binary spatial data.

Main Methods:

• Approximation of the covariance matrix within the marginal cdf of spGLMM using NNGP.
• Development of a prediction algorithm involving sparse or small matrix computations.
• Deployment of an embarrassingly parallel computation strategy.

Main Results:

• The proposed NNGP-based method significantly accelerates predictions for spGLMM.
• The algorithm demonstrates accuracy comparable to traditional methods through simulations.
• The approach is highly scalable for large spatial datasets.

Conclusions:

• The NNGP approximation offers a computationally efficient alternative for spGLMM predictions.
• This facilitates the analysis of large-scale binary spatial data with improved performance.
• The method is validated through extensive simulations and real-world species presence-absence data analysis.