spStack: Bayesian Geostatistics Using Predictive Stacking

This package delivers functions to fit Bayesian hierarchical spatial process models for point-referenced Gaussian, Poisson, binomial, and binary data using stacking of predictive densities. It involves sampling from analytically available posterior distributions conditional upon some candidate values of the spatial process parameters for both Gaussian response model as well as non-Gaussian responses, and, subsequently assimilate inference from these individual posterior distributions using Bayesian predictive stacking. Our algorithm is highly parallelizable and hence, much faster than traditional Markov chain Monte Carlo algorithms while delivering competitive predictive performance.

In context of inference for spatial point-referenced data, Bayesian hierarchical models involve latent spatial processes characterized by spatial process parameters, which besides lacking substantive relevance in scientific contexts, are also weakly identified and hence, impedes convergence of MCMC algorithms. This motivates us to build methodology that involves fast sampling from posterior distributions conditioned on a grid of the weakly identified model parameters and combine the inference by stacking of predictive densities (Yao et. al 2018). We exploit the Bayesian conjugate linear modeling framework for the Gaussian case (Zhang, Tang and Banerjee 2024) and the generalized conjugate multivariate distribution theory (Pan, Zhang, Bradley and Banerjee 2024) to analytically derive the individual posterior distributions.

Details

Package:	spStack
Type:	Package
Version:	0.1.0
License:	GPL-3

Accepts a formula, e.g., y~x1+x2, for most regression models accompanied by candidate values of spatial process parameters, and returns posterior samples of the regression coefficients and the latent spatial random effects. Posterior inference or prediction of any quantity of interest proceed from these samples. Main functions are -
spLMexact()
spGLMexact()
spLMstack()
spGLMstack()

References

Zhang L, Tang W, Banerjee S (2024). "Bayesian Geostatistics Using Predictive Stacking."
doi:10.48550/arXiv.2304.12414 .

Pan S, Zhang L, Bradley JR, Banerjee S (2024). "Bayesian Inference for Spatial-temporal Non-Gaussian Data Using Predictive Stacking." doi:10.48550/arXiv.2406.04655 .

Yao Y, Vehtari A, Simpson D, Gelman A (2018). "Using Stacking to Average Bayesian Predictive Distributions (with Discussion)." Bayesian Analysis, 13(3), 917-1007. doi:10.1214/17-BA1091 .

See also

Useful links:

• https://github.com/SPan-18/spStack-dev

• https://span-18.github.io/spStack-dev/

• Report bugs at https://github.com/SPan-18/spStack-dev/issues

Author

Maintainer: Soumyakanti Pan span18@ucla.edu (ORCID)

Authors:

• Sudipto Banerjee sudipto@ucla.edu