Variational Bayesian methods for spatial data analysis

Qian Ren, Sudipto Banerjee, Andrew O. Finley, James S Hodges

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. However, fitting spatial models often involves expensive matrix decompositions, whose computational complexity increases in cubic order with the number of spatial locations. This situation is aggravated in Bayesian settings where such computations are required once at every iteration of the Markov chain Monte Carlo (MCMC) algorithms. In this paper, we describe the use of Variational Bayesian (VB) methods as an alternative to MCMC to approximate the posterior distributions of complex spatial models. Variational methods, which have been used extensively in Bayesian machine learning for several years, provide a lower bound on the marginal likelihood, which can be computed efficiently. We provide results for the variational updates in several models especially emphasizing their use in multivariate spatial analysis. We demonstrate estimation and model comparisons from VB methods by using simulated data as well as environmental data sets and compare them with inference from MCMC.

Original languageEnglish (US)
Pages (from-to)3197-3217
Number of pages21
JournalComputational Statistics and Data Analysis
Issue number12
StatePublished - Dec 1 2011

Bibliographical note

Copyright 2018 Elsevier B.V., All rights reserved.


  • Bayesian inference
  • Gaussian process
  • Hierarchical models
  • Markov chain Monte Carlo
  • Spatial process models
  • Variational Bayesian


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