Simultaneous credible bands for latent Gaussian models

Sigrunn H. Sørbye*, Haavard Rue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Deterministic Bayesian inference for latent Gaussian models has recently become available using integrated nested Laplace approximations (INLA). Applying the INLA-methodology, marginal estimates for elements of the latent field can be computed efficiently, providing relevant summary statistics like posterior means, variances and pointwise credible intervals. In this article, we extend the use of INLA to joint inference and present an algorithm to derive analytical simultaneous credible bands for subsets of the latent field. The algorithm is based on approximating the joint distribution of the subsets by multivariate Gaussian mixtures. Additionally, we present a saddlepoint approximation to compute Bayesian contour probabilities, representing the posterior support of fixed parameter vectors of interest. We perform a simulation study and apply the given methods to two real examples.

Original languageEnglish (US)
Pages (from-to)712-725
Number of pages14
JournalScandinavian Journal of Statistics
Volume38
Issue number4
DOIs
StatePublished - Dec 1 2011

Keywords

  • Contour probability
  • Gaussian mixtures
  • Highest posterior density region
  • Integrated nested Laplace approximations
  • Simultaneous credible bands

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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