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Approximate inference for disease mapping with sparse Gaussian processes
Author(s) -
Vanhatalo Jarno,
Pietiläinen Ville,
Vehtari Aki
Publication year - 2010
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3895
Subject(s) - inference , computer science , gaussian process , gaussian , statistics , econometrics , artificial intelligence , mathematics , physics , quantum mechanics
Abstract Gaussian process (GP) models are widely used in disease mapping as they provide a natural framework for modeling spatial correlations. Their challenges, however, lie in computational burden and memory requirements. In disease mapping models, the other difficulty is inference, which is analytically intractable due to the non‐Gaussian observation model. In this paper, we address both these challenges. We show how to efficiently build fully and partially independent conditional (FIC/PIC) sparse approximations for the GP in two‐dimensional surface, and how to conduct approximate inference using expectation propagation (EP) algorithm and Laplace approximation (LA). We also propose to combine FIC with a compactly supported covariance function to construct a computationally efficient additive model that can model long and short length‐scale spatial correlations simultaneously. The benefit of these approximations is computational. The sparse GPs speed up the computations and reduce the memory requirements. The posterior inference via EP and Laplace approximation is much faster and is practically as accurate as via Markov chain Monte Carlo. Copyright © 2010 John Wiley & Sons, Ltd.