Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging

Selma Metzner (), Gerd Wübbeler and Clemens Elster
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Selma Metzner: Physikalisch–Technische Bundesanstalt
Gerd Wübbeler: Physikalisch–Technische Bundesanstalt
Clemens Elster: Physikalisch–Technische Bundesanstalt

AStA Advances in Statistical Analysis, 2019, vol. 103, issue 3, No 2, 333-355

Abstract: Abstract We consider the Bayesian inference of nonlinear, large-scale regression problems in which the parameters model the spatial distribution of some property. A homoscedastic Gaussian sampling distribution is supposed as well as certain assumptions about the regression function. Propriety of the posterior and the existence of its moments are explored when using improper prior distributions expressing different levels of prior knowledge, ranging from a purely noninformative prior over intrinsic Gaussian Markov random field priors to a partition prior. The considered class of problems includes magnetic resonance fingerprinting (MRF). We apply an approximate Bayesian inference to this particular application and demonstrate its practicability in dimensions up to $$10^5$$ 10 5 or larger. The benefit of incorporating substantial prior knowledge is illustrated. By analyzing simulated realistic MRF data, it is shown that MAP estimates can significantly improve the results achieved with maximum likelihood estimation.

Keywords: Bayesian inference; Laplace approximation; Large-scale nonlinear regression; Spatial modeling; Quantitative magnetic resonance imaging (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10182-018-00334-0

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