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首页> 外文期刊>AStA Advances in statistical analysis >Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging
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Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging

机译：近似大型贝叶斯空间建模，应用于定量磁共振成像

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摘要

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 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.
机译：我们考虑了非线性，大规模回归问题的贝叶斯推断，其中参数模型一些属性的空间分布。应该是一个关于回归函数的某些假设的同性恋高斯采样分布。在使用表达不同水平的现有知识水平的不正确的分布时，探讨了后续的恰当和其时刻的存在，从而从内在高斯马尔可夫随机场前沿到之前的纯粹非信息范围。被认为的类问题包括磁共振指纹（MRF）。我们对该特定应用应用近似贝叶斯推理，并展示其尺寸直至或更大的实用性。阐述了纳入实质性知识的益处。通过分析模拟的现实MRF数据，显示地图估计可以显着改善最大似然估计所实现的结果。

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