Spatially dependent data arises in many biometric applications, and Gaussian processes are a popular modelling choice for these scenarios. While Bayesian analyses of these problems have proven to be successful, selecting prior distributions for these complex models remains a difficult task. In this work, we propose a principled approach for setting prior distributions for spatial covariance parameters by placing a prior distribution on a measure of model fit. In particular, we derive the distribution of the prior coefficient of determination. Placing a beta prior distribution on this measure induces a generalized beta prime prior distribution on the global variance of the linear predictor in the model. This method can also be thought of as shrinking the fit towards the intercept-only (null) model. We derive an efficient Gibbs sampler for the majority of the parameters and use Metropolis-Hasting updates for the others. Finally, the method is applied to a marine protection area data set. We estimate the effect of marine policies on biodiversity and conclude that no-take restrictions lead to a slight increase in biodiversity and that the majority of the variance in the linear predictor comes from the spatial effect.

翻译：在许多生物鉴别应用中产生了空间依赖数据,Gaussian过程是这些假设情景的流行模型选择。虽然巴伊西亚对这些问题的分析已证明是成功的,但选择这些复杂模型的先前分布仍是一项困难的任务。在这项工作中,我们提出一个原则性办法,根据一个适合模型的尺度,确定空间共变参数的先前分布;特别是,我们得出先前确定系数的分布情况。在这个尺度上预先分配贝塔先期,就模型中线性预测器的全球差异进行普遍化的Beta主位的先前分布。这种方法也可以被视为缩小了对只截取(null)模型的适合性。我们为大多数参数获取高效的Gibs取样器,并为其他参数使用Motopolis-Hasing更新。最后,该方法适用于海洋保护区数据集。我们估计了海洋政策对生物多样性的影响,并得出结论认为,不采取限制措施会导致生物多样性略有增加,线性预测器的大部分差异来自空间效应。