It is not generally feasible to pick any given marginal distribution and assume there will be a way to apply a link function to add fixed and random effects in a spatial generalized linear model. We introduce an adjustment to spatial copula processes called a non-Gaussian translation process that will allow for the specification of any marginal distribution with a closed-form density function in a single unified framework. While translation processes do not preserve the exact marginal structure, they allow for fixed effects to be included in a non-Gaussian spatial model without needing to define a link function, as well as providing a number of other computational and modeling benefits. Non-Gaussian translation processes are compared theoretically and via simulation with traditional link function approaches and spatial copula processes and are shown to perform similarly in cases where all three models can effectively be used. A daily precipitation data set is analyzed with elevation as a predictor variable that includes a majority of observations being 0. Out-of-sample predictions are evaluated, and it is determined that the model is effective when compared to a two-stage prediction model and a Bayesian power truncated normal model.

选择任何给定的边际分布并假设有一种方法可以应用链接函数在空间广义线性模型中添加固定和随机效应，这通常是不可行的。我们引入了对空间 copula 过程的调整，称为非高斯转换过程，它将允许在单个统一框架中指定具有封闭形式密度函数的任何边缘分布。虽然转换过程不会保留精确的边缘结构，但它们允许将固定效应包含在非高斯空间模型中，而无需定义链接函数，并提供许多其他计算和建模优势。非高斯转换过程在理论上和通过模拟与传统的链接函数方法和空间 copula 过程进行了比较，并且在所有三种模型都可以有效使用的情况下表现相似。以高程作为预测变量分析每日降水数据集，其中包括大多数观测值为 0。评估样本外预测，并确定该模型与两阶段预测模型相比是有效的，并且贝叶斯幂截断法线模型。