We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class characterizes spatial variability by a weighted combination of first-order conditional probability mass functions (pmfs) for each one of a given number of neighbors. The approach supports flexible modeling for multivariate dependence through specification of general bivariate discrete distributions that define the conditional pmfs. Moreover, the discrete NNMP allows for construction of models given a pre-specified family of marginal distributions that can vary in space, facilitating covariate inclusion. In particular, we develop a modeling and inferential framework for copula-based NNMPs that can attain flexible dependence structures, motivating the use of bivariate copula families for spatial processes. Compared to the traditional class of spatial generalized linear mixed models, where spatial dependence is introduced through a transformation of response means, our process-based modeling approach provides both computational and inferential advantages. We illustrate the benefits with synthetic data examples and an analysis of North American Breeding Bird Survey data.
翻译:我们引入了一种灵活且可扩缩的贝叶斯地理统计模型,用于提供离散数据,该模型以离散的相邻混合物过渡分布过程(NNMP)的等级为基础,称为离散的NNNMP。拟议类别通过对每个特定邻国的一级有条件概率质量函数(pmfs)进行加权组合,确定空间变异的特点。该方法支持通过对界定有条件pmfs的一般双轨离散分布的规格,为多种变异依赖性进行灵活建模。此外,离散的NNNMP允许根据一个在空间上可以变化的预先确定的边际分布系列构建模型,促进共变式包容。特别是,我们为基于相交的NNNMP开发了一个建模和推断框架,可以实现灵活的依赖结构,鼓励在空间进程中使用双变相交式相交织式组合式。与传统的空间通用线性混合模型类别相比,通过反应手段的转变引入空间依赖性,我们基于过程的建模方法提供了计算和推断的优势。我们用合成数据示例和北美BriA数据调查分析来说明这些效益。