In species distribution modelling, records of species presence are often modelled as a realization of a spatial point process whose intensity is a function of environmental covariates. One way to fit a spatial point process model is to apply logistic regression to an artificial case–control sample consisting of the observed presence records combined with a simulated pattern of background points, usually a uniform random sample from within the study’s spatial domain. In this paper we propose local background sampling as an alternative to uniform background sampling when using logistic regression to fit spatial point process models to data. Our method is similar to the local case–control sampling procedure of Fithian and Hastie (Ann Appl Stat 42:1693–1724, 2014), but differs in that background points are sampled with probability proportional to an initial intensity estimate based on a pilot point process model. We compare local background sampling with uniform background sampling in a simulation study and in an example modelling the distributions of bumble bees (genus Bombus ) in Ontario, Canada. Our results show local background sampling to be more efficient than uniform background sampling in all simulated settings and across all species analysed. Supplementary materials accompanying this paper appear online.

中文翻译：

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通过局部背景采样对仅存在物种数据进行有效建模

在物种分布建模中，物种存在的记录通常被建模为空间点过程的实现，其强度是环境协变量的函数。拟合空间点过程模型的一种方法是将逻辑回归应用于人工病例对照样本，该样本由观察到的存在记录与背景点的模拟模式相结合，通常是来自研究空间域内的均匀随机样本。在本文中，当使用逻辑回归将空间点过程模型拟合到数据时，我们建议局部背景采样作为统一背景采样的替代方案。我们的方法类似于Fithian 和Hastie 的本地病例对照抽样程序（Ann Appl Stat 42:1693–1724, 2014），但不同之处在于背景点的采样概率与基于先导点过程模型的初始强度估计值成正比。我们在模拟研究中比较了局部背景采样与均匀背景采样，并在一个示例中对加拿大安大略省的熊蜂（Bombus 属）的分布进行了建模。我们的结果表明，在所有模拟设置和所有分析的物种中，局部背景采样比均匀背景采样更有效。本文随附的补充材料出现在网上。我们的结果表明，在所有模拟环境中和分析的所有物种中，局部背景采样比均匀背景采样更有效。本文随附的补充材料出现在网上。我们的结果表明，在所有模拟设置和所有分析的物种中，局部背景采样比均匀背景采样更有效。本文随附的补充材料出现在网上。