Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection
Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection
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DOI：
10.1111/rssc.12281
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
Tuomas A. Rajala;D. Murrell;S. Olhede
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文献类型：
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作者：
Tuomas A. Rajala;D. Murrell;S. Olhede
我们提出了一种在非常大的多元空间点模式中检测显著相互作用的方法。因此，这种方法在点过程设置中开发了高维数据理解。该方法利用灵活的吉布斯点过程模型来直接表征不同空间尺度上的点对点相互作用。通过使用吉布斯框架，也可以在小尺度上捕获重要的相互作用。随后，利用伪似然近似拟合Gibbs点过程，并在此似然近似下利用群套索惩罚自动选择显著相互作用。因此，即使在这种情况下，我们也可以稳定地估计多变量相互作用。我们通过模拟研究证明了该方法的可行性，并通过将其应用于83种大型复杂雨林植物种群数据集显示了其功能。
We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology thus develops high dimensional data understanding in the point process setting. The method is based on modelling the patterns by using a flexible Gibbs point process model to characterize point‐to‐point interactions at different spatial scales directly. By using the Gibbs framework significant interactions can also be captured at small scales. Subsequently, the Gibbs point process is fitted by using a pseudolikelihood approximation, and we select significant interactions automatically by using the group lasso penalty with this likelihood approximation. Thus we estimate the multivariate interactions stably even in this setting. We demonstrate the feasibility of the method with a simulation study and show its power by applying it to a large and complex rainforest plant population data set of 83 species.