Spatial point pattern data are routinely encountered. A flexible regression model for the underlying intensity is essential to characterizing the spatial point pattern and understanding the impacts of potential risk factors on such pattern. We propose a Bayesian semiparametric regression model where the observed spatial points follow a spatial Poisson process with an intensity function which adjusts a nonparametric baseline intensity with multiplicative covariate effects. The baseline intensity is piece-wise constant, approached with a powered Chinese restaurant process prior which prevents an unnecessarily large number of pieces. The parametric regression part allows for variable selection through the spike-slab prior on the regression coefficients. An efficient Markov chain Monte Carlo algorithm is developed for the proposed methods. The performance of the methods is validated in an extensive simulation study. In application to the locations of Beilschmiedia pendula trees in the Barro Colorado Island forest dynamics research plot in central Panama, the spatial heterogeneity is attributed to a subset of soil measurements in addition to geographic measurements with a spatially varying baseline intensity.

中文翻译：

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空间点模式的异质性追求与树木位置的应用：贝叶斯半参数资源

通常会遇到空间点模式数据。潜在强度的灵活回归模型对于表征空间点模式和了解潜在风险因素对此类模式的影响至关重要。我们提出了一种贝叶斯半参数回归模型，其中观察到的空间点遵循具有强度函数的空间泊松过程，该函数通过乘法协变量效应调整非参数基线强度。基线强度是分段恒定的，通过一个有动力的中餐馆流程来处理，这可以防止不必要的大量碎片。参数回归部分允许通过回归系数上的尖峰板先验变量选择。针对所提出的方法开发了一种有效的马尔可夫链蒙特卡罗算法。这些方法的性能在广泛的模拟研究中得到了验证。适用于以下地点Beilschmiedia pendula树位于巴拿马中部巴罗科罗拉多岛森林动态研究区，空间异质性归因于土壤测量的子集，以及具有空间变化基线强度的地理测量。