Analyzing Spatial Point Patterns Subject to Measurement Error
Analyzing Spatial Point Patterns Subject to Measurement Error
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DOI：
10.1214/10-ba504
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发表时间：
2010-01-01
影响因子：
4.4
通讯作者：
Gelfand, Alan E.
中科院分区：
文献类型：
--
作者：
Chakraborty, Avishek;Gelfand, Alan E.
我们解决的问题，推理的噪声点模式。不可观测的真点过程被建模为非齐次泊松过程。为了对底层强度表面进行建模，我们使用缩放的高斯混合分布。测量过程中的噪声会导致真实位置的随机位移。我们考虑两种设置。对于有界的感兴趣区域，（i）该位移可能导致边界内的真实位置与该区域外部的“观察到的”位置相关联，从而错过，并且（ii）我们有可能在（i）中，但反之亦然;位移可能带来其真实位置位于该区域外部的观察到的位置。在（i）中，我们只能丢失点，并且根据测量误差的可变性以及靠近边界的真实位置的数量，这可能导致从我们记录的数据集中丢失大量位置。从观测数据中估计强度表面可能会产生误导，特别是在我们感兴趣的域的边界附近。在（ii）下，建模问题更加困难;点可以丢失和获得，并且很难描述我们如何在没有关于感兴趣域之外的基本强度的数据的情况下获得点。在这两种情况下，我们的工作在一个分层贝叶斯框架，modelingthelatentpointpatternusingaCox过程，并给出了过程实现，引入一个合适的测量误差模型。因此，该规范包括作为未知数的点的真实数量。我们讨论了测量误差模型的选择以及由此产生的可辨识性问题。模型拟合使用马尔可夫链蒙特卡罗实现。在对几个合成数据集验证我们的方法后，我们说明了它的应用程序的两个生态数据集。
We address the issue of inference for a noisy point pattern. The unobserved true point process is modelled as a nonhomogeneous Poisson process. For modeling the underlying intensity surface we use a scaled Gaussian mixture distribution. The noise that creeps in during the measurement procedure causes random displacement of the true locations. We consider two settings. Witha bounded region of interest, (i) this displacement may cause a true location within the boundary to be associated with an 'observed' location outside of the region and thus missed and (ii) we have the possibility in (i) but also vice versa; the displacement may bring in an observed location whose true location lies outside the region. Under (i), we can only lose points and, depending on the variability in the measurement error as well as the number of true locations closeto boundary, this can cause a significant number of locations to be lost from our recorded set of data. Estimation of the intensity surface from the observed data can be misleading especially near the boundary of our domain of interest. Under (ii), the modeling problem is more didifficult; points can be both lost and gained and it is challenging to characterize how we may gain points with no data on the underly-ingintensity outside the domain of interest. In both cases, we work within a hierarchical Bayes framework, modelingthelatentpointpatternusingaCoxprocessand, given the process realization, introducing a suitable measurement error model. Hence, the specification includes the true number of points as an unknown. we discuss choice of measurement error model as well as identifiability problems which arise. Models are fitted using an markov chain Monte Carlo implementation. After validating our method against several synthetic datasets we illustrate its application for two ecological datasets.