Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
复制标题
使用过去的主导耦合以及应用于区域交互点过程和小波阈值的完美模拟
DOI：
10.1017/cbo9781139107174.005
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Bernard Walter Silverman
中科院分区：
文献类型：
--
作者：
G. Ambler;Bernard Walter Silverman
我们认为完美的局部稳定点过程的模拟算法的基础上占主导地位的耦合从过去，并将这些方法应用在两个不同的上下文中。一个新的版本的算法是可行的过程，既不是纯粹的吸引力，也不是纯粹的排斥。这些过程包括多尺度区域相互作用过程，能够模拟其聚类结构在不同尺度上变化的点模式。考虑的另一个主题是非参数回归使用小波，在那里我们使用一个合适的面积相互作用过程的离散空间的小波系数的指数建模的概念，如果一个小波系数是非零的，那么它更有可能是相邻的系数也将。与独立阈值系数的标准方法相比，该模型中基于完美模拟的方法显示出有希望的结果。
We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past, and apply these methods in two different contexts. A new version of the algorithm is developed which is feasible for processes which are neither purely attractive nor purely repulsive. Such processes include multiscale area-interaction processes, which are capable of modelling point patterns whose clustering structure varies across scales. The other topic considered is nonparametric regression using wavelets, where we use a suitable area-interaction process on the discrete space of indices of wavelet coefficients to model the notion that if one wavelet coefficient is non-zero then it is more likely that neighbouring coefficients will be also. A method based on perfect simulation within this model shows promising results compared to the standard methods which threshold coefficients independently.