PairPiece(spatstat)
PairPiece()所属R语言包：spatstat
The Piecewise Constant Pairwise Interaction Point Process Model
逐段常对相互作用点过程模型
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Creates an instance of a pairwise interaction point process model with piecewise constant potential function. The model can then be fitted to point pattern data.
一对相互作用的点过程模型具有逐段常势函数创建一个实例。该模型然后可以嵌合点图案数据。
用法----------Usage----------
PairPiece(r)
参数----------Arguments----------
参数：r
vector of jump points for the potential function
的势函数的跳跃点的矢量
Details
详细信息----------Details----------
A pairwise interaction point process in a bounded region is a stochastic point process with probability density of the form
成对的相互作用点的过程中有界区域是一个随机点过程的概率密度的形式
where x[1],…,x[n] represent the points of the pattern. The first product on the right hand side is over all points of the pattern; the second product is over all unordered pairs of points of the pattern.
x[1],…,x[n]代表的模式。右手侧上的第一个产品的全部点的图案;第二产品是对所有无序对点的图案。
Thus each point x[i] of the pattern contributes a factor b(x[i]) to the probability density, and each pair of points x[i], x[j] contributes a factor h(x[i], x[j]) to the density.
因此，每个点x[i]的图案有助于一个因素b(x[i])的概率密度，以及每对点x[i], x[j]贡献因子h(x[i], x[j])的密度。
The pairwise interaction term h(u, v) is called piecewise constant if it depends only on the distance between u and v, say h(u,v) = H(||u-v||), and H is a piecewise constant function (a function which is constant except for jumps at a finite number of places). The use of piecewise constant interaction terms was first suggested by Takacs (1986).
两两交互项h(u, v)被称为分段常量，如果只依赖于之间的距离u和v，说h(u,v) = H(||u-v||)和H是一个分段常数功能（一个函数，它是恒定的跳跃在有限数量的地方除外）。利用的分段常数互动方面的塔卡克斯（1986）首先提出的。
The function ppm(), which fits point process models to point pattern data, requires an argument of class "interact" describing the interpoint interaction structure of the model to be fitted. The appropriate description of the piecewise constant pairwise interaction is yielded by the function PairPiece(). See the examples below.
的功能ppm()，适合点模式数据点过程模型，需要一个参数的类"interact"描述INTERPOINT互动结构的模型被安装。分段常数对相互作用产生的功能PairPiece()适当的描述。请参见下面的例子。
The entries of r must be strictly increasing, positive numbers. They are interpreted as the points of discontinuity of H. It is assumed that H(s) =1 for all s > rmax where rmax is the maximum value in r. Thus the model has as many regular parameters (see ppm) as there are entries in r. The i-th regular parameter theta[i] is the logarithm of the value of the interaction function H on the interval [r[i-1],r[i]).
r的条目必须严格递增的，正数。它们被解释为点的不连续性H。 H(s) =1为所有的s > rmax其中rmax是在r最大值。因此，该模型具有许多常规参数（见ppm）有在r。 i第常参数theta[i]是相互制约功能H上的间隔[r[i-1],r[i])的值的对数。
If r is a single number, this model is similar to the Strauss process, see Strauss. The difference is that in PairPiece the interaction function is continuous on the right, while in Strauss it is continuous on the left.
如果r是一个单一的数字，这种模式是类似施特劳斯进程，看到Strauss。所不同的是在PairPiece的相互作用函数是连续的在右边，而在Strauss它是连续的左方。
The analogue of this model for multitype point processes has not yet been implemented.
尚未实施这种模式下的多点过程的模拟。
值----------Value----------
An object of class "interact" describing the interpoint interaction structure of a point process. The process is a pairwise interaction process, whose interaction potential is piecewise constant, with jumps at the distances given in the vector r.
类的一个对象"interact"描述INTERPOINT互动结构的点处理。这个过程是一对相互作用的过程中，其相互作用势是分段不变的，跳跃的距离向量r。
（作者）----------Author(s)----------
Adrian Baddeley
<a href="mailto:Adrian.Baddeley@csiro.au">Adrian.Baddeley@csiro.au</a>
<a href="http://www.maths.uwa.edu.au/~adrian/">http://www.maths.uwa.edu.au/~adrian/</a>
and Rolf Turner
<a href="mailto:r.turner@auckland.ac.nz">r.turner@auckland.ac.nz</a>
参考文献----------References----------
Estimator for the pair potential of a Gibbsian point process. Statistics 17, 429–433.
参见----------See Also----------
ppm, pairwise.family, ppm.object, Strauss rmh.ppm
ppm，pairwise.family，ppm.object，Straussrmh.ppm
实例----------Examples----------
PairPiece(c(0.1,0.2))
# prints a sensible description of itself[打印本身就是一个明智的描述]
data(cells)
## Not run: [＃不运行：]
ppm(cells, ~1, PairPiece(r = c(0.05, 0.1, 0.2)))
# fit a stationary piecewise constant pairwise interaction process[适合一个固定的分段恒定的两两相互作用的过程]
## End(Not run)[＃（不执行）]
ppm(cells, ~polynom(x,y,3), PairPiece(c(0.05, 0.1)))
# nonstationary process with log-cubic polynomial trend[非平稳过程的log三次多项式趋势]
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-30 13:53:03
