AreaInter(spatstat)
AreaInter()所属R语言包：spatstat
The Area Interaction Point Process Model
区域互动点过程模型
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Creates an instance of the Area Interaction point process model (Widom-Rowlinson penetrable spheres model) which can then be fitted to point pattern data.
建立区域互动点过程模型（Widom - 罗林森穿透球模型），然后可以配点模式数据的一个实例。
用法----------Usage----------
AreaInter(r)
参数----------Arguments----------
参数：r
The radius of the discs in the area interaction process
中的光盘的区域的相互作用过程中的半径
Details
详细信息----------Details----------
This function defines the interpoint interaction structure of a point process called the Widom-Rowlinson penetrable sphere model or area-interaction process. It can be used to fit this model to point pattern data.
此功能定义INTERPOINT互动结构的一个点的过程称为Widom罗林森穿透球模型或区域互动的过程。它可用于以适合此模型的点图案数据。
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 area interaction structure is yielded by the function AreaInter(). 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。适当的描述区域互动结构产生的功能AreaInter()。请参见下面的例子。
In standard form, the area-interaction process (Widom and Rowlinson, 1970; Baddeley and Van Lieshout, 1995) with disc radius r, intensity parameter kappa and interaction parameter gamma is a point process with probability density
在标准的形式，与光盘半径的区域相互作用的过程（Widom和罗林森，1970年Baddeley和范·利斯豪特，1995年）r，强度参数kappa和相互作用参数gamma是一个点过程的概率密度
for a point pattern x, where x[1],…,x[n] represent the points of the pattern, n(x) is the number of points in the pattern, and A(x) is the area of the region formed by the union of discs of radius r centred at the points x[1],…,x[n]. Here alpha is a normalising constant.
点模式x，其中x[1],…,x[n]代表的模式，n(x)是多少点的格局，和A(x)是形成的区域的面积光盘的半径由工会r中心在的点x[1],…,x[n]。这是alpha是归一化常数。
The interaction parameter gamma can be any positive number. If gamma = 1 then the model reduces to a Poisson process with intensity kappa. If gamma < 1 then the process is regular, while if gamma > 1 the process is clustered. Thus, an area interaction process can be used to model either clustered or regular point patterns. Two points interact if the distance between them is less than 2 * r.
相互作用参数gamma可以是任何正数。如果gamma = 1然后，模型简化的泊松过程与强度kappa。如果gamma < 1那么这个过程是有规律的，而如果gamma > 1的过程是聚类。因此，区域互动的过程，可用于模型聚集或经常点模式。交互的两个点，如果它们之间的距离是小于2 * r。
The standard form of the model, shown above, is a little complicated to interpret in practical applications. For example, each isolated point of the pattern x contributes a factor kappa * gamma^(-pi * r^2) to the probability density.
标准形式的模型，上面显示的是一个有点复杂，在实际应用中解释。例如，每一个孤立点的图案x贡献的因素kappa * gamma^(-pi * r^2)的概率密度。
In spatstat, the model is parametrised in a different form, which is easier to interpret. In canonical scale-free form, the probability density is rewritten as
在spatstat，该模型是parametrised以不同的形式，这是比较容易解释。在规范的尺度游离形式，被重写为概率密度
where beta is the new intensity parameter, eta is the new interaction parameter, and C(x) = B(x) - n(x) is the interaction potential. Here
beta是新的强度参数，eta是新的相互作用参数，并C(x) = B(x) - n(x)是潜在的相互作用。这里
is the normalised area (so that the discs have unit area). In this formulation, each isolated point of the pattern contributes a factor beta to the probability density (so the first order trend is beta). The quantity C(x) is a true interaction potential, in the sense that C(x) = 0 if the point pattern x does not contain any points that lie close together (closer than 2*r units apart).
是归一化的区域（使光盘有单位面积）。在此配方中，每一个孤立点的图案有助于一个因素beta的概率密度（因此所述第一阶的趋势是beta）。的数量C(x)是一个真正的相互作用势，在这个意义上，C(x) = 0如果点模式x不包含任何点位于靠近（接近2*r单位除了）。
When a new point u is added to an existing point pattern x, the rescaled potential -C(x) increases by a value between 0 and 1. The increase is zero if u is not close to any point of x. The increase is 1 if the disc of radius r centred at u is completely contained in the union of discs of radius r centred at the data points x[i]. Thus, the increase in potential is a measure of how close the new point u is to the existing pattern x. Addition of the point u contributes a factor beta * eta^delta to the probability density, where delta is the increase in potential.
当一个新的起点u被添加到现有的模式x，重新调整的潜在-C(x)0和1之间的值增加。增加零u如果不靠近任何一点的x。增加光盘的半径r集中在u完全包含在工会的光盘的半径r数据点集中在x[i]。因此，增长潜力是多么接近新的起点u的现有格局x衡量的。加点u贡献的一个因素beta * eta^delta的概率密度，其中delta是增长潜力。
The old parameters kappa,gamma of the standard form are related to the new parameters beta,eta of the canonical scale-free form, by
旧的参数kappa,gamma的标准形式相关的新的参数beta,eta典型的无标度的形式，
and
和
provided gamma and kappa are positive and finite.
提供gamma和kappa是积极的和有限的。
In the canonical scale-free form, the parameter eta can take any nonnegative value. The value eta = 1 again corresponds to a Poisson process, with intensity beta. If eta < 1 then the process is regular, while if eta > 1 the process is clustered. The value eta = 0 corresponds to a hard core process with hard core radius r (interaction distance 2r).
在典型的无标度的形式，参数eta可以任意非负值。的价值eta = 1再次与泊松过程，与强度beta。如果eta < 1那么这个过程是有规律的，而如果eta > 1的过程是聚类。的价值eta = 0硬核与硬核半径的对应r（作用距离2r）。
The nonstationary area interaction process is similar except that the contribution of each individual point x[i] is a function beta(x[i]) of location, rather than a constant beta.
非平稳区域互动的过程是类似的，除了的贡献，每个点x[i]的功能beta(x[i])的位置，而不是一个常数测试。
Note the only argument of AreaInter() is the disc radius r. When r is fixed, the model becomes an exponential family. The canonical parameters log(beta) and log(eta) are estimated by ppm(), not fixed in AreaInter().
需要注意的唯一参数AreaInter()盘半径r。当r是固定的，的模型成为指数的家庭。规范参数log(beta)和log(eta)估计ppm()，而不是固定在AreaInter()。
值----------Value----------
An object of class "interact" describing the interpoint interaction structure of the area-interaction process with disc radius r.
类的一个对象"interact"描述INTERPOINT互动结构的区域互动的过程与光盘半径r。
警告----------Warnings----------
The interaction distance of this process is equal to 2 * r. Two discs of radius r overlap if their centres are closer than 2 * r units apart.
这个过程的作用距离等于2 * r。两个圆盘的半径r重叠，如果他们的中心，是接近2 * r单位除了。
The estimate of the interaction parameter eta is unreliable if the interaction radius r is too small or too large. In these situations the model is approximately Poisson so that eta is unidentifiable. As a rule of thumb, one can inspect the empty space function of the data, computed by Fest. The value F(r) of the empty space function at the interaction radius r should be between 0.2 and 0.8.
的相互作用参数eta的估计是不可靠的，如果的相互作用半径r是过小或过大。在这种情况下，该模型是约泊松使eta是无法识别的。作为一个经验法则，可以检查数据，计算出Fest空的空间功能。该值F(r)的空的空间的函数的相互作用半径r应该是在0.2和0.8之间。
（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----------
Area-interaction point processes. Annals of the Institute of Statistical Mathematics 47 (1995) 601–619.
New model for the study of liquid-vapor phase transitions. The Journal of Chemical Physics 52 (1970) 1670–1684.
参见----------See Also----------
ppm, pairwise.family, ppm.object
ppm，pairwise.family，ppm.object
实例----------Examples----------
# prints a sensible description of itself[打印本身就是一个明智的描述]
AreaInter(r=0.1)
# Note the reach is twice the radius[注意的覆盖范围是半径的两倍]
reach(AreaInter(r=1))
# Fit the stationary area interaction process to Swedish Pines data[适合在固定的区域互动的过程，瑞典松树数据]
data(swedishpines)
ppm(swedishpines, ~1, AreaInter(r=7))
# Fit the stationary area interaction process to `cells'[适合固定的区域互动的过程单元]
data(cells)
ppm(cells, ~1, AreaInter(r=0.06))
# eta=0 indicates hard core process.[η= 0表示硬盘的核心过程。]
# Fit a nonstationary area interaction with log-cubic polynomial trend[适合非平稳区域互动与数三次多项式趋势]
## Not run: [＃不运行：]
ppm(swedishpines, ~polynom(x/10,y/10,3), AreaInter(r=7))
## End(Not run)[＃（不执行）]
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注：
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发表于 2012-9-30 13:09:52
