Jest(spatstat)
Jest()所属R语言包：spatstat
Estimate the J-function
估计J-函数
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimates the summary function J(r) for a point pattern in a window of arbitrary shape.
估计的汇总函数J(r)一个点在一个窗口中任意形状的模式。
用法----------Usage----------
Jest(X, ..., eps=NULL, r=NULL, breaks=NULL, correction=NULL)
参数----------Arguments----------
参数：X
The observed point pattern, from which an estimate of J(r) will be computed. An object of class "ppp", or data in any format acceptable to as.ppp().
观测点的模式，从一个估算的J(r)将被计算。对象的类"ppp"，或任何格式的数据中接受的as.ppp()。
参数：...
Ignored.
忽略。
参数：eps
the resolution of the discrete approximation to Euclidean distance (see below). There is a sensible default.
欧几里德距离（见下文）的分辨率的离散逼近。有一个合理的默认。
参数：r
vector of values for the argument r at which J(r) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on r.
向量参数的值r，J(r)应该进行评估。有一个合理的默认。我们强烈建议用户第一次不指定此参数。请参阅下面的重要条件r。
参数：breaks
An alternative to the argument r. Not normally invoked by the user. See Details section.
替代到的参数r。通常不是由用户调用。见详图。
参数：correction
Optional. Character string specifying the choice of edge correction(s) in Fest and Gest.
可选。字符串指定的选择的边缘校正（S）的Fest和Gest。
Details
详细信息----------Details----------
The J function (Van Lieshout and Baddeley, 1996) of a stationary point process is defined as
J功能（范·利斯豪特和巴德利，1996年）被定义为一个固定的点过程
where G(r) is the nearest neighbour distance distribution function of the point process (see Gest) and F(r) is its empty space function (see Fest).
G(r)是最近的邻居距离分布函数的点处理（见Gest），并F(r)是空的空间功能（见Fest）。
For a completely random (uniform Poisson) point process, the J-function is identically equal to 1. Deviations J(r) < 1 or J(r) > 1 typically indicate spatial clustering or spatial regularity, respectively. The J-function is one of the few characteristics that can be computed explicitly for a wide range of point processes. See Van Lieshout and Baddeley (1996), Baddeley et al (2000), Thonnes and Van Lieshout (1999) for further information.
对于一个完全随机的均匀泊松点过程中，J功能是恒等于1。偏差J(r) < 1或J(r) > 1通常表示的空间聚类或空间的规律性，。 J功能，可以明确地计算了广泛的点过程的一些特点之一。欲了解更多信息，请参见范·利斯豪特和巴德利（1996），亚伦 - 巴德利等人（2000年），Thonnes和范·利斯豪特（1999）。
An estimate of J derived from a spatial point pattern dataset can be used in exploratory data analysis and formal inference about the pattern. The estimate of J(r) is compared against the constant function 1. Deviations J(r) < 1 or J(r) > 1 may suggest spatial clustering or spatial regularity, respectively.
J来自空间的点模式数据集可以用于探索数据分析和正式推理有关的图案的一个估计。比较常数函数J(r)1的估计。偏差J(r) < 1或J(r) > 1可能会建议的空间聚类或空间的规律性，。
This algorithm estimates the J-function from the point pattern X. It assumes that X can be treated as a realisation of a stationary (spatially homogeneous) random spatial point process in the plane, observed through a bounded window. The window (which is specified in X as X$window) may have arbitrary shape.
该算法估计的的J功能点模式X。它假定X可以被视为一个实现了一个固定的（的空间均匀）随机空间点在飞机上，观察到一个有限的窗口。窗口（中指定XX$window的）可以有任意形状的。
The argument X is interpreted as a point pattern object (of class "ppp", see ppp.object) and can be supplied in any of the formats recognised by as.ppp().
参数X被解释为一个点图形对象（类"ppp"，看到ppp.object），并且可以在任何认可的as.ppp()的格式提供。
The functions Fest and Gest are called to compute estimates of F(r) and G(r) respectively. These estimates are then combined by simply taking the ratio J(r) = (1-G(r))/(1-F(r)).
的功能Fest和Gest被称为F(r)和G(r)分别计算估计。然后结合这些估计是简单的比例J(r) = (1-G(r))/(1-F(r))。
In fact three different estimates are computed using different edge corrections (Baddeley, 1998). The Kaplan-Meier estimate (returned as km) is the ratio J = (1-G)/(1-F) of the Kaplan-Meier estimates of 1-F and 1-G computed by Fest and Gest respectively. The reduced-sample or border corrected estimate (returned as rs) is the same ratio J = (1-G)/(1-F) of the border corrected estimates. These estimators are slightly biased for J, since they are ratios of approximately unbiased estimators. The logarithm of the Kaplan-Meier estimate is unbiased for log J.
其实，三种不同的估计，计算使用不同的边缘修正（巴德利，1998年）。 Kaplan-Meier估计（返回为km）的比例是J = (1-G)/(1-F)Kaplan-Meier估计1-F和1-G计算的Fest和 X>“。减少样品或边界纠正预算（返回的Gest）是相同的比例rs校正的边界估计。这些估计是稍微偏J = (1-G)/(1-F)，因为他们比的近似无偏估计。 Kaplan-Meier估计的对数是公正为J。
The uncorrected estimate (returned as un) is the ratio J = (1-G)/(1-F) of the uncorrected (“raw”) estimates of the survival functions of F and G, which are the empirical distribution functions of the empty space distances Fest(X,...)$raw and of the nearest neighbour distances Gest(X,...)$raw. The uncorrected estimates of F and G are severely biased. However the uncorrected estimate of J is approximately unbiased (if the process is close to Poisson); it is insensitive to edge effects, and should be used when edge effects are severe (see Baddeley et al, 2000).
未修正的估计（返回的un）的比例是J = (1-G)/(1-F)裸眼（“原始”）估计的生存功能F和G，这是经验分布函数的空的空间的距离Fest(X,...)$raw和近邻距离Gest(X,...)$raw。裸眼F和G受到严重偏见的估计。然而，裸眼J估计大约是公正的（如果这个过程是接近泊松），它是不敏感的边缘效应，边缘效应时，应使用严重（见巴德利等，2000）。
The algorithm for Fest uses two discrete approximations which are controlled by the parameter eps and by the spacing of values of r respectively. See Fest for details. First-time users are strongly advised not to specify these arguments.
该算法为Fest使用所控制参数eps和由r分别的值的间隔的两个离散近似。见Fest的详细信息。我们强烈建议用户第一次不指定这些参数。
Note that the value returned by Jest includes the output of Fest and Gest as attributes (see the last example below). If the user is intending to compute the F,G and J functions for the point pattern, it is only necessary to call Jest.
请注意，返回的值Jest包括输出Fest和Gest属性（见下面的例子）。如果用户打算计算F,G和J点图案的功能，它是只需要，调用Jest。
值----------Value----------
An object of class "fv", see fv.object, which can be plotted directly using plot.fv.
类的一个对象"fv"，fv.object，它可以绘制直接使用plot.fv的。
Essentially a data frame containing
本质上是一个数据框包含
参数：r
the vector of values of the argument r at which the function J has been estimated
的参数的值的矢量r在哪些函数J已估计
参数：J
the recommended estimate of J(r), which is the Kaplan-Meier estimate km
推荐的估计J(r)，这是Kaplan-Meier估计km
参数：rs
the “reduced sample” or “border correction” estimator of J(r) computed from the border-corrected estimates of F and G
“减少样品”或“边界校正”估计J(r)计算的边界校正估计F和G的从
参数：km
the spatial Kaplan-Meier estimator of J(r) computed from the Kaplan-Meier estimates of F and G
Kaplan-Meier生存的空间估计J(r)F和G从Kaplan-Meier法计算的估计
参数：han
the Hanisch-style estimator of J(r) computed from the Hanisch estimate of G and the Chiu-Stoyan estimate of F
J(r)计算，从Hanisch估计G和照斯托扬估计F的Hanisch风格的估计
参数：un
the uncorrected estimate of J(r) computed from the uncorrected estimates of F and G
未校正的估计J(r)计算的从裸眼估计F和G
参数：theo
the theoretical value of J(r) for a stationary Poisson process: identically equal to 1
J(r)的平稳泊松过程的理论值：恒等于1
The data frame also has attributes
也有属性的数据框
参数：F
the output of Fest for this point pattern, containing three estimates of the empty space function F(r) and an estimate of its hazard function
Fest这点模式，包含三个空的空间功能F(r)，并估计其风险函数估计的输出
参数：G
the output of Gest for this point pattern, containing three estimates of the nearest neighbour distance distribution function G(r) and an estimate of its hazard function
输出Gest这点模式，包含三个估计的最近邻距离分布函数G(r)和风险函数的估计
注意----------Note----------
Sizeable amounts of memory may be needed during the calculation.
在计算过程中，可能需要相当大的数量的内存。
（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----------
In O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. van Lieshout (eds) Stochastic Geometry: Likelihood and Computation. Chapman and Hall, 1998. Chapter 2, pages 37–78.
The empty space hazard of a spatial pattern. Research Report 1994/3, Department of Mathematics, University of Western Australia, May 1994.
Kaplan-Meier estimators of interpoint distance distributions for spatial point processes. Annals of Statistics 25 (1997) 263–292.
Estimating the J function without edge correction. Statistica Neerlandica 54 (2000) 315–328.
Distance transformations in digital images. Computer Vision, Graphics and Image Processing 34 (1986) 344–371.
John Wiley and Sons, 1991.
Academic Press, 1983.
Cambridge University Press, 1988.
Stochastic geometry and its applications. 2nd edition. Springer Verlag, 1995.
A comparative study on the power of Van Lieshout and Baddeley's J-function. Biometrical Journal 41 (1999) 721–734.
A nonparametric measure of spatial interaction in point patterns. Statistica Neerlandica 50 (1996) 344–361.
参见----------See Also----------
Fest, Gest, Kest, km.rs, reduced.sample, kaplan.meier
Fest，Gest，Kest，km.rs，reduced.sample，kaplan.meier
实例----------Examples----------
data(cells)
J <- Jest(cells, 0.01)
plot(J, main="cells data")
# values are far above J = 1, indicating regular pattern[值是远高于J = 1时，表示规则的图案]
data(redwood)
J <- Jest(redwood, 0.01, legendpos="center")
plot(J, main="redwood data")
# values are below J = 1, indicating clustered pattern[值都低于J = 1时，表示聚类图案]
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 13:38:21
