Fest(spatstat)
Fest()所属R语言包：spatstat
Estimate the empty space function F
估计空的空间函数F
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimates the empty space function F(r) from a point pattern in a window of arbitrary shape.
估计的空的空间函数F(r)从在一个窗口中的任意形状的点图案。
用法----------Usage----------
Fest(X, ..., eps, r=NULL, breaks=NULL, correction=c("rs", "km", "cs"))
参数----------Arguments----------
参数：X
The observed point pattern, from which an estimate of F(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F(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
Optional. A positive number. The resolution of the discrete approximation to Euclidean distance (see below). There is a sensible default.
可选。一个正数。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
Optional. Numeric vector. The values of the argument r at which F(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.
可选。数字矢量。的参数的值r，F(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 the Details section.
替代到的参数r。通常不是由用户调用。查看详细信息“一节。
参数：correction
Optional. The edge correction(s) to be used to estimate F(r). A vector of character strings selected from "none", "rs", "km", "cs" and "best".
可选。边缘校正（s）到可以用来估计F(r)。一个向量"none"，"rs"，"km"，"cs"和"best"选择的字符串。
Details
详细信息----------Details----------
The empty space function (also called the “spherical contact distribution” or the “point-to-nearest-event” distribution) of a stationary point process X is the cumulative distribution function F of the distance from a fixed point in space to the nearest point of X.
空空间的功能（也称为“球形接触分布”或“点到最近的事件”分配一个固定的点过程X）的累积分布函数F的从一个固定的点在空间距离的最近点X。
An estimate of F derived from a spatial point pattern dataset can be used in exploratory data analysis and formal inference about the pattern (Cressie, 1991; Diggle, 1983; Ripley, 1988). In exploratory analyses, the estimate of F is a useful statistic summarising the sizes of gaps in the pattern. For inferential purposes, the estimate of F is usually compared to the true value of F for a completely random (Poisson) point process, which is
的一个估计F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（经验Cressie，1991; Diggle，1983;里普利，1988）。在探索性分析，估计F是一个有用的统计总结的大小差距的格局。推理的目的，估计F通常的真正价值F，这是一个完全随机的（泊松）点的过程
where lambda is the intensity (expected number of points per unit area). Deviations between the empirical and theoretical F curves may suggest spatial clustering or spatial regularity.
其中lambda是强度（每单位面积的点的预期数量）。的经验和理论F曲线之间的偏差可能会建议的空间聚类或空间的规律性。
This algorithm estimates the empty space function F 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) may have arbitrary shape.
该算法估计空的空间功能F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（其中指定在X）的可有任意形状。
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 algorithm uses two discrete approximations which are controlled by the parameter eps and by the spacing of values of r respectively. (See below for details.) First-time users are strongly advised not to specify these arguments.
该算法使用两个控制参数eps和由r分别的值的间隔的离散近似。 （请参阅下面的详细信息。）首次强烈建议用户不要指定这些参数。
The estimation of F is hampered by edge effects arising from the unobservability of points of the random pattern outside the window. An edge correction is needed to reduce bias (Baddeley, 1998; Ripley, 1988). The edge corrections implemented here are the border method or "reduced sample" estimator, the spatial Kaplan-Meier estimator (Baddeley and Gill, 1997) and the Chiu-Stoyan estimator (Chiu and Stoyan, 1998).
估计F阻碍了边缘效应所产生的不可观测点的随机模式窗外。边缘校正是必要的减少偏差（巴德雷，1998;里普利，1988）。这里实现的边缘修正边界方法或减少样品“估计，Kaplan-Meier生存空间估计（Baddeley和吉尔，1997年）和照斯托扬（邱和斯托扬，1998年估计）。
Our implementation makes essential use of the distance transform algorithm of image processing (Borgefors, 1986). A fine grid of pixels is created in the observation window. The Euclidean distance between two pixels is approximated by the length of the shortest path joining them in the grid, where a path is a sequence of steps between adjacent pixels, and horizontal, vertical and diagonal steps have length 1, 1 and sqrt(2) respectively in pixel units. If the pixel grid is sufficiently fine then this is an accurate approximation.
我们的实施使得必需使用的距离变换的图像处理算法（Borgefors，1986）。创建像素的细网格，在观察窗口。近似的两个像素之间的欧几里得距离由接合在网格中，其中一条路径是相邻的像素之间的序列的步骤的最短路径的长度，和水平，垂直和对角线的步骤有长度1，1和sqrt(2)分别以像素为单位。如果有足够的像素网格，然后这是一个精确的近似。
The parameter eps is the pixel width of the rectangular raster used to compute the distance transform (see below). It must not be too large: the absolute error in distance values due to discretisation is bounded by eps.
参数eps是用于计算距离变换（见下文）的矩形栅格的像素宽度。它不能过大：由于离散的距离值的绝对误差范围内的eps。
If eps is not specified, the function checks whether the window X$window contains pixel raster information. If so, then eps is set equal to the pixel width of the raster; otherwise, eps defaults to 1/100 of the width of the observation window.
如果eps不指定，函数会检查窗口是否X$window包含的像素点阵信息。否则，如果是这样的话，那么eps被设置等于像素宽度的光栅;eps默认为观察窗口的宽度的1/100。
The argument r is the vector of values for the distance r at which F(r) should be evaluated. It is also used to determine the breakpoints (in the sense of hist for the computation of histograms of distances. The estimators are computed from histogram counts. This introduces a discretisation error which is controlled by the fineness of the breakpoints.
参数r是向量的值的距离r，F(r)应该进行评估。它也可以用来确定断点（在这个意义上hist计算的直方图的距离的估计值，计算从直方图的计数，这引入了一个离散化控制由纤度的断点错误。
First-time users would be strongly advised not to specify r. However, if it is specified, r must satisfy r[1] = 0, and max(r) must be larger than the radius of the largest disc contained in the window. Furthermore, the spacing of successive r values must be very fine (ideally not greater than eps/4).
用户第一次将强烈建议不指定r的。然而，如果它被指定，r必须满足r[1] = 0，和max(r)必须大于包含在窗口中的最大的光盘的半径。此外，必须非常精细的间距连续r值（最好不大于eps/4）。
The algorithm also returns an estimate of the hazard rate function, lambda(r), of F(r). The hazard rate is defined by
该算法也将返回的危险率函数的估计，lambda(r)，F(r)。风险率被定义为
The hazard rate of F has been proposed as a useful exploratory statistic (Baddeley and Gill, 1994). The estimate of lambda(r) given here is a discrete approximation to the hazard rate of the Kaplan-Meier estimator of F. Note that F is absolutely continuous (for any stationary point process X), so the hazard function always exists (Baddeley and Gill, 1997).
F风险率已经提出了作为一个有益的探索的统计（Baddeley和吉尔，1994年）。估计lambda(r)这里给出的是一个离散逼近的危险率的Kaplan-Meier估计F。需要注意的是F是绝对连续的（任何固定点的过程X），所以始终存在的风险函数（Baddeley和吉尔，1997年）。
The naive empirical distribution of distances from each location in the window to the nearest point of the data pattern, is a biased estimate of F. However this is also returned by the algorithm (if correction="none"), as it is sometimes useful in other contexts. Care should be taken not to use the uncorrected empirical F as if it were an unbiased estimator of F.
天真的经验分布在窗口中的最近点的数据模式从每个位置的距离，是一个偏估计F。然而，这是返回的算法（如果correction="none"），有时是有用的，因为它是在其他情况下。应注意不要使用未校正的经验F如果它是一个无偏估计F。
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 up to seven columns:
本质上是一个数据框包含了7列：
参数：r
the values of the argument r at which the function F(r) has been estimated
的参数的值的r在哪些函数F(r)已估计
参数：rs
the “reduced sample” or “border correction” estimator of F(r)
“减少样品”或“边界校正”估计F(r)
参数：km
the spatial Kaplan-Meier estimator of F(r)
Kaplan-Meier生存的空间估计F(r)
参数：hazard
the hazard rate lambda(r) of F(r) by the spatial Kaplan-Meier method
危险率lambda(r)F(r)的空间Kaplan-Meier法
参数：cs
the Chiu-Stoyan estimator of F(r)
照斯托扬估计F(r)
参数：raw
the uncorrected estimate of F(r), i.e. the empirical distribution of the distance from a random point in the window to the nearest point of the data pattern X
F(r)，即在窗口中的一个随机的点的距离的最近点的数据模式的X的经验分布的未校正的估计
参数：theo
the theoretical value of F(r) for a stationary Poisson process of the same estimated intensity.
F(r)一个固定的估计强度的泊松过程的理论价值。
警告----------Warnings----------
The reduced sample (border method) estimator of F is pointwise approximately unbiased, but need not be a valid distribution function; it may not be a nondecreasing function of r. Its range is always within [0,1].
减少样品（境法）估计F逐点约是公正的，但不必是一个有效的分布函数，它可能不会是一个非减函数的r。它的范围是总是在[0,1]。
The spatial Kaplan-Meier estimator of F is always nondecreasing but its maximum value may be less than 1.
的空间的Kaplan-Meier估计的F总是非降，但其最大的值可以是小于1。
The estimate of lambda(r) returned by the algorithm is an approximately unbiased estimate for the integral of lambda() over the corresponding histogram cell. It may exhibit oscillations due to discretisation effects. We recommend modest smoothing, such as kernel smoothing with kernel width equal to the width of a histogram cell.
估计lambda(r)返回的算法是近似无偏估计的积分lambda()超过对应的直方图电池。它可能会出现振荡，由于离散的影响。我们建议适度平滑，如内核的内核宽度的直方图单元格的宽度等于平滑。
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.
Distance transformations in digital images. Computer Vision, Graphics and Image Processing 34 (1986) 344-371.
Estimators of distance distributions for spatial patterns. Statistica Neerlandica 52, 239–246.
John Wiley and Sons, 1991.
Academic Press, 1983.
Cambridge University Press, 1988.
Stochastic geometry and its applications. 2nd edition. Springer Verlag, 1995.
参见----------See Also----------
Gest, Jest, Kest, km.rs, reduced.sample, kaplan.meier
Gest，Jest，Kest，km.rs，reduced.sample，kaplan.meier
实例----------Examples----------
data(cells)
Fc <- Fest(cells, 0.01)
# Tip: don't use F for the left hand side![提示：不要使用F的左边！]
# That's an abbreviation for FALSE[这是一个缩写为FALSE]
plot(Fc)
# P-P style plot[P-P风图]
plot(Fc, cbind(km, theo) ~ theo)
# The empirical F is above the Poisson F[实证F是上面的泊松F]
# indicating an inhibited pattern[表明抑制模式]
## Not run: [＃不运行：]
plot(Fc, . ~ theo)
plot(Fc, asin(sqrt(.)) ~ asin(sqrt(theo)))
## End(Not run)[＃（不执行）]
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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 13:29:00
