使用spatstat，R包模拟混合Geyer模型时，Beta值是多少? [英] what is the Beta valuel when simulate a hybrid Geyer model using spatstat, R package

问题描述

我拟合了一个包含铁杆和geyer饱和分量的混合geyer模型，现在我想在spatstat中通过rmh()模拟拟合的模型，代码如下:

I fit a hybrid geyer model including a hardcore and a geyer saturation components, now I want to simulate the fitted model by rmh() in spatstat, the code is following:

mo.X<-rmhmodel(cif=c("hardcore","geyer"), 
               par=list(list(beta=0.0001746418,hc=30.31542),
                        list(beta=1, gamma=0.4195612,r=122,sat=2)), w=Window(A1a2.unmark))

在模拟混合模型时，有两个beta:hardcore()的beta和geyer()的beta，但是，当拟合实际数据以获取混合模型时，结果中仅提供一个beta值:

there are two beta in simulating the hybrid model: beta for hardcore(), and beta for geyer (), however, when fitting real data to get a hybrid model, only one beta value provided in the result:

unmark.hybrid<-ppm(A1a2.unmark~1,Mo.hybrid, correction="bord")
  unmark.hybrid
    #beta = 0.0001052206
    #Hard core distance:    33.66719
    #gamma:  0.3578263

设置第二个beta = 1是否正确? 感谢您的任何建议.

is it right to set the second beta=1? thanks for any suggestion.

推荐答案

几个点过程模型的混合体的定义是将不同模型的条件强度函数相乘以得出杂种的条件强度.

The definition of a hybrid of several point process models is that the conditional intensity functions of the different models are multiplied together to give the conditional intensity of the hybrid.

在spatstat代码中称为beta的参数是一阶潜在项.对于固定的无标记点过程，此参数是单个数字常数.当您形成混合动力时，原始模型的beta参数将相乘以获得一个单一的数字，即混合动力的beta参数.

The parameter called beta in spatstat code is the first order potential term. For a stationary unmarked point process, this parameter is a single numerical constant. When you form a hybrid, the beta parameters of the original models are multiplied together to obtain a single number which is the beta parameter of the hybrid.

如果将混合模型拟合到数据，则打印的输出仅显示一个beta参数，因为任何固定的未标记点过程都只有一个这样的参数.

If you fit a hybrid model to data, the printed output shows only one beta parameter, because any stationary unmarked point process has only one such parameter.

如果您手动定义了一个混合模型，如您的示例中所示，要通过rmh进行仿真，则您正在构建多个模型的混合模型；您首先必须定义每个模型.模型定义算法rmhmodel期望每个模型都有其自己的beta参数.但是，当形成混合动力时，这些数字将被相乘在一起以给出一个单一的beta值，该值是混合动力模型的一阶电势.

If you define a hybrid model by hand, for simulation by rmh as in your example, then you are building a hybrid of several models; you will first have to define each of these models. The model-defining algorithm rmhmodel expects each of the models to have its own beta parameter. However, when the hybrid is formed, these numbers will just be multiplied together to give a single beta value which is the first order potential of the hybrid model.

通常的做法是将除第一个参数外的所有beta参数都设置为1.您已经在示例中做到了.

The usual practice is to set all of the beta parameters equal to 1 except the first one. You have done that in your example.

有关更多信息，请参见《 空间点模式:R的方法和应用》一书中的第13章

For further information see chapter 13 in the book Spatial Point Patterns: Methodology and Applications with R

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