what is the Beta valuel when simulate a hybrid Geyer model using spatstat, R package

问题

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))

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

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

回答1:

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.

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.

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.

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.

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.

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

来源：https://stackoverflow.com/questions/59389278/what-is-the-beta-valuel-when-simulate-a-hybrid-geyer-model-using-spatstat-r-pac

标签

simulation

spatstat