As the title suggests, I am having a bit of confusion on the effect of first order intensity function. If I have a first order intensity function that says in a certain region the points are much more likely to occur, that means there would be a lot more points occurring in that region and it would appear that the points are clustering in that region and subsequently suggests that in that region the point patterns are clustered. So it seems that inhomogeneity of the first oder intensity affects the second order intensity.

Is this understanding correct?

As the title suggests, I am having a bit of confusion on the effect of first order intensity function. If I have a first order intensity function that says in a certain region the points are much more likely to occur, that means there would be a lot more points occurring in that region and it would appear that the points are clustering in that region and subsequently suggests that in that region the point patterns are clustered. So it seems that inhomogeneity of the first order intensity affects the second order intensity.

My understanding is that the first order intensity function specify the general level of intensity at which the points occur. Then based on that intensity, whether points in a certain region are clustered or repulsive compared to a same intensity Poisson process is then determined by the second order intensity function.

If my understanding is correct, then any point pattern can be regarded as an inhomogeneous Poisson process if we describe the first order intensity as detailed as possible. But of course, that will be a case of overfitting.

Is this understanding correct?