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hello we continue our treatment of intensity and in this set of slides i focus on how to visualize intensity in particular we discussed the notion of spatial heterogeneity and the heat map or the kernel density function which many of you might already be familiar with so the assumption that weve used so far and specifically in the homogeneous planar poisson process which was the formal expression of complete spatial randomness we took the assumption of spatial homogeneity what does that mean that means that the intensity is the same everywhere so if we express the intensity at a given location s as lambda s then in essence spatial homogeneity means that lambda s equals the same lambda no matter where you are that is the fundamental assumption behind a poisson process so homogeneity of course if thats not the case then we have spatial heterogeneity and in that case the intensity lambda s does vary with location s and so if it varies with location how do we figure out what the intensit