It would be useful to provide an update on the latest in spatial point pattern analysis. For national grants etc. the ball has moved for spatial point analysis from geary-g stats etc to SPDEs (Stochastic Partial Differential Equations) implemented through INLAs (Integrated Nested Laplace Transformations). It all sounds very math-y but it’s quite easily implemented through R software (it’s more of a problem with R install than running the codes!). It’s useful with big data.
SPDE : according to Blangiardo & Cameletti “…spatial process is second-order stationary if the mean function is constant in space …but [sic] …The disadvantage of the modeling approach involving the spatial covariance function is known as “big n problem” (Banerjee et al., 2004; Jona Lasinio et al., 2013) and concerns the computational costs required for algebra operations with dense covariance … In particular dense matrix operations scale cubically with the matrix size, given by the number [emphasis me because of big data] of locations where the process is observed. A computationally effective alternative is given by the stochastic partial differential equation (SPDE) approach (Lindgren et al., 2011) and consists in performing the computations using a GMRF [Gaussian Markov Random Field] representation of the GF [gaussian field], thus allowing us to adopt the INLA approach. …”
An open source version (code included can be found here http://www.statistica.it/marta/stbook/Chapter6.R) : https://sites.google.com/a/r-inla.org/stbook/ chapter 6 “…point level—presenting Bayesian kriging through the stochastic partial differential equations (SPDE) approach and showing how to model observed data and also to predict for new spatial locations…”