A function to compute segregation probabilities from a multivariate LGCP. See the vignette "Bayesian_lgcp" for a full explanation of this.
segProbs(obj, domprob)an lgcpPredictMultitypeSpatialPlusParameters object
the threshold beyond which we declare a type as dominant e.g. a value of 0.8 would mean we would consider each type to be dominant if the conditional probability of an event of a given type at that location exceeded 0.8.
an lgcpgrid object contatining the segregation probabilities.
We suppose there are K point types of interest. The model for point-type k is as follows:
X_k(s) ~ Poisson[R_k(s)]
R_k(s) = C_A lambda_k(s) exp[Z_k(s)beta_k+Y_k(s)]
Here X_k(s) is the number of events of type k in the computational grid cell containing the point s, R_k(s) is the Poisson rate, C_A is the cell area, lambda_k(s) is a known offset, Z_k(s) is a vector of measured covariates and Y_i(s) where i = 1,...,K+1 are latent Gaussian processes on the computational grid. The other parameters in the model are beta_k , the covariate effects for the kth type; and eta_i = [log(sigma_i),log(phi_i)], the parameters of the process Y_i for i = 1,...,K+1 on an appropriately transformed (again, in this case log) scale.
The term 'conditional probability of type k' means the probability that at a particular location, x, there will be an event of type k, we denote this p_k(x).
It is also of interest to scientists to be able to illustrate spatial regions where a genotype dominates a posteriori. We say that type k dominates at position x if p_k(x)>c, where c (the parameter domprob) is a threshold is a threshold set by the user. Let A_k(c,q) denote the set of locations x for which P[p_k(x)>c|X] > q.
As the quantities c and q tend to 1 each area A_k(c,p) shrinks towards the empty set; this happens more slowly in a highly segregated pattern compared with a weakly segregated one.
The function segProbs computes P[p_k(x)>c|X] for each type, from which plots of P[p_k(x)>c|X] > q can be produced.