Potential modeling with uncertain covariables

Published potential mapping procedures usually presume that the covariables are known.
However, covariables are usually interpolated by kriging. In sparsely covered regions reported covariables can seriously differ from the actual situation on the ground. When regressing to the mean we often nd the variation of covariables underestimated, leading to an overestimation of dependence. Similar effects can be observed when the fitted model is applied to prediction: The potential seems promising, but is underestimated in sparsely observed regions.
In earlier publications it has been shown that a Cox regression model is more general than weights of evidence methods, and also independent of a grid with a user defined resolution.
Therefore our investigation is based on this model class. Here we compare four different estimation procedures for Cox regression models: (i) the pseudolikelihood method put forward by Baddeley, (ii) a numerical solution of the full Maximum Likelihood approach based on kriged covariables, (iii) an approximation of the full Maximum Likelihood approach based on the conditional distribution of the covariables, and (iv) the MCMC based Bayesian solution.
The first two methods neglect the uncertainty of the covariables, the latter two account for it. For simulated examples with known true parameters we can show a substantial decrease of estimation errors when the uncertainty is considered.
It can be shown that the estimation error reported by the methods neglecting the uncertainty of covariables seriously underestimates the actual uncertainty of the parameter estimate.