## 2 Predictive Methodology, Terminology, and Analytical Procedures
Cross validation is a strategy for assessing the quality of our prediction modeling and also for comparing different prediction patterns, produced either by varying the number of ISPs or the mathematical models. The results of cross validations are tables of prediction scores for numbers or proportions of occurrence pixels in the SA. How do we interpret these dimensionless integrated scores generated for each pixel of a SA and ranging between a minimum and a maximum? Given the number of transformations from the original map unit names or continuous values used to compute the ISPs and their conversion into relative scores, these are considered here as impossible to interpret directly by recognizing systematic changes or breaks. Instead, the prediction scores are easily converted into equal-area ranks after sequencing them in decreasing order. It was found convenient to obtain 200 ranks each corresponding to 0.5% of the SA. By equal-area ranking the prediction scores, it becomes practical and simple to display the prediction patterns and generate cross-validation tables of proportions of validation occurrences for each rank and cumulative tables of these proportions to be represented as curves. A consequence of iterative cross validation is that a different prediction pattern is generated each time so that the set of patterns can be used to further characterize the initial prediction pattern obtained using all the occurrences in the DSP. We can then pile up the patterns and, if their numbers are sufficiently large, apply some form of statistics to obtain average and variance for each stuck of pixels in the SA. We have defined \"target pattern\" as what we wish to have--a representation of all past and future landslide occurrences (as susceptibility scores and associated uncertainty scores). In our case, some form of averaging the ranks of the prediction patterns from the iterations. We have defined \"uncertainty patterns\" as the expression of deviations from these averages. From practice, we have found that a very robust means for generating a target pattern is selecting the median rank for each pixel from the iteration prediction patterns, and for the uncertainty pattern, the rank of the ranges of deviations from the median ranks. Furthermore, three assumptions must be reasonably satisfied [6], namely, (a1) the known landslide occurrences, the DSPs, are a \"random selection\" of all existing ones, known and unknown (allowing to extend the favorability function from the TA to the entire SA); (a2) the ISPs are correlated with the target pattern (allowing to estimate the function using the known part of the target pattern in the TA); and (a3) the process of slope failure is not random and follows a certain rule (allowing to model the favorability function). Target and uncertainty patterns have opened the way to further characterize prediction patterns. Some of these will be discussed in Section 4. Let us now consider some favorability modeling functions of empirical likelihood ratios commonly applied and used here in our analyses. They are fuzzy set membership function [7], linear and logistic regression functions [8; 9], empirical likelihood ratio function [10; 11; 12], and Bayesian predictive discriminant function [13]. We will abbreviate them as FZ, LI, LO, LR, and BP, respectively. The modeling functions imply different representation and combination rules of spatial relationships [5; 7; 14]. We will not discuss theoretical aspects of the modeling functions here because they were amply dealt with in the above-mentioned contributions [5; 7; 10; 11; 12; 13; 14]. The focus of our study is the characterization and interpretation of prediction patterns, independently of the particular prediction models applied. Our concern is that their applications to the same input data generate prediction patterns whose scores are in entirely different units, and these are considered as not interpretable or comparable except in terms of equal-area ranking. Moreover, they require entirely different combination rules.