## 2 Predictive Methodology, Terminology, and Analytical Procedures  
A unified framework for modeling prediction patterns was proposed by [PERSON] and [PERSON] (1993) [5]. It was termed the \"favorability function\" and is used in the applications that are the focus of this contribution. The term favorability was selected for its generality in the meaning intended to be comprehensive and unified to cover a variety of mathematical interpretations. The following is a summary of the concepts in the modeling, the terminology used, and the processing strategy that enables us to assess spatial uncertainty. A study area (SA) is first assumed to be selected by experts as sufficiently representative of the processes that are considered hazardous within it. Hopefully then, the statistics from spatial quantitative data available in the SA are suitable for information extraction by modeling. A second assumption is that we can have at least two subareas. First, an occurrence subarea is identified as affected by the hazardous landslide process, with the known presence of landslide trigger areas of a specific and congruous dynamic type. Then, another subarea is selected of non-occurrences in which landslides are known to be absent (or are unknown if present). The occurrence subarea is where the occurrences are located and characterized, and it is considered a training area (TA) for establishing the spatial relationships. Generally, the nonoccurrence subarea is the complement of the occurrence subarea within the SA. In some cases, however, the nonoccurrence subarea is only part of the SA or even outside the SA. This could also be the case with the occurrence area. Commonly, the occurrence subarea is a very small portion of the SA. A third assumption is that future occurrences within the SA will be similar in type and setting to the known ones. To allow favorability function prediction modeling, a proposition is constructed as follows:  
\[\text{F}_{i}\text{: that a point }i\text{ in the SA will be affected by a future landslide }|\text{ the presence of spatial evidence.} \tag{1}\]  
The symbol \(|\) indicates \"given.\" The proposition is to be supported as true by means of the known occurrence distribution and their setting. The setting is considered spatial evidence. Therefore, the proposition links the occurrence locations (or their neighborhoods) and their setting as multivariate context. To satisfy the proposition as a mathematical statement, both the digital images representing the occurrence locations and their setting have to be transformed into spatial relationships. These new images have been termed the direct supporting pattern (DSP). They are the indexed occurrence locations. Indirect supporting patterns of the proposition (ISPs) are termed the images of their setting. The term \"pattern\" is used to indicate the results of this functional transformation into spatial relationships. The landslide occurrences are converted into clusters of adjacent picture elements or pixels with a numerical value sequentially identifying each occurrence. The image pixel values of the settings are transformed into normalized frequencies if derived from categorical maps such as lithology or land use. Continuous field digital images, such as elevation or slope angles, are transformed into density functions. The ratios of the normalized frequencies and the density functions for the TA are divided by those of the nonoccurrence subareas within the SA. These ratios are termed empirical likelihood ratios (ELRs). We could also apply other types of normalization; nevertheless, the end results would have the same purpose and functionality. ELRs, as described, range in value between zero and infinity and provide a measure of support of the proposition in (1). Many different mathematical models can be used to convert and integrate the ratios into prediction patterns that classify the SA into levels of likelihood of future landslide occurrence.