## 3 Prioritizing Geo-Spatial Data Collection
### Prioritized Sampling  
The first prioritization stage is based on the above described concept of _focus maps_[11]. In order to compute the focus map, each of the input layers is mapped (normalized) into a sampling probability. This mapping can be either linear or non-linear (see [11] for examples) and is selected by associating sampling probabilities to locations according to the value assumed by the layer itself. For instance we can consider as input layers the distribution of insurance policies. The mapped layer will exhibit higher sampling probabilities where the spatial density of policies is higher. The mapped layers, now defining different sampling probabilities, can be combined by a pooling procedure. The pooling can be multiplicative, additive, or mixed, depending on the way the joint sampling probability should be implemented; a multiplicative pooling will associate small sampling probabilities to locations where at least one of the input layers has a low probability. Conversely, additive pooling will associate higher sampling probability where at least one of the input layers has high probability. By changing the weights (keeping the sum of the weights to 1), the relative importance of the datasets also changes. With log-linear pooling, the weights can be further increased in order to make the resulting survey more selective. As the absolute values of the weights increase (keeping constant the relative ratio), only the highest values (thus indicating a higher priority) are retained (see Figure 4).  
Different focus maps, based on different input layers, can be implemented to drive the optimization and prioritization of the data collection, according to the specific operational stage. In order to analyze the building stock in a pre-event stage, the expected distribution of seismic hazard could be combined with the density of insurance policies and the distribution of buildings. An example of a pre-event focus map is provided in Figure 4. For post-event damage assessment, a preliminary distribution of physical damage obtained by remote sensing or direct inspection could be combined with the expected distribution of road blockages.  
Once the focus map is computed, it can be used to generate a set of sampling points in the area to be surveyed. Different sampling schemes can be used depending on the application. If, for example, an average estimate of the population of interest is needed, a _stratified sampling_ would provide suitable estimates [12]. For the purpose of the current application a _probability-proportional-to-size_ (PPS) scheme [12] has been applied, in order to generate sampling points that are directly related to the computed _focus map_. In this way, points with a higher sampling probability will have a higher priority in the survey. The density of the points is positively correlated with the value of the focus map. The number of generated points is an additional parameter that affects the overall process. For instance, too  
Figure 3: Diagram showing the prioritization work-flow with iterative multi-stage sampling.  
many points will tend to saturate the area, therefore decreasing the efficiency of the optimization process. Moreover, by choosing a smaller sampling set, it is possible to realize an iterative sampling scheme. The sampling set represents the location of points that would be good candidates for collecting field data, based on the input indicators and their mapping scheme.