## 3 Prioritizing Geo-Spatial Data Collection
### Predictive Sampling  
The available information layers have been successfully used to design and optimize surveys of the study area, but in general such quantities of information, extensive both in spatial coverage and attributes, are usually not available. Hence, computing a focus map to drive the prioritization of the data collection in other locations would not be straightforward. We can, however, suppose that at least a limited amount of data would always be available, since in the process of activating the policies, TCIP collects ancillary data, and the penetration of TCIP in the insurance market is close to 40% in Turkey. The available information could in this case still be used to generate \"virtual\" layers to further constrain the focus maps. These layers would then be used to generate _a priori_ probability distributions based on statistical inference. In order to exemplify the possible practical application, we applied multinomial logistic regression techniques to infer the probability that a building could host a certain number of policies based on a set of available attributes. The attributes can include the number of stories, the construction type, the usage, and any combination of socioeconomic data that is somehow expected to be correlated with the likelihood of the purchase of earthquake insurance. Figure 5: Composition of the training dataset of 1000 buildings randomly selected among the 19,158 buildings of the original dataset (“_count_” refers to the number of TCIP policies in the building). This type of information is available at very high resolution in Istanbul as well as in other large settlements in Turkey, and the trend is expected to improve in the next years. In order to simulate a \"data-poor\" case, where only limited information is available for making inferences, 1000 buildings were randomly sampled from the original population of 19,158 available in Besiktas (5.2% of the overall population). The selected buildings covered 1523 policies, with a relative distribution in terms of usage, apartments, and offices depicted in Figure 5.  
The selected data and used to train a logistical regression engine, whose functional form is:  
\[p\big{(}pn_{i}\big{)}\sim\beta_{0}+\sum\beta_{j}\ast\mathit{attr}_{j} \tag{1}\]  
where \(p(pn_{i})\) represents the probability of finding in a building a number of policies belonging to the interval \(i\), and \(\beta_{j}\) is the regression coefficient of attribute \(j\). The considered attributes (available for the buildings sampled) are listed in Table 1. The variable encoding the number of policies has been subdivided into five intervals, shown in Table 2.  
From the analysis of the coefficients computed by the regression, it can be noted that the variables _stories_, _apartments_, and _offices_ show a positive correlation with the number of policies, while the variables _usage (mixed residential)_ and _carparks_ show a negative correlation, relatively strong for the usage type'mixed residential'. The number of policies obtained by the computed regression has been compared with the observed ones for a further dataset of 10,000 buildings uncorrelated with the one used for training. The regression algorithm provides for each tested building the probability of finding a number of policies within one of five intervals: 0, 1-2, 3-5, 6-10, and \(>\)10. These probabilities can be aggregated to compute a single scalar index that represents the \"susceptibility\" of the considered buildings to host earthquake insurance policies (see Equation (2)):  
\[\mathit{index}=\frac{1}{5}\sum_{i}\ast p_{i} \tag{2}\]