# The Role of Data-Driven Methodologies in Weather Index Insurance
## 4 Methodology  
Index insurance indemnifies the policyholder based on the observable value of the predefined index which is highly correlated with losses. There are values or thresholds which define the trigger signal of indemnities. In the context of machine learning, this corresponds to a classification problem, allowing researchers to predict the occurrence of a loss event. In this study, we use historic flood data as a proxy of losses. Particularly, we use two data-driven methodologies to model the relationship between the loss occurrences with weather indices. The purpose of these models is to determine the occurrence of flood events based solely on the selected weather indices values. The time period used to train the models extends from 3 June 2000 to 31 December 2021. The starting date was selected due to the historical availability of the GPM time series (Table 1), while the end date was selected due to the lack of availability of data in the flood record database.  
Results obtained by [PERSON] et al. [31] showed that logistic regression models provide good results when explaining loss events through weather indices. However, given that this is a linear model, its predictive capacity is significantly limited when compared to more flexible models. Thus, logistic regression was used as a base model to provide a reference point when assessing the performance of a more complex model, namely ANN. Given that the goal is to compare a linear and interpretable base model with a highly non-linear black-box model, other possible non-linear models, such as decision trees and support vector machines, are not considered.  
The particular aim of applying highly non-linear models is to lower the basis risk in future designs of index insurance instruments.  
Consider the occurrence of floods caused by weather events for each time unit \(t=1,\ldots,T\) for a region G, where \(L_{t}\) is a binary variable such as:  
\[L_{t}=\begin{cases}1&\quad\text{if $a$ flood is present in $G$}\\ 0&\quad\text{if $a$ flood is not present in $G$}\end{cases} \tag{8}\]  
The objective is to predict the likelihood of a flood event using weather variables from satellite images. The model has a probabilistic variable output which is used to optimize the cut points in which indemnities are disbursed. This last step is performed from a two-party perspective, considering that both parties have different costs.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Database** & **Type** & **Resolution** & **Frequency** & **Coverage** & **Time Lapse** & **Latency** & **Reference** \\ \hline CHIRPS & Satellite & 0.05\({}^{\circ}\) & 1 d & 50\({}^{\circ}\) S–50\({}^{\circ}\) N & January 1981–Present & 3 weeks & [32] \\  & estimation & & & & & & \\ PERSIANN-CDR & Satellite & 0.25\({}^{\circ}\) & 1 d & 60\({}^{\circ}\) S–60\({}^{\circ}\) N & January 1983–Present & 48 h & [33] \\  & & & & & & & \\ GPM & Satellite & 0.10\({}^{\circ}\) & 30 min & 60\({}^{\circ}\) S–60\({}^{\circ}\) N & June 2000–Present & 12 h & [35] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristics of the selected (quasi-)global precipitation databases.  
Moreover, probabilistic outputs can also provide an uncertain measure that can be used by final users once the model is implemented [31].  
Figure 3 summarizes the methodology used in this study which is adapted from two recent methodologies: [PERSON] et al. [24] and [PERSON] et al. [31].