Development of a Matrix Based Statistical Framework to Compute Weight for Composite Hazards, Vulnerability and Risk Assessments

Abstract

Selection of relative weights for different indicators is a critical step during assessment of composite hazards, vulnerability, and risk. While assigning weight to an indicator, it is important to consider the influence of an individual indicator on a particular composite index. In general, the larger the weight of the indicator, the higher the importance of that indicator compared to other indicators. In this study, a new matrix based statistical framework (MSF) for weight assignment is developed that can be considered as the simplest and most accurate method for assigning weights for a large number of indicators. This method (MSF) is based on the valuation of the correlation matrix and Eigenvector associated with Eigenvalue. Relying on the inter build up methodology, MSF can fulfill some built-in gaps among other weightage methods. It can also directly give the ‘decision’ to select the relative weights that are found from the Eigenvector corresponding to the largest Eigenvalue. The new method is applied by assigning weights to 15 socio-economic indicators and assessed vulnerability and risk in the Bangladesh coast. While comparing with other weight methods, it is found that MSF gives the most acceptable physical explanation about the relative values of weights of indicators. In terms of accuracy, MSF is found to be most accurate compared to other weight methods. When large numbers of indicators are involved in an application, MSF is found to be relatively simple and easy to apply compared to other methods.