Correlations and copulas for decision and risk analysis

Article Abstract:

The use of correlations and copulas is presented as an alternative approach for modeling uncertainty in decision and risk analysis. Traditionally, the modelling procedure has been to describe a joint distribution of the random variables as a product of marginal and conditional distributions. However, the required number of probability assessments in this conventional approach can increase exponentially with the number of variables. The solution is a method where a joint distribution is formulated through the use of a copula, which necessitates only marginal distributions and measures of dependence among the random variables. A complete copula-based joint distribution can be generated through the use of assessed rank-order correlations and marginal distributions, which minimizes the number of required assessments and lessens the need to search for conditional independence.

Asset & Risk Management, Models, Risk assessment, Correlation (Statistics), Uncertainty (Information theory)

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A graphical analysis of ratio-scaled paired comparison data

Article Abstract:

A graphical technique similar to multidimensional scaling is proposed for representing individual preferences in the context of Saaty's (1977) Analytic Hierarchy Process (AHP). Based on Gower's 1977 work, this proposed method enables agents to form a global vision of alternatives available to them and to identify cardinal and ordinal inconsistencies in their judgments. The study demonstrates the formulation of the ordinal and cardinal versions of Gower plots, as well as their application in helping individuals picture their preferences, spot discrepancies in judgment and implement remedial measures. The Gower plots are shown to be an effective instrument for diagnosis in the context of AHP.

Analysis, Graphic methods, Judgments, Judgments (Law)

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