Sensitivity Analysis of Models with Input Codependencies
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Assuming a set of variates are independent and normally distributed is commonplace in statistics. In this thesis, we consider the consequences of these assumptions as they pertain to global sensitivity analysis. We begin by illustrating how the notion of sensitivity becomes distorted in the presence of codependent model inputs. This observation motivates us to develop a new methodology which accommodates for input codependencies. Our methodology can be summarized through three points: First, a new form of sensitivity is presented which performs as well as the classical form but can be obtained at a fraction of the computational cost. Second, we define a measure which quantifies the extent of distortion caused by codependent inputs. The third point is regarding the modelling of said codependencies. The multivariate normal distribution is a natural choice for modelling codependent inputs; however, our methodology uses a copula-based approach instead. Copulas are a contemporary strategy for constructing multivariate distributions whereby the marginal and joint behaviours are treated separately. As a result, a practitioner has more flexibility when modelling inputs.