Sensitivity and uncertainty analysis is becoming increasingly widespread in many fields of engineering and sciences, encompassing practically all of the experimental data-processing activities and many computational modeling and process simulation activities. There are many methods, based either on deterministic or statistical concepts, for performing sensitivity and uncertainty analysis. However, a precise, unified terminology across all methods does not seem to exist, yet often, identical words (e.g., "sensitivity") may not necessarily describe identical quantities, particularly when stemming from conceptually distinct (statistical versus deterministic) methods. Furthermore, the relative strengths and weaknesses of the various methods do not seem to have been reviewed comparatively in the literature published thus far.

This paper is the first part of a comparative review, written in two parts, that focuses on the salient features of the statistical and deterministic methods currently used for local and global sensitivity and uncertainty analysis of both large-scale computational models and indirect experimental measurements. Deterministic methods are analyzed in Part I, while statistical methods are highlighted in Part II.

Part I of this review commences by highlighting the deterministic methods for computing local sensitivities, namely, the so-called Brute-Force Method (based on recalculations), the Direct Method (including the Decoupled Direct Method), the Green's Function Method, the Forward Sensitivity Analysis Procedure (FSAP), and the Adjoint Sensitivity Analysis Procedure (ASAP). Except for the Brute-Force Method, it is emphasized that local sensitivities can be computed exactly and exhaustively only by using deterministic methods. Furthermore, it is noted that the Direct Method and the FSAP require at least as many model evaluations as there are parameters, while the ASAP requires a single model evaluation of an appropriate adjoint model whose source term is related to the response under investigation. If this adjoint model is developed simultaneously with the original model, then the adjoint model requires relatively modest additional resources to develop and implement. If, however, the adjoint model is constructed a posteriori, considerable skills may be required for its successful development and implementation. Nevertheless, the ASAP is the most efficient method to use for computing local sensitivities of large-scale systems, where the number of parameters, and parameter variations, exceeds the number of responses of interest.

The Global ASAP (GASAP) is also highlighted as it appears to be the only deterministic method published thus far for performing genuinely global analysis of nonlinear systems. The GASAP uses both the forward and the adjoint sensitivity systems to explore, exhaustively and efficiently, the entire phase-space of system parameters and dependent variables in order to obtain complete information about the important global features of the physical system, namely, the critical points of the response and the bifurcation branches and/or turning points of the system's state variables.