Sensitivity analysis

Sensitivity analysis: strategies, methods, concepts, examples
David J. Pannell
School of Agricultural and Resource Economics, University of Western Australia, Crawley 6009, Australia

Abstract
The parameter values and assumptions of any model are subject to change and error. Sensitivity analysis (SA), broadly defined, is the investigation of these potential changes and errors and their impacts on conclusions to be drawn from the model. There is a very large literature on procedures and techniques for SA. This paper is a selective review and overview of theoretical and methodological issues in SA. There are many possible uses of SA, described here within the categories of decision support, communication, increased understanding or quantification of the system, and model development. The paper focuses somewhat on decision support. It is argued that even the simplest approaches to SA can be theoretically respectable in decision support if they are done well. Many different approaches to SA are described, varying in the experimental design used and in the way results are processed. Possible overall strategies for conducting SA are suggested. It is proposed that when using SA for decision support, it can be very helpful to attempt to identify which of the following forms of recommendation is the best way to sum up the implications of the model: (a) do X, (b) do either X or Y depending on the circumstances, (c) do either X or Y, whichever you like, or (d) if in doubt, do X. A system for reporting and discussing SA results is recommended.
1. Introduction
The parameter values and assumptions of any model are subject to change and error. Sensitivity analysis (SA), broadly defined, is the investigation of these potential changes and errors and their impacts on conclusions to be drawn from the model (e. g. Baird, 1989). SA can be easy to do, easy to understand, and easy to communicate. It is possibly the most useful and most widely used technique

available to modellers who wish to support decision makers. The importance and usefulness of SA is widely recognised:
“A methodology for conducting a [sensitivity] analysis… is a well established requirement of any scientific discipline. A sensitivity and stability analysis should be an integral part of any solution methodology. The status of a solution cannot be understood without such information. This has been well recognised since the inception of scientific inquiry and has been explicitly addressed from the beginning of mathematics”. (Fiacco, 1983, p3).
There is a very large and diverse literature on SA, including a number of reviews (e. g. Clemson et al., 1995; Eschenbach and Gimpel, 1990; Hamby, 1994; Lomas and Eppel, 1992; Rios Insua, 1990; Sobieszczanski-Sobieski, 1990; Tzafestas et al., 1988). However, the existing literature is limited in a number of respects. Most of what has been written about sensitivity analysis has taken a very narrow view of what it is and what it can be useful for. A large proportion of the literature is highly mathematical and rather theoretical in nature. Even those papers with a focus on applied methodology have tended to concentrate on systems and procedures which are relatively time consuming and complex to implement. There has been almost no discussion of procedures and methodological issues for simple approaches to sensitivity analysis. (Eschenbach and McKeague, 1989, is a rare exception). This is remarkable, considering the usefulness and extremely wide usage of simple approaches.
My aim in this paper is, in part, to fill this gap.