Sensitivity analysis in statistics

Statistical models are simplification of reality; we rarely expect the model to be exactly true. Nevertheless, when we select a statistical technique and a perform statistical inference, we often act as if the model is true. This is often justified by claiming that "small" deviations from the model cause only "small" deviations from the theoretical properties of the selected inferential techniques or cause only minor changes in the results produced by the inference. U nfortunately, th is argument need not be trlle. In some appl ications apparently small changes in a model. a 11l0del asslImption, or a data point, can have very large effects on the results. For this reason, statistical analysis is viewed in this paper as a cyclical process. Such a process takes inputs and produces outputs in an iterative or cyclical way; a way in which the outputs can be used to diagnose, validate, criticise, and possibly alter the inputs. We also describe a general framework, referred to as the sensitivity function, for assessing the sensitivity of the outpllts to small changes in the input at a given cycle of the statistical process. We give several examples from variolls areas in statistics illustrating the general applicability of the sensitivity fUl1ction and show how and where the sensitivity function fits into the statistical cycle. Some applicatiol1s of the sensitivity function lead to known statistical techniqlles. while other applications produce new ones.