  One can argue that one of the main roles of the subject of statistics is to
characterize what the evidence in collected data says about questions of
scientific interest. There are two broad questions that we will refer to as the
estimation question and the hypothesis assessment question. For estimation, the
evidence in the data should determine a particular value of an object of
interest together with a measure of the accuracy of the estimate, while for
hypothesis assessment, the evidence in the data should provide evidence in
favor of or against some hypothesized value of the object of interest together
with a measure of the strength of the evidence. This will be referred to as the
evidential approach to statistical reasoning which can be contrasted with the
behavioristic or decision-theoretic approach where the notion of loss is
introduced and the goal is to minimize expected losses. While the two
approaches often lead to similar outcomes, this is not always the case and it
is commonly argued that the evidential approach is more suited to scientific
applications. This paper traces the history of the evidential approach and
summarizes current developments.
