The main purpose of statistical theory is to derive from observations of a
random phenomenon an inference about the probability distribution underlying
this phenomenon. That is, it provides either an analysis (description)
of a past phenomenon, or some predictions about a future phenomenon of
a similar nature. In this book, we insist on the decision-oriented aspects of
statistical inference because, first, these analysis and predictions are usually
motivated by an objective purpose (whether a company should launch
a new product, a racing boat should modify its route, a new drug should be
put on the market, an individual should sell shares, etc.) having measurable
consequences (monetary results, position at the end of the race, recovery
rate of patients, benefits, etc.). Second, to propose inferential procedures
implies that one should stand by them, i.e., that the statistician thinks they
are preferable to alternative procedures. Therefore, there is a need for an
evaluative tool that allows for the comparison of different procedures; this is
the purpose of Decision Theory. As with most formal definitions, this view
of Statistics ignores some additional aspects of statistical practice such as
those related to data collection (surveys, design of experiments, etc.). This
book does, as well, although we do not want to diminish the importance of
these omitted topics.