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 event of a similar nature. In this book, we insist on the decision-oriented aspects of statistical inference, because, first, these analyses and predictions are usually motivated by an objective purpose (whether a company should launch a new product, a racing boat should modify its route, an individual should sell shares, etc.) which have measurable consequences (monetary results, position at the end of the race, 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 evaluation tool which allows for the comparison of different procedures; this is the purpose of Decision Theory. As with most formal definitions, this view of Statistics blatantly ignores some additional aspects of statistical practice like those related to data collection (surveys, design of experiments, etc.), but so does this book, although we do not want to diminish the importance of these omitted topics. We also insist on the fact that Statistics should be considered an interpretation of natural phenomena, rather than an explanation. In fact, statistical inference is based on a probabilistic modeling of the observed phenomenon and implies a necessarily reductive formalization step since without this probabilistic support, it cannot provide any useful conclusion (or decision).
KeywordsPosterior Distribution Likelihood Function Prior Distribution Maximum Likelihood Estimator Likelihood Principle
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