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The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation (Springer Texts in Statistics)

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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.

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