Resumo:
In this paper, we argue that the primary goal of the foundations of statistics
is to provide data analysts with a set of guiding principles that are guaranteed
to lead to valid statistical inference. This leads to two new questions: “what
is valid statistical inference?” and “do existing methods achieve this?” Towards
answering these questions, this paper makes three contributions. First, we express
statistical inference as a process of converting observations into degrees of belief, and
we give a clear mathematical definition of what it means for statistical inference
to be valid. Second, we evaluate existing approaches Bayesian and frequentist
approaches relative to this definition and conclude that, in general, these fail to
provide valid statistical inference. This motivates a new way of thinking, and our
third contribution is a demonstration that the inferential model framework meets
the proposed criteria for valid and prior-free statistical inference, thereby solving
perhaps the most important unsolved problem in statistics
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