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A Mathematical Theory of Arguments for Statistical Evidence (Paperback)
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A Mathematical Theory of Arguments for Statistical Evidence (Paperback)
Series: Contributions to Statistics
Expected to ship within 10 - 15 working days
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The subject of this book is the reasoning under uncertainty based
on sta tistical evidence, where the word reasoning is taken to mean
searching for arguments in favor or against particular hypotheses
of interest. The kind of reasoning we are using is composed of two
aspects. The first one is inspired from classical reasoning in
formal logic, where deductions are made from a knowledge base of
observed facts and formulas representing the domain spe cific
knowledge. In this book, the facts are the statistical observations
and the general knowledge is represented by an instance of a
special kind of sta tistical models called functional models. The
second aspect deals with the uncertainty under which the formal
reasoning takes place. For this aspect, the theory of hints [27] is
the appropriate tool. Basically, we assume that some uncertain
perturbation takes a specific value and then logically eval uate
the consequences of this assumption. The original uncertainty about
the perturbation is then transferred to the consequences of the
assumption. This kind of reasoning is called assumption-based
reasoning. Before going into more details about the content of this
book, it might be interesting to look briefly at the roots and
origins of assumption-based reasoning in the statistical context.
In 1930, R. A. Fisher [17] defined the notion of fiducial
distribution as the result of a new form of argument, as opposed to
the result of the older Bayesian argument.
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