The title of this book is ambiguous, and intentionally so. On the one hand, Abstract Inference can refer to problems of statistical inference when the sample space is an abstract space. On the other, it can refer to the case when the parameter space is an abstract space. Abstract sample spaces have been dealt with in considerable depth in the literature, and especially in the important case when they form function spaces over some given set ? of arguments: statistical inference in stochastic processes. Beginning with our 1950 monograph (see the Bibliography at the end of this book), many mathematicians have studied this topic. Today several of the basic problems have been solved, resulting in a vast literature, in part motivated by applications among which communication engineering should be mentioned first. The theory is still in active development, as can be seen in the leading journals of mathematical statistics and probability theory. This research effort has resulted in an elegant theory, nearing completion in at least in some respects, and with a multitude of applications.

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