I just received my copy of *Introduction to statistical inference*, by Jack C. Kiefer (Springer, 1987). After having read the first two chapters I wonder: How come I didn’t start with that book when I was studying elementary statistics!

I recently had to give a short series of lectures on statistics (at a very introductory level) where I started with an illustration of a coin tossing experiment (starting at slide #7). Well, now that I have read Kiefer’s first chapter I feel like the take-away message was already there:

A typical problem in probability theory is of the following form: A sample space and underlying function are specified, and we are asked to compute the probability of a given chance event. (…) In a typical problem of statistics it is not a single underlying probability law which is specified, but rather a *class* of laws, any of which may *possibly* be the one which actually governs the chance device or experiment whose outcome we shall observe. We know that the underlying probability law is a member of this class, but we do not know which one it is. The object might then be to determine a “good” way of guessing, on the basis of the outcome of the experiment, which of the *possible* underlying probability laws is the *one* which actually governs the experiment whose outcome we are to observe.

And the ensuing discussion (including chapter 2) drives the reader toward the specification of a statistical problem based on a simple coin experiment.

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