Modes of Parametric Statistical Inference / Wiley Series in Probability and Statistics (PDF)

A fascinating investigation into the foundations of statistical
inference

This publication examines the distinct philosophical foundations of
different statistical modes of parametric inference. Unlike many
other texts that focus on methodology and applications, this book
focuses on a rather unique combination of theoretical and
foundational aspects that underlie the field of statistical
inference. Readers gain a deeper understanding of the evolution and
underlying logic of each mode as well as each mode's strengths and
weaknesses.

The book begins with fascinating highlights from the history of
statistical inference. Readers are given historical examples of
statistical reasoning used to address practical problems that arose
throughout the centuries. Next, the book goes on to scrutinize four
major modes of statistical inference:

* Frequentist

* Likelihood

* Fiducial

* Bayesian

The author provides readers with specific examples and
counterexamples of situations and datasets where the modes yield
both similar and dissimilar results, including a violation of the
likelihood principle in which Bayesian and likelihood methods
differ from frequentist methods. Each example is followed by a
detailed discussion of why the results may have varied from one
mode to another, helping the reader to gain a greater understanding
of each mode and how it works. Moreover, the author provides
considerable mathematical detail on certain points to highlight key
aspects of theoretical development.

The author's writing style and use of examples make the text clear
and engaging. This book is fundamental reading for graduate-level
students in statistics as well as anyone with an interest in the
foundations of statistics and the principles underlying statistical
inference, including students in mathematics and the philosophy of
science. Readers with a background in theoretical statistics will
find the text both accessible and absorbing.