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A Comparison of the Bayesian and Frequentist Approaches to Estimation (eBook, PDF)

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This monograph contributes to the area of comparative statistical inference. Attention is restricted to the important subfield of statistical estimation. The book is intended for an audience having a solid grounding in probability and statistics at the level of the year-long undergraduate course taken by statistics and mathematics majors. The necessary background on Decision Theory and the frequentist and Bayesian approaches to estimation is presented and carefully discussed in Chapters 1-3. The "threshold problem" -- identifying the boundary between Bayes estimators which tend to outperform standard frequentist estimators and Bayes estimators which don't -- is formulated in an analytically tractable way in Chapter 4. The formulation includes a specific (decision-theory based) criterion for comparing estimators. The centerpiece of the monograph is Chapter 5 in which, under quite general conditions, an explicit solution to the threshold is obtained for the problem of estimating a scalar parameter under squared error loss. The six chapters that follow address a variety of other contexts in which the threshold problem can be productively treated. Included are treatments of the Bayesian consensus problem, the threshold problem for estimation problems involving of multi-dimensional parameters and/or asymmetric loss, the estimation of nonidentifiable parameters, empirical Bayes methods for combining data from 'similar' experiments and linear Bayes methods for combining data from 'related' experiments. The final chapter provides an overview of the monograph's highlights and a discussion of areas and problems in need of further research. F. J. Samaniego is a Distinguished Professor of Statistics at the University of California, Davis. He served as Theory and Methods Editor of the Journal of the American Statistical Association (2003-05), was the 2004 recipient of the Davis Prize for Undergraduate Teaching and Scholarly Achievement, and is an electedFellow of the ASA, the IMS and the RSS and an elected Member of the ISI.

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From the reviews:

"Intended to be broad, including an advanced undergraduate audience ... and the book would more likely benefit more senior readers. A Comparison is pleasant to read, written in a congenial style ... and the decision-theoretic background is well-set. Its self-declared purpose ... is commendable in that an objective comparison of Bayesian versus frequentist estimators should appeal to anyone." (Christian P. Robert, International Statistical Review, Vol. 79 (1), 2011)

"Samaniego presents a unique approach to comparing the Bayesian and frequentist schools of thought. ... provides extensive overviews of the decision-theoretic framework, the frequentist approach to estimation, and the Bayesian approach to

estimation. I found the coverage of these topics strong and the writing interesting. ... I can see A Comparison of the Bayesian and Frequentist Approaches to Estimation serving the needs of a special topics course or serving nicely as a reference book for a more general course on Bayesian statistics or mathematical statistics." (Andrew Neath, Journal of the American Statistical Association, Vol. 106 (496), December, 2011)

"The main theme of the monograph is 'comparative statistical inference'. The author provides ideas and examples which can assist a statistician in comparing the performance one can expect from using either Bayesian or classical solutions in estimation problems. ... contains a summary and synthesis of the main themes of the monograph and provides a general set of conclusions and recommendations regarding the types of problems in which the Bayesian approach to estimation stands to provide reliable and preferred solutions ... ." (Alicja Jokiel-Rokita, Mathematical Reviews, Issue 2011 g)

"Francisco J. Samaniego's A Comparison of the Bayesian and Frequentist Approaches to Estimation is an extremely well written book. Filled with amusing wordplay and clear descriptions, the book lays out acase for both Bayesian and frequentist estimators. ... easily approachable to graduate students and has exercises following each section ... . an engaging, quick read that acquaints the reader with ways to produce and judge estimators for many problems. ... a nice overview for those seeking a framework for comparison of these estimators." (Elizabeth Ben Ward, SIAM Review, Vol. 54 (1), 2012)

"Samaniego explores some of the traditional approaches to comparing Bayes and frequentist estimators. ... He includes appropriate references for the reader who wishes to study the problems in more detail than given in the book. ... This book is very worthwhile because it will stimulate research, thought, and discussion about its subject matter and related issues. In conclusion Samaniego invites the reader to: 'Add your imprint to this work! You are cordially and enthusiastically invited to the party.'" (Marvin H. J. Gruber, Technometrics, Vol. 53 (3), August, 2011)

"The book under review is addressed to the audience of academics and practitioners who are open to using either frequentist or Bayesian methods in the considered problems ... . It will be appropriate as a text either for an advanced undergraduate course or for a graduate-level course or seminar. The book consists of 12 chapters and an Appendix." (Joseph Melamed, Zentralblatt MATH, Vol. 1204, 2011)

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