by José M. Bernardo and Adrian F. M. Smith Wiley, Chichester, 1994 586pp., cloth, ISBN 0-471-92416-4

The volume attempts to provide a fairly complete overview of what the authors regard as key concepts, results and issues in Bayesian Statistics.

Some excerpts from published reviews follow in chronological order of publication:

J. Ital. Statist. Soc. 1 (1994) pp. 155-160, reviewed by Ludovico Piccinato "This long awaited volume is written in a particularly clear style; no preliminary knowledge of Statistics is assumed and all the chapters end with a section, named Discussion and further references, where the authors discuss in detail the options taken in the text and the main alternative considered in the literature. The book succeeds in two goals which are, at first sight, quite far form each other: the first goal is to propose an organic unitary treatment, centered about an innovative philosophical core, and the second one is to provide a general review of Bayesian literature of all the schools."...

J. Roy. Statist. Soc. Ser. A 158 (1995), pp. 340-341, reviewed by Dennis Lindley "This book ought to, and I hope will, be very influencial in the development of statistics...The writing is extremely clear. The mathematical treatment is usually simple with only occasional excursions, being necessary for honesty, into elaborate technicalities... Teachers could use the book as a text about final-year or diploma level... Furthermore, some of the treatment is original, so that it reads more like a monograph.... because of the books's importance, my advice to every Fellow is to read the more accessible parts of this book, to consider the reasons for adopting the Bayesian approach and, if not satisfied, to say why not... here is the most important book on theory to appear for several years."

Inst. Math. and Appl. Bull. 31 (1995), p. 62, reviewed by David Percy "What a wonderful book this is! Mathematicians, statisticians and probabilists have long been awaiting a modern comprehensive treatise on Bayesian methodology and this text offers part of the solution."...

J. Amer. Statist. Assoc. 91 (1996), pp. 906-907 , reviewed by James Dickey and Morris Eaton "This first of three planned volumes is a well written introduction to (indeed a treatise on) the theory of Bayesian statistics. It is well written in the sense of being alert, explicit, and articulate about assumptions, competing attitudes, levels of abstraction, scope of applicability, implications, interpretations, and relevance of the theory developed.'...

SIAM Rev 39 (1997), pp 142-144 , reviewed by Mark Berliner "...This book is not really a text. Rather, I find it nearly encyclopedic in both intent and outcome. One can find authoritative discussion and references on "everything" Bayesian. Compiling the 65 pages of references was a service itself.... I strongly recommend the book... the overall breadth of coverage and competency of presentation are exemplary. The authors have taken on a difficult task and produced a classic. I think one of the most common phrases in Bayesian research articles will soon be 'see Bernardo and Smith (1994) for further discussion and references'."