“By and large this book is at its best in developing the mathematical consequences of the theory and at its worst when dealing with the underlying ideas and concepts, which seems unfortunate since Bayesian statistics is above all an attempt to deal realistically with the nature of uncertainty and decision making.” B. Hill, JASA, 1986, p.569
“Unfortunately, those who had hoped for a serious contribution to the question will be disappointed.” B. Hill, JASA, 1986, p.569
“If the primary concern is mathematical convenience, not content or meaning, then the enterprise is a very different matter from what most of us think of as Bayesian approach.” B. Hill, JASA, 1986, p.570
“Perhaps in a century or two statisticians and probabilists will reach a similar state of maturity.” B. Hill, JASA, 1986, p.570
“Perhaps this is a good place to mention that the notation in the book is formidable. Bayes’s theorem appears in a form that is almost unrecognizable. As elsewhere, the mathematical treatment is elegant. but none of the deeper issues about the meaning and interpretation of conditional probability is discussed.” B. Hill, JASA, 1986, p.570
“The reader will find many intriguing ideas, much that is outrageous, and even some surprises (the likelihood principle is not mentioned, and conditional inference is just barely mentioned).” B. Hill, JASA, 1986, p.571
“What is disappointing to me is that with a little more discipline and effort with regard to the ideas underlying Bayesian statistics, this book could have been a major contribution to the theory.” B. Hill, JASA, 1986, p.571
Another review by William Sudderth (1985, Bulletin of the American Mathematical Society) is much kinder to the book, except for the complaint that “the pace is brisk and sometimes hard to follow”.