Product Description

The mathematical implications of personal beliefs and values in science and commerce

Amid a worldwide resurgence of interest in subjectivist statistical method, this book offers a fresh look at the role of personal judgments in statistical analysis. Frank Lad demonstrates how philosophical attention to meaning provides a sensible assessment of the prospects and procedures of empirical inferential learning.

Operational Subjective Statistical Methods offers a systematic investigation of Bruno de Finetti's theory of probability and logic of uncertainty, which recognizes probability as the measure of personal uncertainty at the heart of its mathematical presentation. It identifies de Finetti's "fundamental theorem of coherent provision" as the unifying structure of probabilistic logic, and highlights the judgment of exchangeability rather than causal independence as the key probabilistic component of statistical inference.

Broad in scope, yet firmly grounded in mathematical detail, this text/reference

Invites readers to address the subjective personalist meaning of probability as motivating the mathematical construction

• Contains numerous examples and problems, including computing problems using Matlab, assuming no background in Matlab
• Explains how to use the material in three distinct sequential courses in math and statistics, as well as in courses at the graduate level in applied fields
• Provides an introductory basis for understanding more complex structures of statistical analysis

Complete with fifty illustrations, Operational Subjective Statistical Methods makes an intriguing discipline accessible to professionals, students, and the interested general reader. It contains a wealth of teaching and research material, and offers profound insight into the relationship between philosophy, faith, and scientific method.

Product Details

• Amazon Sales Rank: #2773486 in Books
• Published on: 1996-09-27
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 512 pages

Review
"...has a merit for everyone who wonders about the foundations of inference..." -- Australian & New Zealand J Statistics, 2000

From the Publisher
The first book to present Bruno de Finetti's theory of probability and logic of uncertainty in a systematic format. The author identifies de Finetti's "fundamental theorem of coherent prevision" as the unifying structure of probabilistic logic, highlighting the judgment of exchangeability rather than causal independence as the key probabilistic component of statistical inference. Throughout the text, readers are invited to address the subjective personalistic meaning of probability as motivating the mathematical construction. Philosophical attention to meaning is shown to support a difference approach to statistical practice that is widely prevalent today. Includes numerous examples, problems, and illustrations to facilitate understanding.

From the Back Cover
The mathematical implications of personal beliefs and values in science and commerce

Amid a worldwide resurgence of interest in subjectivist statistical method, this book offers a fresh look at the role of personal judgments in statistical analysis. Frank Lad demonstrates how philosophical attention to meaning provides a sensible assessment of the prospects and procedures of empirical inferential learning.

Operational Subjective Statistical Methods offers a systematic investigation of Bruno de Finetti's theory of probability and logic of uncertainty, which recognizes probability as the measure of personal uncertainty at the heart of its mathematical presentation. It identifies de Finetti's "fundamental theorem of coherent provision" as the unifying structure of probabilistic logic, and highlights the judgment of exchangeability rather than causal independence as the key probabilistic component of statistical inference.

Broad in scope, yet firmly grounded in mathematical detail, this text/reference

Invites readers to address the subjective personalist meaning of probability as motivating the mathematical construction Contains numerous examples and problems, including computing problems using Matlab, assuming no background in Matlab Explains how to use the material in three distinct sequential courses in math and statistics, as well as in courses at the graduate level in applied fields Provides an introductory basis for understanding more complex structures of statistical analysis

Complete with fifty illustrations, Operational Subjective Statistical Methods makes an intriguing discipline accessible to professionals, students, and the interested general reader. It contains a wealth of teaching and research material, and offers profound insight into the relationship between philosophy, faith, and scientific method.

Customer Reviews

A Serious Construction of Applied Subjective Statistical Methods
Wow! I was really disappointed to read the two Amazon reviews of my book,
Operational Subjective Statistical Methods: a mathematical,
philosophical, and historical introduction (New York: John Wiley, 1996).
Whatever the disposition of the authors regarding the merits of the
book, both of them give a completely erroneous impression of what the book
is about. I have been motivated to review it briefly myself. In the first
place, the book is a mathematics book, replete with 87 definitions and 76
theorems, in addition to numerous examples and problems in every chapter.
The central mathematical development exposits de Finetti's fundamental
theorem of prevision, generated by an understanding that the
condition of coherency of previsions motivates the application of the
separating hyperplane theorem. Moreover, the book develops a virtually
complete discussion of exchangeability and partial exchangeability via
symmetry with respect to a finite number of sufficient statistics.
References are made to 387 books and articles, noted in the bibliography.
These include many more books than the mere thirty proclaimed by Amazon.
Mathematically, the book introduces the pathbreaking insights of Bruno
de Finetti to readers who have studied beyond calculus to a course in linear algebra.
The book is philosophical in the sense that explicit attention is given to
the meaning of the mathematical constructions as they are made.
Philosophical comments are appropriately interspersed throughout the text
when difficult points require them. It is true that in this feature the
book differs from most formalist or Platonic mathematics texts that rely
heavily on metaphysical assertions while ignoring them or suppressing any
reference to them. However, the central philosophical discussion and
historical development of the subjectivist statistical method feature
largely in the first chapter, which is written for any educated reader
who is interested in the role of beliefs and values in a post-mechanistic
understanding of science. The book does not focus on a comparison between
various points of view about probability. Rather it unabashedly develops
the implications of the subjective viewpoint a la Bruno de Finetti
into a practical, applied and computable statistical programme for
inferential statistics. This is based on the use of scored sequential
forecasting of observable quantities, a procedure explicitly proposed as
completely replacing the meaningless attempts to test the values of model
parameters that has dominated applied statistics through the twentieth
century and beyond. One will not find any discussion at all about the
choice of levels of type I error at which to test hypotheses, as claimed
by one reviewer. Despite the disclaimer of the other, the computable and
practical alternative to hypothesis testing is completely constructed,
analysed and applied in one large example regarding the forecasting of
international currency exchange rates, and is discussed in numerous
other examples as well. This book is a serious and lively presentation
of the subjectivist alternative to current statistical imagination and
practice. The development is truly novel. Notice the extensive list of
"statistically improbably phrases" constructed from Amazon's SIP
scanning program. I am pleased to read and to discuss both positive and
negative comments of readers who address the mathematical constructions
developed in my book. However, neither of these first two reviewers in
Amazon does this. Don't be misled! Pick up a copy from your local
university library and take a look for yourself. You may be intrigued
enough to buy your own copy and work at it.

An excellent historical and philosophical introduction
The title of the book is inverted.It should simply omit the word "mathematical" or move it to the end of the title,since the author really concentrates on the difficult philosophical issues that ,in effect,have been swept under the rug,so to speak,since the conflicts that arose in the early 1930's between Egon Pearson and Jerzy Neyman,on the one hand,and Sir Ronald Fisher on the other hand.Lad(L)does an excellent job of covering the historical controversy,as well as showing the differing methodological philosophies underlying the different positions.A reader will discover the potential logical quagmires one can quickly find himself in if he asks the question,"What does a 95% confidence interval mean ?" or "What is the justification for choosing a .01 level of significance as opposed to a.10 level of significance?" or"What explanation makes logical sense to a client if I tell him I am only not rejecting his null hypothesis at the .01 level of significance,but that I am definitely rejecting his null hypothesis at the .05 level of significance?".This book will alert the careful reader that there are many holes in the logical foundation supporting the Neyman- Pearson approach to hypothesis testing.Whether the subjectivist approach can adequately plug these gaps is another question that the author deals with in an unconvincing way, in this reviewers opinion.Perhaps the answer lies in a more careful examination of the logical approach to probability.

disappointingly useless.
For the most part, I'm very open to alternative perspectives in mathematics, statistics, and economics. I liked the premise of this book and the subjective critique, but reading was nothing other than disappointment. This is a philosophical rant which devotes a great deal of time to bashing the standard objective perspective of statistics, but provides very little substantive in its place.

Take, for instance, hypothesis testing. Suppose we run a regression and estimate some vector of coefficients beta. This estimated beta is a random variable, since it depends on the x variables that we drew. One of the first things we ask is, "what is the probability of coming up with [this estimated value of beta], given that the true value is [something]?" This is an objectivist's view -- that there exists some "true value." The idea that this is some "true value" or "true distribution" underlies most of modern statistics. The operational subjectivist's argument is that it's meaningless to talk about such things -- there is no way we could possibly recover this "true value", so what's the sense in comparing things to it?

The author has a good point here. But then the question is, so what? What can we do with this alternative perspective, other than throw rocks at objectivists? The only times the book provides practical techniques (a subjectivist interpretation of hypothesis testing, for example) it turns out to be little other than a relabelling of the usual model.

So. I returned the book to Amazon. I'm glad for looking at it, because I'd been intrigued by the idea -- but now I realize that there's just not a whole lot there, at least not in this author's presentation.