Decision Theory: Principles and Approaches / Edition 1

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $67.73
Usually ships in 1-2 business days
(Save 40%)
Other sellers (Hardcover)
  • All (5) from $67.73   
  • New (3) from $83.73   
  • Used (2) from $67.73   


Decision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives. This book:
• Provides a rich collection of techniques and procedures.
• Discusses the foundational aspects and modern day practice.
• Links foundations to practical applications in biostatistics, computer science, engineering and economics.
• Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics. Decision Theory is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book.

Read More Show Less

Editorial Reviews

From the Publisher
“Also anyone interested in learning more about decision theoretic experimental design (a topic of growing interest for example in sequential clinical trials) will find a useful overview and a good starting point for further investigations.”  (Stat Papers, 2011)

  "Decision theory is fundamental to all scientific disciplines., including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book." (Mathematical Reviews, 2011)

Read More Show Less

Product Details

Table of Contents



1 Introduction.

1.1 Controversies.

1.2 A guided tour of decision theory.

Part One: Foundations.

2 Coherence.

2.1 The “Dutch Book” theorem.

2.2 Temporal coherence.

2.3 Scoring rules and the axioms of probabilities.

2.4 Exercises.

3 Utility.

3.1 St. Petersburg paradox.

3.2 Expected utility theory and the theory of means.

3.3 The expected utility principle.

3.4 The von Neumann–Morgenstern representation theorem.

3.5 Allais’ criticism.

3.6 Extensions.

3.7 Exercises.

4 Utility in action.

4.1 The “standard gamble”.

4.2 Utility of money.

4.3 Utility functions for medical decisions.

4.4 Exercises.

5 Ramsey and Savage.

5.1 Ramsey’s theory.

5.2 Savage’s theory.

5.3 Allais revisited.

5.4 Ellsberg paradox.

5.5 Exercises.

6 State independence.

6.1 Horse lotteries.

6.2 State-dependent utilities.

6.3 State-independent utilities.

6.4 Anscombe–Aumann representation theorem.

6.5 Exercises.

Part Two Statistical Decision Theory.

7 Decision functions.

7.1 Basic concepts.

7.2 Data-based decisions.

7.3 The travel insurance example.

7.4 Randomized decision rules.

7.5 Classification and hypothesis tests.

7.6 Estimation.

7.7 Minimax–Bayes connections.

7.8 Exercises.

8 Admissibility.

8.1 Admissibility and completeness.

8.2 Admissibility and minimax.

8.3 Admissibility and Bayes.

8.4 Complete classes.

8.5 Using the same α level across studies with different sample sizes is inadmissible.

8.6 Exercises.

9 Shrinkage.

9.1 The Stein effect.

9.2 Geometric and empirical Bayes heuristics.

9.3 General shrinkage functions.

9.4 Shrinkage with different likelihood and losses.

9.5 Exercises.

10 Scoring rules.

10.1 Betting and forecasting.

10.2 Scoring rules.

10.3 Local scoring rules.

10.4 Calibration and refinement.

10.5 Exercises.

11 Choosing models.

11.1 The “true model” perspective.

11.2 Model elaborations.

11.3 Exercises.

Part Three Optimal Design.

12 Dynamic programming.

12.1 History.

12.2 The travel insurance example revisited.

12.3 Dynamic programming.

12.4 Trading off immediate gains and information.

12.5 Sequential clinical trials.

12.6 Variable selection in multiple regression.

12.7 Computing.

12.8 Exercises.

13 Changes in utility as information.

13.1 Measuring the value of information.

13.2 Examples.

13.3 Lindley information.

13.4 Minimax and the value of information.

13.5 Exercises.

14 Sample size.

14.1 Decision-theoretic approaches to sample size.

14.2 Computing.

14.3 Examples.

14.4 Exercises.

15 Stopping.

15.1 Historical note.

15.2 A motivating example.

15.3 Bayesian optimal stopping.

15.4 Examples.

15.5 Sequential sampling to reduce uncertainty.

15.6 The stopping rule principle.

15.7 Exercises.


A.1 Notation.

A.2 Relations.

A.3 Probability (density) functions of some distributions.

A.4 Conjugate updating.



Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)