INFORMATION-GAP DECISION THEORY:
DECISIONS UNDER SEVERE UNCERTAINTY
Yakov Ben-Haim
Technion - Israel Institute of Technology
Academic Press, 2001. ISBN: 0-12-088251-5
Reviews
"Professor Yakov Ben-Haim has written a landmark book ... His
information-gap modeling approach to decision making under uncertainty
constitutes a new and revolutionary approach for addressing tough
decision problems when little information is available."
Prof. Keith Hipel, Dept. of Systems Design Engineering, University
of Waterloo, Canada.
Pre-publication review.
"The book is self-sufficient and unique and it is a must-read
treatise for all students and professionals working in the area of
structural safety and reliability and for those involved in
decision-making processes accompanied by severe lack of
information."
Prof. Chris P. Pantelides, Dept. of Civil and Environmental
Engineering, University of Utah
ASCE Journal of Structural Engineering, May 2002, p.688.
"The book presents a distinctive new theory of decision making under severe uncertainty. ... [T]his is a very comprehensive, focused and interesting book."
Prof. Daniel Sipper, Dept. of Industrial Engineering, Tel Aviv University, Interfaces, Journal of the Institute For Operations Research and Management Sciences (INFORMS), May-June 2003, vol.33, \#3, pp.85-86.
Ben-Haim has "written a book that is ... ambitious in its aim, broad in its scope and profound in its philosophical grounding."
"Tackling a problem with info-gap theory will take intelligence, ingenuity and honesty. Yakov Ben-Haim's impressive book convinces that investment of these precious resources in an info-gap model will yield valuable insights and improved decisions."
Prof. Jim Hall, School of Civil Engineering and Geosciences, University of Newcastle-upon-Tyne
International Journal of General Systems, 32(2) (2003) 204-206.
Samples
Table of Content: pdf file.
Section 3.1. Robustness and Opportunity:
pdf file.
Section 3.3.2. Structural Reliabilitity:
pdf file.
Section 3.3.6. Portfolio investment: pdf
file.
Abstract
Everyone makes decisions, but not everyone is a decision analyst.
A decision analyst uses quantitative models and computational methods
to formulate decision algorithms, assess decision performance,
identify and evaluate options, determine trade-offs and risks,
evaluate strategies for investigation, and so on. This book is
written for decision analysts.
The term "decision analyst" covers an extremely broad range of
practitioners. Virtually all engineers involved in design (of
buildings, machines, processes, etc.) or analysis (of safety,
reliability, feasibility, etc.) are decision analysts, usually without
calling themselves by this name. In addition to engineers, decision
analysts work in planning offices for public agencies, in project
management consultancies, they are engaged in manufacturing process
planning and control, in financial planning and economic analysis, in
decision support for medical or technological diagnosis, and so on and
on. Decision analysts provide quantitative support for the
decision-making process in all areas where systematic decisions are
made.
The power of analysis in any field derives from generality and
abstraction. This is true of decision analysis, and it gives rise to
generic theories such as info-gap decision theory. The decision
analyst thus faces a double challenge: to master the abstractions as
well as to bring them down to earth. This book assumes familiarity
with university mathematics. However, the emphasis is not on theorems
and proofs but rather on how to formulate and analyze decisions. The
book is practical, but from a theoretical perspective. As Boltzmann
put it, nothing is more practical than theory. This book is therefore
full of equations as well as examples from a plethora of fields.
Info-gap decision theory is radically different from all current
theories of decision under uncertainty. The difference originates in
the modelling of uncertainty as an information gap rather than as a
probability. The need for info-gap modelling and management of
uncertainty arises in dealing with severe lack of information and
highly unstructured uncertainty. What is an information gap? How is
it quantified? How does one use info-gap ideas to analyze such
central (and traditionally probabilistic) concepts as risk, gambling,
reliability and so on? This book addresses these and many other
questions. New theories are like virgin orchards, and much fruit is
ripe and ready to eat. But the quest for fuller answers, and even for
new questions, is still at full steam. The reader is invited to join
the search.
On-line Ordering
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Academic Press
Brief Table of Contents
Chapter 1: Overview
Chapter 2: Uncertainty
Chapter 3: Robustness and Opportunity
Chapter 4: Value Judgments
Chapter 5: Antagonistic and Sympathetic Immunities
Chapter 6: Gambling and Risk Sensitivity
Chapter 7: Value of Information
Chapter 8: Learning
Chapter 9: Coherent Uncertainties and Consensus
Chapter 10: Retrospective Essay: Risk Assessment in Project Management
Chapter 11: Hybrid Uncertainties
Chapter 12: Implications of Info-Gap Uncertainty
References
Author Index
Subject Index
Full Table of Contents
Chapter 1 Overview 1
Chapter 2 Uncertainty 9
- 2.1 Historical Perspective 9
- 2.2 Info-Gap Uncertainty, Probability and Fuzziness 12
- 2.3 Some Info-Gap Models 16
- 2.4 Uncertainty and Convexity 25
- 2.5 Axioms of Info-Gap Uncertainty 26
- 2.6 Problems 27
Chapter 3 Robustness and Opportunity 31
- 3.1 Robustness and Opportunity 32
- 3.1.1 A First Look 32
- 3.1.2 Reward Functions 33
- 3.1.3 Generic Decision Algorithms 35
- 3.1.4 Multi-Criterion Reward 37
- 3.1.5 Three Components of Info-Gap Decision Models 38
- 3.1.6 Preferences 38
- 3.1.7 Trade-Offs 40
- 3.2 Production-Volume With Uncertain Costs 41
- 3.3 Simple Examples 50
- 3.3.1 Engineering Design: Cantilever 50
- 3.3.2 Structural Reliability 54
- 3.3.3 Sequential Decisions 57
- 3.3.4 Project Management 61
- 3.3.5 Manufacturing Process Control 66
- 3.3.6 Portfolio Investment 70
- 3.3.7 Search and Evasion 75
- 3.3.8 Robustness and Opportunity 77
- 3.4 General Robustness and Opportunity Functions 81
- 3.5 Problems 84
Chapter 4 Value Judgments 99
- 4.1 Normalization 100
- 4.2 Analogical Reasoning 102
- 4.3 Calibration by Consequence Severity 104
- 4.3.1 Robustness Function for Environmental Management 105
- 4.3.2 Calibration by Consequence Severity 107
- 4.4 Calibration by Information 108
- 4.5 Rationality and Preference 108
- 4.6 Problems 111
Chapter 5 Antagonistic and Sympathetic Immunities 113
- 5.1 Immunity Functions 114
- 5.2 Reward-Coherent Action 116
- 5.3 Vibrating Mechanical Contact 118
- 5.4 Multi-Tasking of Computer Jobs 121
- 5.4.1 Formulation 121
- 5.4.2 Deriving Robustness and Opportunity Functions 124
- 5.4.3 Results 127
- 5.5 Problems 130
Chapter 6 Gambling and Risk-Sensitivity 133
- 6.1 Preview 134
- 6.2 Risk-Sensitivity and the Robustness Curve 135
- 6.3 Risk Sensitivity and Two Robustness Curves 137
- 6.4 Initial Commitment and Uncertain Future 140
- 6.4.1 Uniformly Bounded Uncertainty 142
- 6.4.2 Fourier Bounded Uncertainty 143
- 6.5 Risk-Sensitivity, Robustness and Opportunity 144
- 6.6 Risk-Neutral Line 147
- 6.7 Pure Competition With Uncertain Cost 151
- 6.8 Summary 153
- 6.9 Risk Assessment in Project Management 155
- 6.10 More on the Robustness Premium 157
- 6.11 Robustness-Premium and Resource Commitment 160
- 6.12 Problems 163
Chapter 7 Value of Information 169
- 7.1 Informativeness of an Info-Gap Model 170
- 7.2 Demand Value of Information 172
- 7.3 Uncertain Loads on a Cantilever 174
- 7.4 Cantilever: Disjoint Info-Gap Models 178
- 7.5 Gathering Information in Project Management 180
- 7.6 Windfall Cost of Information 181
- 7.6.1 Formulation 182
- 7.6.2 Discussion 184
- 7.7 Initial Commitment and Uncertain Future: Revisited 186
- 7.8 The Allais `Paradox' 189
- 7.8.1 Formulation 189
- 7.8.2 Probability-Uncertainty 190
- 7.8.3 Utility-Uncertainty 192
- 7.9 The Ellsberg `Paradox' 194
- 7.10 Expected-Utility Risk Aversion 196
- 7.11 Problems 197
Chapter 8 Learning 201
- 8.1 Learning and Deciding 201
- 8.2 Info-Gap Supervision of a Classifier 203
- 8.2.1 Robustness of a Classifier 203
- 8.2.2 Asymptotic Robustness 204
- 8.2.3 Robust Optimal Classifier 206
- 8.2.4 A Proof 208
- 8.2.5 Robust Severe Tests of Truth 209
- 8.2.6 Up-Dating Info-Gap Models 210
- 8.2.7 Plantar Pressures in Metatarsal Pathology 213
- 8.3 Acoustic Noise 216
- 8.3.1 Empirical Robustness 217
- 8.3.2 Up-Dating the Acoustic Uncertainty Model 219
- 8.4 Summary 221
- 8.5 Problems 223
Chapter 9 Coherent Uncertainties and Consensus 227
- 9.1 Preference Preservation Under Altered Information 228
- 9.2 Examples of Coherent Uncertainties 231
- 9.3 Principal-Agent Contract Bidding 236
- 9.4 Proofs 240
- 9.5 Problems 242
Chapter 10 Retrospective Essay: Risk Assessment in Project
Management 245
- 10.1 Info-gap Uncertainty: What Is It? 246
- 10.2 Info-gap Uncertainties in Project Management 246
- 10.3 Robustness: Greatest Tolerable Info-gap Uncertainty 249
- 10.4 Value Judgments: How Robust Is Robust Enough? 250
- 10.5 Risk and the Robustness-vs.-Reward Trade-off 252
- 10.6 Improving Robustness by Gathering Information 253
- 10.7 Improving Robustness by Re-Structuring 255
- 10.8 The Other Face of Uncertainty: Opportunity 256
- 10.9 Final Comment: Quantitative Decision Support Systems 258
Chapter 11 Hybrid Uncertainties 263
- 11.1 Info-Gap Uncertainty in a Poisson Process 263
- 11.2 Embedded Probability Densities 267
- 11.3 Probabilistic Info-Gap Parameter 269
- 11.4 Problems 271
Chapter 12 Implications of Info-Gap Uncertainty 273
- 12.1 Holism and Uncertainty 274
- 12.2 Language, Meaning and Uncertainty 277
- 12.3 Warrant and Uncertainty 281
- 12.4 Credence for Info-Gap Inference 287
- 12.4.1 Info-Gap Inference and Robust Severe Tests 288
- 12.4.2 Warrant and Credence 290
- 12.4.3 Credibility of Info-Gap Inference 293
- 12.4.4 Info-Gap Inference with the Opportunity Function 295
- 12.5 Risk and Uncertainty 296
References 303
Author Index 312
Subject Index 319