Info-Gap Decision Theory (eBook)

Front Cover 1
Contents 6
Preface to the 1st edition 12
Preface to the 2nd edition 14
1 Overview 18
2 Uncertainty 26
2.1 Historical Perspective 26
2.2 Is Ignorance Probabilistic? 29
2.3 Info-Gap Uncertainty, Probability and Fuzziness 31
2.4 Uncertainty and Convexity 35
2.5 Some Info-Gap Models 37
2.6 ‚ Axioms of Info-Gap Uncertainty 48
2.7 Problems 49
3 Robustness and Opportuneness 54
3.1 Robustness and Opportuneness 55
3.1.1 A First Look 55
3.1.2 Immunity Functions 56
3.1.3 Generic Decision Algorithms 58
3.1.4 Multi-Criterion Reward 60
3.1.5 Three Components of Info-Gap Decision Models 61
3.1.6 Preferences 62
3.1.7 Trade-Offs 63
3.1.8 Zero Robustness and Preference Reversal 65
3.2 Simple Examples 66
3.2.1 Engineering Design: Cantilever 67
3.2.2 Structural Reliability 71
3.2.3 Structural Reliability with Uncertain Probability 73
3.2.4 Set-Points for Process Control 75
3.2.5 Sequential Decisions 77
3.2.6 Project Scheduling with Uncertain Task Durations 81
3.2.7 Portfolio Investment 87
3.2.8 Monetary Policy 92
3.2.9 Search and Evasion 95
3.2.10 Assay Design: Environmental Monitoring 97
3.2.11 Bio-Terror Preparedness with Epidemiological Models 100
3.2.12 Drug Selection 103
3.2.13 Estimating an Uncertain Probability Density 105
3.3 Production Volume With Uncertain Costs 108
3.4 ‚ General Robustness and Opportuneness Functions 116
3.5 Problems 120
4 Value Judgments 132
4.1 Normalization 133
4.2 Analogical Reasoning 134
4.3 Calibration by Consequence Severity 138
4.3.1 Robustness Function for Environmental Management 138
4.3.2 Calibration by Consequence Severity 140
4.4 Rationality and Preference 141
4.5 Problems 144
5 Antagonistic and Sympathetic Immunities 146
5.1 Immunity Functions 147
5.2 Reward-Coherent Action 149
5.3 Vibrating Mechanical Contact 150
5.4 Multi-Tasking of Computer Jobs 154
5.4.1 Formulation 154
5.4.2 Deriving Robustness and Opportuneness Functions 157
5.4.3 Results 160
5.5 Problems 163
6 Gambling and Risk Sensitivity 166
6.1 Preview 167
6.2 Risk Sensitivity and the Robustness Curve 168
6.3 Risk Sensitivity and Two Robustness Curves 170
6.4 Initial Commitment and Uncertain Future 173
6.4.1 Uniformly Bounded Uncertainty 175
6.4.2 Ellipsoidal Fourier Uncertainty 177
6.5 Risk Sensitivity, Robustness and Opportuneness 177
6.6 Risk-Neutral Line 180
6.7 Pure Competition with Uncertain Cost 183
6.8 Interim Summary 186
6.9 Risk Assessment in Project Management 188
6.10 ‚ More on the Robustness Premium 189
6.11 ‚ Robustness Premium and Resource Commitment 193
6.12 Problems 196
7 Value of Information 202
7.1 Informativeness of an Info-Gap Model 203
7.2 Demand Value of Information 205
7.3 Uncertain Loads on a Cantilever 207
7.4 Cantilever: Simple and Complex Info-Gap Models 211
7.5 Gathering Information in Project Management 213
7.6 Windfall Cost of Information 214
7.6.1 Formulation 215
7.6.2 Discussion 216
7.7 Initial Commitment and Uncertain Future: Revisited 218
7.8 Problems 220
8 Learning 224
8.1 Learning and Deciding 224
8.2 Info-Gap Supervision of a Classifier 226
8.2.1 Robustness of a Classifier 226
8.2.2 Asymptotic Robustness 227
8.2.3 Robust-Optimal Classifier 229
8.2.4 ‚ A Proof 231
8.2.5 Robust Severe Tests of Truth 232
8.2.6 Updating Info-Gap Models 233
8.2.7 Plantar Pressures in Metatarsal Pathology 236
8.3 Acoustic Noise 239
8.3.1 Empirical Robustness 240
8.3.2 Updating the Acoustic Uncertainty Model 242
8.4 Summary 243
8.5 Problems 245
9 Coherent Uncertainties and Consensus 248
9.1 Preference Preservation Under Altered Information 249
9.2 Examples of Coherent Uncertainties 252
9.3 Principal-Agent Contract Bidding 258
9.4 ‚ Proofs 261
9.5 Problems 263
10 Hybrid Uncertainties 266
10.1 Info-Gap Uncertainty in a Poisson Process 267
10.2 Embedded Probability Densities 270
10.3 Example: Endangered Species 273
10.4 Example: Serving an Uncertain Queue 276
10.5 Probabilistic Info-Gap Parameter 279
10.6 Problems 281
11 Robust-Satisficing Behavior 284
11.1 The Ellsberg 'Paradox' 285
11.2 The Allais 'Paradox' 288
11.2.1 Formulation 289
11.2.2 Probability Uncertainty 290
11.2.3 Utility Uncertainty 293
11.3 Info-Gap Analysis of Expected-Utility Risk Aversion 294
11.4 Probability of Success 296
11.4.1 Robust-Satisficing and Direct-Optimizing 297
11.4.2 Satisficing and Survival 300
11.5 The Equity Premium Puzzle: A Solution 301
11.5.1 Introduction 301
11.5.2 Dynamics, Uncertainty and Robustness 302
11.5.3 Asset-Pricing Relation 304
11.5.4 Equity Premium 307
11.5.5 Stationarity 309
11.5.6 Discussion 310
12 Retrospective Essay: Risk Assessment in Project Management 314
12.1 Info-Gap Uncertainty: What Is It? 315
12.2 Info-Gap Uncertainties in Project Management 316
12.3 Robustness: Greatest Tolerable Info-Gap 319
12.4 Value Judgments: How Robust Is Robust Enough? 320
12.5 Risk and the Robustness-vs.-Reward Trade-off 323
12.6 Improving Robustness by Gathering Information 325
12.7 Improving Robustness by Restructuring 327
12.8 What Should We Optimize? 328
12.9 The Other Face of Uncertainty: Opportuneness 330
12.10 Quantitative Decision Support Systems 332
13 Implications of Info-Gap Uncertainty 334
13.1 Holism and Uncertainty 335
13.2 Language, Meaning and Uncertainty 338
13.3 Warrant and Uncertainty 342
13.4 Credence for Info-Gap Inference 348
13.4.1 Info-Gap Inference and Robust Severe Tests 349
13.4.2 Warrant and Credence 351
13.4.3 Credibility of Info-Gap Inference 354
13.4.4 Info-Gap Inference with the Opportuneness Function 356
13.5 Risk and Uncertainty 358
References 364
Author Index 374
A 374
B 374
C 374
D 374
E 375
F 375
G 375
H 375
J 375
K 375
L 375
M 375
N 376
O 376
P 376
Q 376
R 376
S 376
T 376
V 376
W 376
Y 377
Z 377
Subject Index 378
A 378
B 378
C 378
D 379
E 379
F 380
G 380
H 380
I 380
K 381
L 381
M 381
N 382
O 382
P 382
Q 383
R 383
S 384
T 384
U 384
V 385
W 385