Probabilistic Forecasts and Optimal Decisions
John Wiley & Sons Inc (Verlag)
978-1-394-22186-8 (ISBN)
Decision theory is a body of thought and research seeking to apply a mathematical-logical framework to assessing probability and optimizing decision-making. It has developed robust tools for addressing all major challenges to decision making. Yet the number of variables and uncertainties affecting each decision outcome, many of them beyond the decider’s control, mean that decision-making is far from a ‘solved problem’. The tools created by decision theory remain to be refined and applied to decisions in which uncertainties are prominent.
Probabilistic Forecasts and Optimal Decisions introduces a theoretically-grounded methodology for optimizing decision-making under conditions of uncertainty. Beginning with an overview of the basic elements of probability theory and methods for modeling continuous variates, it proceeds to survey the mathematics of both continuous and discrete models, supporting each with key examples. The result is a crucial window into the complex but enormously rewarding world of decision theory.
Readers of Probablistic Forecasts and Optimal Decisions will also find:
Extended case studies supported with real-world data
Mini-projects running through multiple chapters to illustrate different stages of the decision-making process
End of chapter exercises designed to facilitate student learning
Probabilistic Forecasts and Optimal Decisions is ideal for advanced undergraduate and graduate students in the sciences and engineering, as well as predictive analytics and decision analytics professionals.
Roman Krzysztofowicz, PhD, is Professor of Systems Engineering in the School of Engineering and Applied Science and Professor of Statistics in the College and Graduate School of Arts and Sciences at the University of Virginia, Charlottesville, USA. He has previously held faculty posts at the University of Arizona and MIT, and his Bayesian Forecast-Decision Theory supplies a unified framework for the design and analysis of probabilistic forecast systems coupled with optimal decision systems.
Preface xxi
About the Companion Website xxiii
1 Forecast–Decision Theory 1
1.1 Decision Problem 1
1.2 Forecast–Decision System 2
1.3 Rational Deciding 4
1.4 Mathematical Modeling 5
1.5 Notes on Using the Book 6
Bibliographical Notes 7
Part I Elements of Probability 9
2 Basic Elements 11
2.1 Sets and Functions 11
2.2 Variates and Sample Spaces 13
2.3 Distributions 14
2.4 Moments 16
2.5 The Uniform Distribution 18
2.6 The Gaussian Distributions 19
2.7 The Gamma Function 29
2.8 The Incomplete Gamma Function 32
Exercises 34
3 Distribution Modeling 37
3.1 Distribution Modeling Methodology 37
3.2 Constructing Empirical Distribution 37
3.3 Specifying the Sample Space 39
3.4 Hypothesizing Parametric Models 40
3.5 Estimating Parameters 42
3.6 Evaluating Goodness of Fit 42
3.7 Illustration of Modeling Methodology 49
3.8 Derived Distribution Theory 51
Exercises 60
Mini-Projects 66
Part II Discrete Models 73
4 Judgmental Forecasting 75
4.1 A Perspective on Probability 75
4.2 Judgmental Probability 78
4.3 Forecasting Fraction of Events 81
4.4 Revising Probability Sequentially 83
4.5 Analysis of Judgmental Task 97
Historical Notes 98
Bibliographical Notes 98
Exercises 98
Mini-Projects 105
5 Statistical Forecasting 109
5.1 Bayesian Forecaster 109
5.2 Samples and Examples 112
5.3 Modeling and Estimation 114
5.4 An Application 117
5.5 Informativeness of Predictor 123
Bibliographical Notes 127
Exercises 127
Mini-Projects 130
6 Verification of Forecasts 143
6.1 Data and Inputs 143
6.2 Calibration 149
6.3 Informativeness 156
6.4 Verification Scores 163
6.5 Forecast Attributes and Mental Processes 166
6.6 Concepts and Proofs 168
Bibliographical Notes 170
Exercises 170
Mini-Projects 174
7 Detection-Decision Theory 179
7.1 Prototypical Decision Problems 179
7.2 Basic Decision Model 180
7.3 Decision with Perfect Forecast 187
7.4 Decision Model with Forecasts 190
7.5 Informativeness of Forecaster 193
7.6 Concepts and Proofs 194
Bibliographical Notes 198
Exercises 198
Mini-Projects 205
8 Various Discrete Models 209
8.1 Search Planning Model 209
8.2 Flash-Flood Warning Model 219
Bibliographical Note 229
Exercises 230
Mini-Projects 233
Part III Continuous Models 237
9 Judgmental Forecasting 239
9.1 A Perspective on Forecasting 239
9.2 Judgmental Distribution Function 240
9.3 Parametric Distribution Function 249
9.4 Group Forecasting 257
9.5 Adjusting Distribution Function 258
9.6 Applications 259
9.7 Judgment, Data, Analytics 261
9.8 Concepts and Proofs 261
Bibliographical Notes 263
Exercises 263
Mini–Projects 267
10 Statistical Forecasting 273
10.1 Bayesian Forecaster 273
10.2 Bayesian Gaussian Forecaster 275
10.3 Estimation and Validation 278
10.4 Informativeness of Predictor 280
10.5 Communication of Probabilistic Forecast 283
10.6 Application 284
10.7 Forecaster of the Sum of Two Variates 290
10.8 Prior and Posterior Sums 293
10.9 Concepts and Proofs 298
Bibliographical Notes 301
Exercises 302
Mini-Projects 306
11 Verification of Forecasts 315
11.1 Data and Inputs 315
11.2 Calibration 317
11.3 Informativeness 323
11.4 Verification of Bayesian Forecaster 329
11.5 Analysis of Judgmental Task 333
11.6 Applications 338
11.7 Concepts and Proofs 340
Bibliographical Notes 343
Exercises 343
Mini-Projects 346
12 Target-Decision Theory 353
12.1 Target-Setting Problem 353
12.2 Two-Piece Linear Opportunity Loss 355
12.3 Incomplete Expectations 359
12.4 Quadratic Difference Opportunity Loss 362
12.5 Impulse Utility 363
12.6 Implications for Analysts 365
12.7 Weapon-Aiming Model 367
12.8 Weapon-Aiming-with-Friend Model 369
12.9 General Modeling Methodology 374
12.10 General Forecast–Decision System 376
Bibliographical Notes 382
Exercises 382
13 Inventory and Capacity Models 387
13.1 Inventory Systems 387
13.2 Basic Inventory Model 389
13.3 Model with Initial Stock Level 396
13.4 Capacity Planning Model 400
13.5 Inventory and Macroeconomy 402
13.6 Concepts and Proofs 403
Exercises 405
Mini-Projects 410
14 Investment Models 413
14.1 Investment Choice Problem 413
14.2 Stochastic Dominance Relation 415
14.3 Utility Function 417
14.4 Investment Choice Model 425
14.5 Capital Allocation Model 430
14.6 Portfolio Design Model 435
14.7 Concepts and Proofs 442
Bibliographical Notes 446
Exercises 447
Mini-Projects 451
15 Various Continuous Models 457
15.1 Asking Price Model 457
15.2 Yield Control Model: Airline Reservations 461
15.3 Yield Control Model: College Admissions 467
Note on Principles 471
Note on Bargaining Market 471
Exercises 471
Mini-Projects 473
A Rationality Postulates 479
B Parameter Estimation Methods 489
C Special Univariate Distributions 493
The Greek Alphabet 527
References 529
Index 535
| Erscheint lt. Verlag | 26.12.2024 |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 209 x 261 mm |
| Gewicht | 1501 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Technik ► Elektrotechnik / Energietechnik | |
| Wirtschaft ► Betriebswirtschaft / Management ► Unternehmensführung / Management | |
| ISBN-10 | 1-394-22186-X / 139422186X |
| ISBN-13 | 978-1-394-22186-8 / 9781394221868 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
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