Account for uncertainties and optimize decision-making with this thorough exposition 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…mehr
Account for uncertainties and optimize decision-making with this thorough exposition 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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
Inhaltsangabe
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
