{"product_id":"probabilistic-forecasts-and-optimal-decisions-isbn-9781394221868","title":"Probabilistic Forecasts and Optimal Decisions","description":"\u003cp\u003e\u003cb\u003eAccount for uncertainties and optimize decision-making with this thorough exposition\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eDecision 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. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eProbabilistic Forecasts and Optimal Decisions\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eReaders of \u003ci\u003eProbablistic Forecasts and Optimal Decisions\u003c\/i\u003e will also find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eExtended case studies supported with real-world data\u003c\/li\u003e\n\u003cli\u003eMini-projects running through multiple chapters to illustrate different stages of the decision-making process\u003c\/li\u003e\n\u003cli\u003eEnd of chapter exercises designed to facilitate student learning\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eProbabilistic Forecasts and Optimal Decisions\u003c\/i\u003e is ideal for advanced undergraduate and graduate students in the sciences and engineering, as well as predictive analytics and decision analytics professionals. \u003c\/p\u003e\u003cp\u003ePreface xxi\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Forecast–Decision Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Decision Problem 1\u003c\/p\u003e \u003cp\u003e1.2 Forecast–Decision System 2\u003c\/p\u003e \u003cp\u003e1.3 Rational Deciding 4\u003c\/p\u003e \u003cp\u003e1.4 Mathematical Modeling 5\u003c\/p\u003e \u003cp\u003e1.5 Notes on Using the Book 6\u003c\/p\u003e \u003cp\u003eBibliographical Notes 7\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Elements of Probability 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Basic Elements 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Sets and Functions 11\u003c\/p\u003e \u003cp\u003e2.2 Variates and Sample Spaces 13\u003c\/p\u003e \u003cp\u003e2.3 Distributions 14\u003c\/p\u003e \u003cp\u003e2.4 Moments 16\u003c\/p\u003e \u003cp\u003e2.5 The Uniform Distribution 18\u003c\/p\u003e \u003cp\u003e2.6 The Gaussian Distributions 19\u003c\/p\u003e \u003cp\u003e2.7 The Gamma Function 29\u003c\/p\u003e \u003cp\u003e2.8 The Incomplete Gamma Function 32\u003c\/p\u003e \u003cp\u003eExercises 34\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Distribution Modeling 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Distribution Modeling Methodology 37\u003c\/p\u003e \u003cp\u003e3.2 Constructing Empirical Distribution 37\u003c\/p\u003e \u003cp\u003e3.3 Specifying the Sample Space 39\u003c\/p\u003e \u003cp\u003e3.4 Hypothesizing Parametric Models 40\u003c\/p\u003e \u003cp\u003e3.5 Estimating Parameters 42\u003c\/p\u003e \u003cp\u003e3.6 Evaluating Goodness of Fit 42\u003c\/p\u003e \u003cp\u003e3.7 Illustration of Modeling Methodology 49\u003c\/p\u003e \u003cp\u003e3.8 Derived Distribution Theory 51\u003c\/p\u003e \u003cp\u003eExercises 60\u003c\/p\u003e \u003cp\u003eMini-Projects 66\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Discrete Models 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Judgmental Forecasting 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 A Perspective on Probability 75\u003c\/p\u003e \u003cp\u003e4.2 Judgmental Probability 78\u003c\/p\u003e \u003cp\u003e4.3 Forecasting Fraction of Events 81\u003c\/p\u003e \u003cp\u003e4.4 Revising Probability Sequentially 83\u003c\/p\u003e \u003cp\u003e4.5 Analysis of Judgmental Task 97\u003c\/p\u003e \u003cp\u003eHistorical Notes 98\u003c\/p\u003e \u003cp\u003eBibliographical Notes 98\u003c\/p\u003e \u003cp\u003eExercises 98\u003c\/p\u003e \u003cp\u003eMini-Projects 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Statistical Forecasting 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Bayesian Forecaster 109\u003c\/p\u003e \u003cp\u003e5.2 Samples and Examples 112\u003c\/p\u003e \u003cp\u003e5.3 Modeling and Estimation 114\u003c\/p\u003e \u003cp\u003e5.4 An Application 117\u003c\/p\u003e \u003cp\u003e5.5 Informativeness of Predictor 123\u003c\/p\u003e \u003cp\u003eBibliographical Notes 127\u003c\/p\u003e \u003cp\u003eExercises 127\u003c\/p\u003e \u003cp\u003eMini-Projects 130\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Verification of Forecasts 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Data and Inputs 143\u003c\/p\u003e \u003cp\u003e6.2 Calibration 149\u003c\/p\u003e \u003cp\u003e6.3 Informativeness 156\u003c\/p\u003e \u003cp\u003e6.4 Verification Scores 163\u003c\/p\u003e \u003cp\u003e6.5 Forecast Attributes and Mental Processes 166\u003c\/p\u003e \u003cp\u003e6.6 Concepts and Proofs 168\u003c\/p\u003e \u003cp\u003eBibliographical Notes 170\u003c\/p\u003e \u003cp\u003eExercises 170\u003c\/p\u003e \u003cp\u003eMini-Projects 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Detection-Decision Theory 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Prototypical Decision Problems 179\u003c\/p\u003e \u003cp\u003e7.2 Basic Decision Model 180\u003c\/p\u003e \u003cp\u003e7.3 Decision with Perfect Forecast 187\u003c\/p\u003e \u003cp\u003e7.4 Decision Model with Forecasts 190\u003c\/p\u003e \u003cp\u003e7.5 Informativeness of Forecaster 193\u003c\/p\u003e \u003cp\u003e7.6 Concepts and Proofs 194\u003c\/p\u003e \u003cp\u003eBibliographical Notes 198\u003c\/p\u003e \u003cp\u003eExercises 198\u003c\/p\u003e \u003cp\u003eMini-Projects 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Various Discrete Models 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Search Planning Model 209\u003c\/p\u003e \u003cp\u003e8.2 Flash-Flood Warning Model 219\u003c\/p\u003e \u003cp\u003eBibliographical Note 229\u003c\/p\u003e \u003cp\u003eExercises 230\u003c\/p\u003e \u003cp\u003eMini-Projects 233\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Continuous Models 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Judgmental Forecasting 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 A Perspective on Forecasting 239\u003c\/p\u003e \u003cp\u003e9.2 Judgmental Distribution Function 240\u003c\/p\u003e \u003cp\u003e9.3 Parametric Distribution Function 249\u003c\/p\u003e \u003cp\u003e9.4 Group Forecasting 257\u003c\/p\u003e \u003cp\u003e9.5 Adjusting Distribution Function 258\u003c\/p\u003e \u003cp\u003e9.6 Applications 259\u003c\/p\u003e \u003cp\u003e9.7 Judgment, Data, Analytics 261\u003c\/p\u003e \u003cp\u003e9.8 Concepts and Proofs 261\u003c\/p\u003e \u003cp\u003eBibliographical Notes 263\u003c\/p\u003e \u003cp\u003eExercises 263\u003c\/p\u003e \u003cp\u003eMini–Projects 267\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Statistical Forecasting 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Bayesian Forecaster 273\u003c\/p\u003e \u003cp\u003e10.2 Bayesian Gaussian Forecaster 275\u003c\/p\u003e \u003cp\u003e10.3 Estimation and Validation 278\u003c\/p\u003e \u003cp\u003e10.4 Informativeness of Predictor 280\u003c\/p\u003e \u003cp\u003e10.5 Communication of Probabilistic Forecast 283\u003c\/p\u003e \u003cp\u003e10.6 Application 284\u003c\/p\u003e \u003cp\u003e10.7 Forecaster of the Sum of Two Variates 290\u003c\/p\u003e \u003cp\u003e10.8 Prior and Posterior Sums 293\u003c\/p\u003e \u003cp\u003e10.9 Concepts and Proofs 298\u003c\/p\u003e \u003cp\u003eBibliographical Notes 301\u003c\/p\u003e \u003cp\u003eExercises 302\u003c\/p\u003e \u003cp\u003eMini-Projects 306\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Verification of Forecasts 315\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Data and Inputs 315\u003c\/p\u003e \u003cp\u003e11.2 Calibration 317\u003c\/p\u003e \u003cp\u003e11.3 Informativeness 323\u003c\/p\u003e \u003cp\u003e11.4 Verification of Bayesian Forecaster 329\u003c\/p\u003e \u003cp\u003e11.5 Analysis of Judgmental Task 333\u003c\/p\u003e \u003cp\u003e11.6 Applications 338\u003c\/p\u003e \u003cp\u003e11.7 Concepts and Proofs 340\u003c\/p\u003e \u003cp\u003eBibliographical Notes 343\u003c\/p\u003e \u003cp\u003eExercises 343\u003c\/p\u003e \u003cp\u003eMini-Projects 346\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Target-Decision Theory 353\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Target-Setting Problem 353\u003c\/p\u003e \u003cp\u003e12.2 Two-Piece Linear Opportunity Loss 355\u003c\/p\u003e \u003cp\u003e12.3 Incomplete Expectations 359\u003c\/p\u003e \u003cp\u003e12.4 Quadratic Difference Opportunity Loss 362\u003c\/p\u003e \u003cp\u003e12.5 Impulse Utility 363\u003c\/p\u003e \u003cp\u003e12.6 Implications for Analysts 365\u003c\/p\u003e \u003cp\u003e12.7 Weapon-Aiming Model 367\u003c\/p\u003e \u003cp\u003e12.8 Weapon-Aiming-with-Friend Model 369\u003c\/p\u003e \u003cp\u003e12.9 General Modeling Methodology 374\u003c\/p\u003e \u003cp\u003e12.10 General Forecast–Decision System 376\u003c\/p\u003e \u003cp\u003eBibliographical Notes 382\u003c\/p\u003e \u003cp\u003eExercises 382\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Inventory and Capacity Models 387\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Inventory Systems 387\u003c\/p\u003e \u003cp\u003e13.2 Basic Inventory Model 389\u003c\/p\u003e \u003cp\u003e13.3 Model with Initial Stock Level 396\u003c\/p\u003e \u003cp\u003e13.4 Capacity Planning Model 400\u003c\/p\u003e \u003cp\u003e13.5 Inventory and Macroeconomy 402\u003c\/p\u003e \u003cp\u003e13.6 Concepts and Proofs 403\u003c\/p\u003e \u003cp\u003eExercises 405\u003c\/p\u003e \u003cp\u003eMini-Projects 410\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Investment Models 413\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Investment Choice Problem 413\u003c\/p\u003e \u003cp\u003e14.2 Stochastic Dominance Relation 415\u003c\/p\u003e \u003cp\u003e14.3 Utility Function 417\u003c\/p\u003e \u003cp\u003e14.4 Investment Choice Model 425\u003c\/p\u003e \u003cp\u003e14.5 Capital Allocation Model 430\u003c\/p\u003e \u003cp\u003e14.6 Portfolio Design Model 435\u003c\/p\u003e \u003cp\u003e14.7 Concepts and Proofs 442\u003c\/p\u003e \u003cp\u003eBibliographical Notes 446\u003c\/p\u003e \u003cp\u003eExercises 447\u003c\/p\u003e \u003cp\u003eMini-Projects 451\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Various Continuous Models 457\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Asking Price Model 457\u003c\/p\u003e \u003cp\u003e15.2 Yield Control Model: Airline Reservations 461\u003c\/p\u003e \u003cp\u003e15.3 Yield Control Model: College Admissions 467\u003c\/p\u003e \u003cp\u003eNote on Principles 471\u003c\/p\u003e \u003cp\u003eNote on Bargaining Market 471\u003c\/p\u003e \u003cp\u003eExercises 471\u003c\/p\u003e \u003cp\u003eMini-Projects 473\u003c\/p\u003e \u003cp\u003eA Rationality Postulates 479\u003c\/p\u003e \u003cp\u003eB Parameter Estimation Methods 489\u003c\/p\u003e \u003cp\u003eC Special Univariate Distributions 493\u003c\/p\u003e \u003cp\u003eThe Greek Alphabet 527\u003c\/p\u003e \u003cp\u003eReferences 529\u003c\/p\u003e \u003cp\u003eIndex 535\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eRoman Krzysztofowicz, PhD, \u003c\/b\u003eis 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\u003cb\u003e.\u003c\/b\u003e   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eAccount for uncertainties and optimize decision-making with this thorough exposition\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eDecision 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. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eProbabilistic Forecasts and Optimal Decisions\u003c\/i\u003e 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. \u003c\/p\u003e\u003cp\u003eReaders of \u003ci\u003eProbablistic Forecasts and Optimal Decisions\u003c\/i\u003e will also find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eExtended case studies supported with real-world data\u003c\/li\u003e\n\u003cli\u003eMini-projects running through multiple chapters to illustrate different stages of the decision-making process\u003c\/li\u003e\n\u003cli\u003eEnd of chapter exercises designed to facilitate student learning\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eProbabilistic Forecasts and Optimal Decisions\u003c\/i\u003e is ideal for advanced undergraduate and graduate students in the sciences and engineering, as well as predictive analytics and decision analytics professionals.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989856927973,"sku":"NP9781394221868","price":117.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781394221868.jpg?v=1761785694","url":"https:\/\/k12savings.com\/products\/probabilistic-forecasts-and-optimal-decisions-isbn-9781394221868","provider":"K12savings","version":"1.0","type":"link"}