Decision Making and Forecasting: with Emphasis on Model Building and Policy Analysis

Authors

Kneale T. Marshall
Professor of Operations Research, Operations Research Department, Naval Postgraduate School, Monterey, California 93943

Robert M. Oliver
Professor Emeritus, Department of Industrial Engineering and Operations Research, University of California at Berkeley

Publisher

McGraw-Hill Professional Book Group
McGraw Hill Reference Page to "Decision Making and Forecasting"

ISBN Numbers

Synopsis

This book discusses how to design and analyse the most important features of realistic decision problems in analytical models that reveal structure and give insight. Emphasis is on good model formulation using graphical techniques with influence diagrams and decision trees. DECISION MAKING AND FORECASTING shows how forecasting must be integrated with decision making in a coherent manner and makes frequent use of the economic value of forecasts.

Features

Table of Contents

Preface xv

1 	BASIC CONCEPTS 1
	1.1 	Introduction  1
	1.2	The Importance of Models in Decision Making  2
	1.3	The Nature of a Decision Problem  3
	1.4	Modeling Uncertainty with Probability  4
	1.5	A Brief Review of Probability  6
		Outcomes, Events, and Probabilities  7
		Conditional Probability and Independence  10
		Partitions and the Law of Total Probability  12
		Bayes' Rule  13
		Random Variables and Distributions  14
		Expected Values  18
		Marginal, Conditional, and Joint Probabilities  20
		Probabilities and Odds  22
		Conditional Independence  23
		Coherence  24
	1.6	The Role of Forecasting  24
	1.7	Elements of Influence Diagrams and Decision Trees  26
		Directed Arcs in Influence Diagrams  27
		Branches in Decision Trees  27
	1.8	The Decision Sapling  28
		The Value of Perfect Information  32
	1.9	Criteria for Comparing Results  33
	1.10	Clarifying Terminology  35
	1.11	Book Overview  36
	1.12	Summary and Insights  39
		Problems  40

2	USING BASELINE FORECASTS 43
	2.1	Introduction  43
	2.2	A Crop Protection Decision  46
	2.3	A Decision in Football  48
		The Coach's Decision  48
		Betting on the Football Game  50
		Analysis of the Football Betting Problem  52
		An Alternate Modeling of Outcomes: Point Scores  55
	2.4	A Limited Life Inventory Problem  56
		Marginal Analysis  58
	2.5	The Newsboy Problem  59
	2.6	The Value of Perfect Information  63
	2.7	Airline Seat Allocation Based on Price and Demand  65
		Space Allocation for Two Passenger Classes  65
		Two-Class Space Allocation with Perfect Information  69
		Discount-Seat Allocations in One Passenger Class  71
		A Dynamic Decision Model  73
	2.8	Pricing and Marketing of Hotel Rooms  74
	2.9	The Newsboy Problem with Additional Information  77
	2.10	Summary and Insights  78
		Problems  79

3	FORECASTS FOR DECISION MODELS 83
	3.1	Introduction  83
	3.2	The Role and Value of Forecasts  84
		Some Examples of Forecasts  88
	3.3	Several Types of Forecasts  88
		Point Forecasts  89
		Probability and Odds Forecasts  90
		Categorical Forecasts  92
	3.4	Decision Probabilities, Likelihoods, and Bayes' Rule  95
		Decision Probabilities and Likelihoods  96
		Bayes' Rule with Probability Forecasts  97
		Bayes' Rule with Categorical Forecasts  99
		Summary of Results in Matrix Notation  101
		Sensitivity of Decision Probabilities  101
		Node and Arc Reversal with Bayes' Rule  103
		Using Bayes' Rule with Odds  105
	3.5	Multiple Likelihoods and Dependent Forecasts  108
		Two Forecasts for a Single Event  109
		Likelihoods for Four Colon Cancer Tests  111
		Forecasts for Sequential Tests  115
	3.6	Optimal Crop Protection  116
	3.7	Credit Scoring Decisions  121
		Notation for Scores and Forecasts  121
		Expected Profit and Risk of an Individual  124
		Expected Profit for the Portfolio  126
		3.8 Summary and Insights  128
		Problems  130

4	MODEL BUILDING 133
	4.1	Introduction  133
	4.2	Constructing Influence Diagrams  135
		The Procedure  136
		Arc Reversal and Cycles  139
		No-Forgetting Arcs  140
		Perfect Information  141
	4.3	Examples of Model Formulations  143
		A Decision to Seed Clouds in Hurricanes  144
		Keeping Good Credit Accounts at a Bank  148
		A Navy Mobile Basing Decision Problem  152
		Colon Cancer Diagnosis  156
	4.4	Building and Solving Decision Trees  160
		Node Outcome and Alternative Sets  161
		Drawing Consistent Decision Trees  164
		Perfect Information  166
		Decision Tree Solutions  167
	4.5	The Bank Credit Problem  169
		The Economic Value of a Performance Forecast  171
		Perfect Information about Performance  172
	4.6	Colon Cancer Decision Problems  173
		Sequential Decisions for Colon Cancer Detection  177
	4.7	Irrelevant Decisions and a Game-Show Problem  179
	4.8	A Budget Planning Problem  182
	4.9	Summary and Insights  187
		Problems  190

5	MODEL ANALYSIS 192
	5.1	Introduction  192
	5.2	Betting on the Football Game  193
	5.3	An Expert Opinion Model  197
		An Aircraft Part Decision Problem  199
		A Crop Protection Problem  202
	5.4	Sensitivity Analysis Using Decision Probabilities  204
		The Economic Value of a Forecast  207
	5.5	Sensitivity Analysis Using Forecast Likelihoods  210
	5.6	Problems with One or More Forecasts  213
		Optimal Policies and Expected Returns  215
		A Numeric Example  217
		A Single Decision with Two Forecasts  219
	5.7	Sequential Decisions Using Sequential Forecasts  222
	5.8	Summary and Insights  227
		Problems  229

6	SUBJECTIVE MEASURES AND UTILITY 232
	6.1	Introduction  232
	6.2	Basics of Utility Theory  233
		Indifference Probabilities and Certainty Equivalents  234
		Assumptions of Utility Theory  235
	6.3	Determination of Utility Functions  237
		Utilities as Indifference Probabilities  238
		Utilities from Certainty Equivalents  239
		Cautionary Comments  240
	6.4	Examples of Utility Functions  241
		An Exponential Utility Function  242
		A Logarithmic Utility Function  243
	6.5	Measures of Risk  244
		Risk Premium  245
		A Risk Aversion Function  245
	6.6	Some Properties of Utility Functions  248
	6.7	Summary and Insights  249
		Problems  250

7	MULTIATTRIBUTE PROBLEMS 252
	7.1	Introduction  252
	7.2	A Decision Sapling with Two Attributes  253
	7.3	The Crop Protection Problem with Two Attributes  256
	7.4	Car Ranking and Replacement  258
		Ranking Cars by Preference  258
		Car Replacement  261
	7.5	The Added Cost of Conflict Resolution  263
		Car Ranking Revisited  265
	7.6	Assessment of Trade-Offs through Preferences  266
		Two Attributes  267
		Many Attributes and Alternatives  268
		Ranking Cars Using Three Attributes  269
		The Car Replacement Problem Revisited  270
	7.7	A Hierarchical Multiattribute Model  271
		A Hierarchical Cost-Benefit Model  272
		* The Two-Hierarchy Multigroup Model  275
		* Tradeoff Weights through Indifference Probabilities  276
	7.8	The Analytic Hierarchy Process  278
		Ranking Alternatives with AHP  280
		Avoiding Rank Reversal in AHP  284
		Finding the Weights in AHP  286
	7.9	A Budget Planning Example with Three Attributes  288
	7.10*	Multiattribute Utility  291
		An Example with Two Attributes  295
	7.11	Summary and Insights  298
		Problems  300

8	FORECAST PERFORMANCE 303
	8.1	Introduction  303
	8.2	Forecast Calibration  304
		Calibration of Categorical Forecasts  304
		Calibration of Probability Forecasts  305
		Calibration in Expectation  307
	8.3	Forecast Discrimination  308
		Discrimination in Probability Forecasts  309
		Discriminating Categorical Forecasts  312
	8.4	Comparing Discrimination and Calibration  315
	8.5	Forecast Correlation  317
	8.6	Measuring Forecast Performance with Brier Scores  318
		An Example  319
	8.7	Calibration Effects in Decision Models  320
		Effect of Calibration on Crop Protection Policies  320
		Uncalibrated Forecasts in a Credit Portfolio  323
		Stable Likelihoods  325
		Numeric Example  328
	8.8	Coherent Categorical and Probability Forecasts  328
		The Protect Decision with a Categorical Forecast  330
	8.9	Coherent Aggregation of Categorical Forecasts  331
	8.10	Forecast Aggregation and Optimal Decisions  333
	8.11	Summary and Insights  336
		Problems  340

9	ADVANCED CONCEPTS 342
	9.1	Introduction  342
	9.2	Classifying Influence Diagrams  343
		A Proper Influence Diagram  345
		Influence Diagrams in Extensive Form  347
		Irrelevant Decision and Chance Nodes  349
	9.3	Chance Influence Diagrams  350
		Directed Graphs, Predecessor and Successor Sets  351
		Equivalent Chance Influence Diagrams  353
		Bayes' Rule and Arc Reversal  354
		Barren Nodes  356
		Cancer Diagnosis  357
		Arc Reversal and Barren Node Removal  360
	9.4	Path History and Rollback Computations  362
		A History Vector Algorithm  363
		Engine Maintenance  364
		Rollback Using Path History Vectors  365
		A Nuclear Reactor Decision Example  366
	9.5	Multiattribute Rollback with and without Trade-Offs  370
		Calculating Noninferior Points with Two Attributes  370
		Rollback with Linear Trade-Offs  371
		Reactor Decision Revisited  372
		Economic Value per Life Saved  375
		History and Rollback with Nonlinear Utilities  376
		Nonlinear Utilities in the Nuclear Reactor Problem  379
	9.6	Reducing Influence Diagrams  381
		Equivalent Influence Diagrams  381
		An Example of EFID Reduction  384
		Chance Node Removal through Expectation  385
		Node Removal through Maximization  387
		Revisiting the Aircraft Part Problem  388
	9.7	Summary and Insights  390
		Problems  393
	
References 394

Author INDEX 399

Subject Index 403

Errata

Errata Sheet (in postscript)