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Foreword.Preface.PART ONE. SURVEY OF PROBABILITY THEORY.Chapter 1. Introduction.Chapter 2. Experiments, Sample Spaces, and Probability.2.1 Experiments and Sample Spaces.2.2 Set Theory.2.3 Events and Probability.2.4 Conditional Probability.2.5 Binomial Coefficients.Exercises.Chapter 3. Random Variables, Random Vectors, and Distributions Functions.3.1 Random Variables and Their Distributions.3.2 Multivariate Distributions.3.3 Sums and Integrals.3.4 Marginal Distributions and Independence.3.5 Vectors and Matrices.3.6 Expectations, Moments, and Characteristic Functions.3.7 Transformations of Random Variables.3.8 Conditional Distributions.Exercises.Chapter 4. Some Special Univariate Distributions.4.1 Introduction.4.2 The Bernoulli Distributions.4.3 The Binomial Distribution.4.4 The Poisson Distribution.4.5 The Negative Binomial Distribution.4.6 The Hypergeometric Distribution.4.7 The Normal Distribution.4.8 The Gamma Distribution.4.9 The Beta Distribution.4.10 The Uniform Distribution.4.11 The Pareto Distribution.4.12 The t Distribution.4.13 The F Distribution.Exercises.Chapter 5. Some Special Multivariate Distributions.5.1 Introduction.5.2 The Multinomial Distribution.5.3 The Dirichlet Distribution.5.4 The Multivariate Normal Distribution.5.5 The Wishart Distribution.5.6 The Multivariate t Distribution.5.7 The Bilateral Bivariate Pareto Distribution.Exercises.PART TWO. SUBJECTIVE PROBABILITY AND UTILITY.Chapter 6. Subjective Probability.6.1 Introduction.6.2 Relative Likelihood.6.3 The Auxiliary Experiment.6.4 Construction of the Probability Distribution.6.5 Verification of the Properties of a Probability Distribution.6.6 Conditional Likelihoods.Exercises.Chapter 7. Utility.7.1 Preferences Among Rewards.7.2 Preferences Among Probability Distributions.7.3 The Definitions of a Utility Function.7.4 Some Properties of Utility Functions.7.5 The Utility of Monetary Rewards.7.6 Convex and Concave Utility Functions.7.7 The Anxiomatic Development of Utility.7.8 Construction of the Utility Function.7.9 Verification of the Properties of a Utility Function.7.10 Extension of the Properties of a Utility Function to the Class ?E.Exercises.PART THREE. STATISTICAL DECISION PROBLEMS.Chapter 8. Decision Problems.8.1 Elements of a Decision Problem.8.2 Bayes Risk and Bayes Decisions.8.3 Nonnegative Loss Functions.8.4 Concavity of the Bayes Risk.8.5 Randomization and Mixed Decisions.8.6 Convex Sets.8.7 Decision Problems in Which ~2 and D Are Finite.8.8 Decision Problems with Observations.8.9 Construction of Bayes Decision Functions.8.10 The Cost of Observation.8.11 Statistical Decision Problems in Which Both ? and D contains Two Points.8.12 Computation of the Posterior Distribution When the Observations Are Made in More Than One Stage.Exercises.Chapter 9. Conjugate Prior Distributions.9.1 Sufficient Statistics.9.2 Conjugate Families of Distributions.9.3 Construction of the Conjugate Family.9.4 Conjugate Families for Samples from Various Standard Distributions.9.5 Conjugate Families for Samples from a Normal Distribution.9.6 Sampling from a Normal Distribution with Unknown Mean and Unknown Precision.9.7 Sampling from a Uniform Distribution.9.8 A Conjugate Family for Multinomial Observations.9.9 Conjugate Families for Samples from a Multivariate Normal Distribution.9.10 Multivariate Normal Distributions with Unknown Mean Vector and Unknown Precision matrix.9.11 The Marginal Distribution of the Mean Vector.9.12 The Distribution of a Correlation.9.13 Precision Matrices Having an Unknown Factor.Exercises.Chapter 10. Limiting Posterior Distributions.10.1 Improper Prior Distributions.10.2 Improper Prior Distributions for Samples from a Normal Distribution.10.3 Improper Prior Distributions for Samples from a Multivariate Normal Distribution.10.4 Precise Measurement.10.5 Convergence of Posterior Distributions.10.6 Supercontinuity.10.7 Solutions of the Likelihood Equation.10.8 Convergence of Supercontinuous Functions.10.9 Limiting Properties of the Likelihood Function.10.10 Normal Approximation to the Posterior Distribution.10.11 Approximation for Vector Parameters.10.12 Posterior Ratios.Exercises.Chapter 11. Estimation, Testing Hypotheses, and linear Statistical Models.11.1 Estimation.11.2 Quadratic Loss.11.3 Loss Proportional to the Absolute Value of the Error.11.4 Estimation of a Vector.11.5 Problems of Testing Hypotheses.11.6 Testing a Simple Hypothesis About the Mean of a Normal Distribution.11.7 Testing Hypotheses about the Mean of a Normal Distribution.11.8 Deciding Whether a Parameter Is Smaller or larger Than a Specific Value.11.9 Deciding Whether the Mean of a Normal Distribution Is Smaller or larger Than a Specific Value.11.10 Linear Models.11.11 Testing Hypotheses in Linear Models.11.12 Investigating the Hypothesis That Certain Regression Coefficients Vanish.11.13 One-Way Analysis of Variance.Exercises.PART FOUR. SEQUENTIAL DECISIONS.Chapter 12. Sequential Sampling.12.1 Gains from Sequential Sampling.12.2 Sequential Decision Procedures.12.3 The Risk of a Sequential Decision Procedure.12.4 Backward Induction.12.5 Optimal Bounded Sequential Decision procedures.12.6 Illustrative Examples.12.7 Unbounded Sequential Decision Procedures.12.8 Regular Sequential Decision Procedures.12.9 Existence of an Optimal Procedure.12.10 Approximating an Optimal Procedure by Bounded Procedures.12.11 Regions for Continuing or Terminating Sampling.12.12 The Functional Equation.12.13 Approximations and Bounds for the Bayes Risk.12.14 The Sequential Probability-ratio Test.12.15 Characteristics of Sequential Probability-ratio Tests.12.16 Approximating the Expected Number of Observations.Exercises.Chapter 13. Optimal Stopping.13.1 Introduction.13.2 The Statistician's Reward.13.3 Choice of the Utility Function.13.4 Sampling Without Recall.13.5 Further Problems of Sampling with Recall and Sampling without Recall.13.6 Sampling without Recall from a Normal Distribution with Unknown Mean.13.7 Sampling with Recall from a Normal Distribution with Unknown Mean.13.8 Existence of Optimal Stopping Rules.13.9 Existence of Optimal Stopping Rules for Problems of Sampling with Recall and Sampling without Recall.13.10 Martingales.13.11 Stopping Rules for Martingales.13.12 Uniformly Integrable Sequences of Random Variables.13.13 Martingales Formed from Sums and Products of Random Variables.13.14 Regular Supermartingales.13.15 Supermartingales and General Problems of Optimal Stopping.13.16 Markov Processes.13.17 Stationary Stopping Rules for Markov Processes.13.18 Entrance-fee Problems.13.19 The Functional Equation for a Markov Process.Exercises.Chapter 14. Sequential Choice of Experiments.14.1 Introduction.14.2 Markovian Decision Processes with a Finite Number of Stages.14.3 Markovian Decision Processes with an Infinite Number of Stages.14.4 Some Betting Problems.14.5 Two-armed-bandit Problems.14.6 Two-armed-bandit Problems When the Value of One Parameter Is Known.14.7 Two-armed-bandit Problems When the Parameters Are Dependent.14.8 Inventory Problems.14.9 Inventory Problems with an Infinite Number of Stages.14.10 Control Problems.14.11 Optimal Control When the Process Cannot Be Observed without Error.14.12 Multidimensional Control Problems.14.13 Control Problems with Actuation Errors.14.14 Search Problems.14.15 Search Problems with Equal Costs.14.16 Uncertainty Functions and Statistical Decision Problems.14.17 Sufficient Experiments.14.18 Examples of Sufficient Experiments.Exercises.References.Supplementary Bibliography.Name Index.Subject Index.

The principles of shared decision making are well documented but there is a lack of guidance about how to accomplish the approach in routine clinical practice. Our aim here is to translate existing conceptual descriptions into a three-step model that is practical, easy to remember, and can act as a guide to skill development. Achieving shared decision making depends on building a good relationship in the clinical encounter so that information is shared and patients are supported to deliberate and express their preferences and views during the decision making process. To accomplish these tasks, we propose a model of how to do shared decision making that is based on choice, option and decision talk. The model has three steps: a) introducing choice, b) describing options, often by integrating the use of patient decision support, and c) helping patients explore preferences and make decisions. This model rests on supporting a process of deliberation, and on understanding that decisions should be influenced by exploring and respecting "what matters most" to patients as individuals, and that this exploration in turn depends on them developing informed preferences.

I. Introduction.- II. Multiple Attribute Decision Making - An Overview.- 2.1 Basics and Concepts.- 2.2 Classifications of MADM Methods.- 2.2.1 Classification by Information.- 2.2.2 Classification by Solution Aimed At.- 2.2.3 Classification by Data Type.- 2.3 Description of MADM Methods.- Method (1): DOMINANCE.- Method (2): MAXIMIN.- Method (3): MAXIMAX.- Method (4): CONJUNCTIVE METHOD.- Method (5): DISJUNCTIVE METHOD.- Method (6): LEXICOGRAPHIC METHOD.- Method (7): LEXICOGRAPHIC SEMIORDER METHOD.- Method (8): ELIMINATION BY ASPECTS (EBA).- Method (9): LINEAR ASSIGNMENT METHOD (LAM).- Method (10): SIMPLE ADDITIVE WEIGHTING METHOD (SAW).- Method (11): ELECTRE (Elimination et Choice Translating Reality).- Method (12): TOPSIS (Technique for Order Preference by Similarity to Ideal Solution).- Method (13): WEIGHTED PRODUCT METHOD.- Method (14): DISTANCE FROM TARGET METHOD.- III. Fuzzy Sets and their Operations.- 3.1 Introduction.- 3.2 Basics of Fuzzy Sets.- 3.2.1 Definition of a Fuzzy Set.- 3.2.2 Basic Concepts of Fuzzy Sets.- 3.2.2.1 Complement of a Fuzzy Set.- 3.2.2.2 Support of a Fuzzy Set.- 3.2.2.3 ?-cut of a Fuzzy Set.- 3.2.2.4 Convexity of a Fuzzy Set.- 3.2.2.5 Normality of a Fuzzy Set.- 3.2.2.6 Cardinality of a Fuzzy Set.- 3.2.2.7 The mth Power of a Fuzzy Set.- 3.3 Set-Theoretic Operations with Fuzzy Sets.- 3.3.1 No Compensation Operators.- 3.3.1.1 The Min Operator.- 3.3.2 Compensation-Min Operators.- 3.3.2.1 Algebraic Product.- 3.3.2.2 Bounded Product.- 3.3.2.3 Hamacher's Min Operator.- 3.3.2.4 Yager's Min Operator.- 3.3.2.5 Dubois and Prade's Min Operator.- 3.3.3 Full Compensation Operators.- 3.3.3.1 The Max Operator.- 3.3.4 Compensation-Max Operators.- 3.3.4.1 Algebraic Sum.- 3.3.4.2 Bounded Sum.- 3.3.4.3 Hamacher's Max Operator.- 3.3.4.4 Yager's Max Operator.- 3.3.4.5 Dubois and Prade's Max Operator.- 3.3.5 General Compensation Operators.- 3.3.5.1 Zimmermann and Zysno's ? Operator.- 3.3.6 Selecting Appropriate Operators.- 3.4 The Extension Principle and Fuzzy Arithmetics.- 3.4.1 The Extension Principle.- 3.4.2 Fuzzy Arithmetics.- 3.4.2.1 Fuzzy Number.- 3.4.2.2 Addition of Fuzzy Numbers.- 3.4.2.3 Subtraction of Fuzzy Numbers.- 3.4.2.4 Multiplication of Fuzzy Numbers.- 3.4.2.5 Division of Fuzzy Numbers.- 3.4.2.6 Fuzzy Max and Fuzzy Min.- 3.4.3 Special Fuzzy Numbers.- 3.4.3.1 L-R Fuzzy Number.- 3.4.3.2 Triangular (or Trapezoidal) Fuzzy Number.- 3.4.3.3 Proof of Formulas.- 3.4.3.3.1 The Image of Fuzzy Number N.- 3.4.3.3.2 The Inverse of Fuzzy Number N.- 3.4.3.3.3 Addition and Subtraction.- 3.4.3.3.4 Multiplication and Division.- 3.5 Conclusions.- IV. Fuzzy Ranking Methods.- 4.1 Introduction.- 4.2 Ranking Using Degree of Optimality.- 4.2.1 Baas and Kwakernaak's Approach.- 4.2.2 Watson et al.'s Approach.- 4.2.3 Baldwin and Guild's Approach.- 4.3 Ranking Using Hamming Distance.- 4.3.1 Yager's Approach.- 4.3.2 Kerre's Approach.- 4.3.3 Nakamura's Approach.- 4.3.4 Kolodziejczyk's Approach.- 4.4 Ranking Using ?-Cuts.- 4.4.1 Adamo's Approach.- 4.4.2 Buckley and Chanas' Approach.- 4.4.3 Mabuchi's Approach.- 4.5 Ranking Using Comparison Function.- 4.5.1 Dubois and Prade's Approach.- 4.5.2 Tsukamoto et al.'s Approach.- 4.5.3 Delgado et al.'s Approach.- 4.6 Ranking Using Fuzzy Mean and Spread.- 4.6.1 Lee and Li's Approach.- 4.7 Ranking Using Proportion to The Ideal.- 4.7.1 McCahone's Approach.- 4.8 Ranking Using Left and Right Scores.- 4.8.1 Jain's Approach.- 4.8.2 Chen's Approach.- 4.8.3 Chen and Hwang's Approach.- 4.9 Ranking with Centroid Index.- 4.9.1 Yager's Centroid Index.- 4.9.2 Murakami et al.'s Approach.- 4.10 Ranking Using Area Measurement.- 4.10.1 Yager's Approach.- 4.11 Linguistic Ranking Methods.- 4.11.1 Efstathiou and Tong's Approach.- 4.11.2 Tong and Bonissone's Approach.- V. Fuzzy Multiple Attribute Decision Making Methods.- 5.1 Introduction.- 5.2 Fuzzy Simple Additive Weighting Methods.- 5.2.1 Baas and Kwakernaak's Approach.- 5.2.2 Kwakernaak's Approach.- 5.2.3 Dubois and Prade's Approach.- 5.2.4 Cheng and McInnis's Approach.- 5.2.5 Bonissone's Approach.- 5.3 Analytic Hierarchical Process (AHP) Methods.- 5.3.1 Saaty's AHP Approach.- 5.3.2 Laarhoven and Pedrycz's Approach.- 5.3.3 Buckley's Approach.- 5.4 Fuzzy Conjunctive/Disjunctive Method.- 5.4.1 Dubois, Prade, and Testemale's Approach.- 5.5 Heuristic MAUF Approach.- 5.6 Negi's Approach.- 5.7 Fuzzy Outranking Methods.- 5.7.1 Roy's Approach.- 5.7.2 Siskos et al.'s Approach.- 5.7.3 Brans et al.'s Approach.- 5.7.4 Takeda's Approach.- 5.8 Maximin Methods.- 5.8.1 Gellman and Zadeh's Approach.- 5.8.2 Yager's Approach.- 5.9 A New Approach to Fuzzy MADM Problems.- 5.9.1 Converting Linguistic Terms to Fuzzy Numbers.- 5.9.2 Converting Fuzzy Numbers to Crisp Scores.- 5.9.3 The Algorithm.- VI. Concluding Remarks.- 6.1 MADM Problems and Fuzzy Sets.- 6.2 On Existing MADM Solution Methods.- 6.2.1 Classical Methods for MADM Problems.- 6.2.2 Fuzzy Methods for MADM Problems.- 6.2.2.1 Fuzzy Ranking Methods.- 6.2.2.2 Fuzzy MADM Methods.- 6.3 Critiques of the Existing Fuzzy Methods.- 6.3.1 Size of Problem.- 6.3.2 Fuzzy vs. Crisp Data.- 6.4 A New Approach to Fuzzy MADM Problem Solving.- 6.4.1 Semantic Modeling of Linguistic Terms.- 6.4.2 Fuzzy Scoring System.- 6.4.3 The Solution.- 6.4.4 The Advantages of the New Approach.- 6.5 Other Multiple Criteria Decision Making Methods.- 6.5.1 Multiple Objective Decision Making Methods.- 6.5.2 Methods of Group Decision Making under Multiple Criteria.- 6.5.2.1 Social Choice Theory.- 6.5.2.2 Experts Judgement/Group Participation.- 6.5.2.3 Game Theory.- 6.6 On Future Studies.- 6.6.1 Semantics of Linguistic Terms.- 6.6.2 Fuzzy Ranking Methods.- 6.6.3 Fuzzy MADM Methods.- 6.6.4 MADM Expert Decision Support Systems.- VII. Bibliography.

BACKGROUND: Diagnostic and prognostic models are typically evaluated with measures of accuracy that do not address clinical consequences. Decision-analytic techniques allow assessment of clinical outcomes but often require collection of additional information and may be cumbersome to apply to models that yield a continuous result. The authors sought a method for evaluating and comparing prediction models that incorporates clinical consequences,requires only the data set on which the models are tested,and can be applied to models that have either continuous or dichotomous results. METHOD: The authors describe decision curve analysis, a simple, novel method of evaluating predictive models. They start by assuming that the threshold probability of a disease or event at which a patient would opt for treatment is informative of how the patient weighs the relative harms of a false-positive and a false-negative prediction. This theoretical relationship is then used to derive the net benefit of the model across different threshold probabilities. Plotting net benefit against threshold probability yields the "decision curve." The authors apply the method to models for the prediction of seminal vesicle invasion in prostate cancer patients. Decision curve analysis identified the range of threshold probabilities in which a model was of value, the magnitude of benefit, and which of several models was optimal. CONCLUSION: Decision curve analysis is a suitable method for evaluating alternative diagnostic and prognostic strategies that has advantages over other commonly used measures and techniques.

This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob-abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. 1.

By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of alternatives whose boundaries are not sharply defined. An example of a fuzzy constraint is: “The cost of A should not be substantially higher than α,” where α is a specified constant. Similarly, an example of a fuzzy goal is: “x should be in the vicinity of x 0 ,” where x 0 is a constant. The italicized words are the sources of fuzziness in these examples. Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value. The use of these concepts is illustrated by examples involving multistage decision processes in which the system under control is either deterministic or stochastic. By using dynamic programming, the determination of a maximizing decision is reduced to the solution of a system of functional equations. A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.

This paper introduces a three-item “Cognitive Reflection Test” (CRT) as a simple measure of one type of cognitive ability—the ability or disposition to reflect on a question and resist reporting the first response that comes to mind. The author will show that CRT scores are predictive of the types of choices that feature prominently in tests of decision-making theories, like expected utility theory and prospect theory. Indeed, the relation is sometimes so strong that the preferences themselves effectively function as expressions of cognitive ability—an empirical fact begging for a theoretical explanation. The author examines the relation between CRT scores and two important decision-making characteristics: time preference and risk preference. The CRT scores are then compared with other measures of cognitive ability or cognitive “style.” The CRT scores exhibit considerable difference between men and women and the article explores how this relates to sex differences in time and risk preferences. The final section addresses the interpretation of correlations between cognitive abilities and decision-making characteristics.

As reflected in the amount of controversy, few areas in psychology have undergone such dramatic conceptual changes in the past decade as the emerging science of heuristics. Heuristics are efficient cognitive processes, conscious or unconscious, that ignore part of the information. Because using heuristics saves effort, the classical view has been that heuristic decisions imply greater errors than do "rational" decisions as defined by logic or statistical models. However, for many decisions, the assumptions of rational models are not met, and it is an empirical rather than an a priori issue how well cognitive heuristics function in an uncertain world. To answer both the descriptive question ("Which heuristics do people use in which situations?") and the prescriptive question ("When should people rely on a given heuristic rather than a complex strategy to make better judgments?"), formal models are indispensable. We review research that tests formal models of heuristic inference, including in business organizations, health care, and legal institutions. This research indicates that (a) individuals and organizations often rely on simple heuristics in an adaptive way, and (b) ignoring part of the information can lead to more accurate judgments than weighting and adding all information, for instance for low predictability and small samples. The big future challenge is to develop a systematic theory of the building blocks of heuristics as well as the core capacities and environmental structures these exploit.

A survey is presented of current methods for decision tree classifier (DTC) designs and the various existing issues. After considering potential advantages of DTCs over single-state classifiers, the subjects of tree structure design, feature selection at each internal node, and decision and search strategies are discussed. The relation between decision trees and neutral networks (NN) is also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The psychological principles that govern the perception of decision problems and the evaluation of probabilities and outcomes produce predictable shifts of preference when the same problem is framed in different ways. Reversals of preference are demonstrated in choices regarding monetary outcomes, both hypothetical and real, and in questions pertaining to the loss of human lives. The effects of frames on preferences are compared to the effects of perspectives on perceptual appearance. The dependence of preferences on the formulation of decision problems is a significant concern for the theory of rational choice.

A revolution in the science of emotion has emerged in recent decades, with the potential to create a paradigm shift in decision theories. The research reveals that emotions constitute potent, pervasive, predictable, sometimes harmful and sometimes beneficial drivers of decision making. Across different domains, important regularities appear in the mechanisms through which emotions influence judgments and choices. We organize and analyze what has been learned from the past 35 years of work on emotion and decision making. In so doing, we propose the emotion-imbued choice model, which accounts for inputs from traditional rational choice theory and from newer emotion research, synthesizing scientific models.

Decisions involve many intangibles that need to be traded off. To do that, they have to be measured along side tangibles whose measurements must also be evaluated as to, how well, they serve the objectives of the decision maker. The Analytic Hierarchy Process (AHP) is a theory of measurement through pairwise comparisons and relies on the judgements of experts to derive priority scales. It is these scales that measure intangibles in relative terms. The comparisons are made using a scale of absolute judgements that represents, how much more, one element dominates another with respect to a given attribute. The judgements may be inconsistent, and how to measure inconsistency and improve the judgements, when possible to obtain better consistency is a concern of the AHP. The derived priority scales are synthesised by multiplying them by the priority of their parent nodes and adding for all such nodes. An illustration is included.

From the Publisher: The past decade has seen considerable theoretical and applied research on Markov decision processes, as well as the growing use of these models in ecology, economics, communications engineering, and other fields where outcomes are uncertain and sequential decision-making processes are needed. A timely response to this increased activity, Martin L. Puterman's new work provides a uniquely up-to-date, unified, and rigorous treatment of the theoretical, computational, and applied research on Markov decision process models. It discusses all major research directions in the field, highlights many significant applications of Markov decision processes models, and explores numerous important topics that have previously been neglected or given cursory coverage in the literature. Markov Decision Processes focuses primarily on infinite horizon discrete time models and models with discrete time spaces while also examining models with arbitrary state spaces, finite horizon models, and continuous-time discrete state models. The book is organized around optimality criteria, using a common framework centered on the optimality (Bellman) equation for presenting results. The results are presented in a theorem-proof format and elaborated on through both discussion and examples, including results that are not available in any other book. A two-state Markov decision process model, presented in Chapter 3, is analyzed repeatedly throughout the book and demonstrates many results and algorithms. Markov Decision Processes covers recent research advances in such areas as countable state space models with average reward criterion, constrained models, and models with risk sensitive optimality criteria. It also explores several topics that have received little or no attention in other books, including modified policy iteration, multichain models with average reward criterion, and sensitive optimality. In addition, a Bibliographic Remarks section in each chapter comments on relevant historic

PRELIMINARIES. Geographical Data, Information, and Decision Making. Introduction to GIS. Introduction to Multicriteria Decision Analysis. SPATIAL MULTICRITERIA DECISION ANALYSIS. Evaluation Criteria. Decision Alternatives and Constraints. Criterion Weighing. Decision Rules. Sensitivity Analysis. MULTICRITERIA-SPATIAL DECISION SUPPORT SYSTEMS. Spatial Decision Support Systems. MC-SDSS: Case Studies. Glossary. Selected Bibliography. Indexes.

How do executive teams make rapid decisions in the high-velocity microcomputer industry? This inductive study of eight microcomputer firms led lo propositions exploring that question. Fast decision makers use more, not less, information than do slow decision makers. The former also develop more, not fewer, alternatives, and use a two-tiered advice process. Conflict resolution and integration among strategic decisions and tactical plans are also critical to the pace of decision making. Finally, fast decisions hased on this pattem of hehaviors lead to superior performance. In October 1984, Gavilan Computer filed for bankruptcy protection under Chapter 11. Despite a $31 million stake from venture capitalists, Gavilan experienced delays and indecision that ultimately cost the firm its early technical and market advantages. The firm&amp;apos;s leading-edge technology hecame a &amp;amp;quot;me too &amp;amp;quot; one and competitors flooded its empty market niche. As the firm died, one executive mourned: &amp;amp;quot;We missed the window &amp;amp;quot; (Hof, 1984).

Predation has long been implicated as a major selective force in the evolution of several morphological and behavioral characteristics of animals. The importance of predation during evolutionary time is clear, but growing evidence suggests that animals also have the ability to assess and behaviorally influence their risk of being preyed upon in ecological time (i.e., during their lifetime). We develop an abstraction of the predation process in which several components of predation risk are identified. A review of the literature indicates that an animal's ability to assess and behaviorally control one or more of these components strongly influences decision making in feeding animals, as well as in animals deciding when and how to escape predators, when and how to be social, or even, for fishes, when and how to breathe air. This review also reveals that such decision making reflects apparent trade-offs between the risk of predation and the benefits to be gained from engaging in a given activity. Despite this body of evidence, several areas in the study of animal behavior have received little or no attention from a predation perspective. We identify several such areas, the most important of which is that dealing with animal reproduction. Much work also remains regarding the precise nature of the risk of predation and how it is actually perceived by animals, and the extent to which they can behaviorally control their risk of predation. Mathematical models will likely play a major role in future work, and we suggest that modelers strive to consider the potential complexity in behavioral responses to predation risk. Overall, since virtually every animal is potential prey for others, research that seriously considers the influence of predation risk will provide significant insight into the nature of animal behavior.

Much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes. The dilemma between overfitting and achieving maximum accuracy is seldom resolved. A method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity. The classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector, that is, trees constructed in randomly chosen subspaces. The subspace method is compared to single-tree classifiers and other forest construction methods by experiments on publicly available datasets, where the method's superiority is demonstrated. We also discuss independence between trees in a forest and relate that to the combined classification accuracy.

The modern theory of decision making under risk emerged from a logical analysis of games of chance rather than from a psychological analysis of risk and value. The theory was conceived as a normative model of an idealized decision maker, not as a description of the behavior of real people. In Schumpeter's words, it "has a much better claim to being called a logic of choice than a psychology of value" (1954, p. 1058).

The diffusion decision model allows detailed explanations of behavior in two-choice discrimination tasks. In this article, the model is reviewed to show how it translates behavioral data-accuracy, mean response times, and response time distributions-into components of cognitive processing. Three experiments are used to illustrate experimental manipulations of three components: stimulus difficulty affects the quality of information on which a decision is based; instructions emphasizing either speed or accuracy affect the criterial amounts of information that a subject requires before initiating a response; and the relative proportions of the two stimuli affect biases in drift rate and starting point. The experiments also illustrate the strong constraints that ensure the model is empirically testable and potentially falsifiable. The broad range of applications of the model is also reviewed, including research in the domains of aging and neurophysiology.