Modeling Uncertainty - An Examination of Stochastic Theory … · MODELING UNCERTAINTY An...
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MODELING UNCERTAINTY An Examination of Stochastic Theory, Methods, and Applications
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MODELING UNCERTAINTYAn Examination of Stochastic Theory,Methods, and Applications
Vanderbei, R. / LINEAR PROGRAMMING: Foundations and ExtensionsJaiswal, N.K. / MILITARY OPERATIONS RESEARCH: Quantitative Decision MakingGal, T. & Greenberg, H. / ADVANCES IN SENSITIVITY ANALYSIS AND
PARAMETRIC PROGRAMMINGPrabhu, N.U. / FOUNDATIONS OF QUEUEING THEORY
Fang, S.-C., Rajasekera, J.R. & Tsao, H.-S.J. / ENTROPY OPTIMIZATIONAND MATHEMATICAL PROGRAMMING
Yu, G. / OPERATIONS RESEARCH IN THE AIRLINE INDUSTRYHo, T.-H. & Tang, C. S. / PRODUCT VARIETY MANAGEMENTEl-Taha, M. & Stidham , S. / SAMPLE-PATH ANALYSIS OF QUEUEING SYSTEMSMiettinen, K. M. / NONLINEAR MULTIOBJECTIVE OPTIMIZATIONChao, H. & Huntington, H. G. / DESIGNING COMPETITIVE ELECTRICITY MARKETSWeglarz, J. / PROJECT SCHEDULING: Recent Models, Algorithms & ApplicationsSahin, I. & Polatoglu, H. / QUALITY, WARRANTY AND PREVENTIVE MAINTENANCETavares, L. V. / ADVANCED MODELS FOR PROJECT MANAGEMENTTayur, S., Ganeshan, R. & Magazine, M. / QUANTITATIVE MODELING FOR SUPPLY
CHAIN MANAGEMENTWeyant, J./ ENERGY AND ENVIRONMENTAL POLICY MODELINGShanthikumar, J.G. & Sumita, U./APPLIED PROBABILITY AND STOCHASTIC PROCESSESLiu, B. & Esogbue, A.O. / DECISION CRITERIA AND OPTIMAL INVENTORY PROCESSESGal, T., Stewart, T.J., Hanne, T./ MULTICRITERIA DECISION MAKING: Advances in MCDM
Models, Algorithms, Theory, and ApplicationsFox, B. L./ STRATEGIES FOR QUASI-MONTE CARLOHall, R.W. / HANDBOOK OF TRANSPORTATION SCIENCEGrassman, W.K./ COMPUTATIONAL PROBABILITYPomerol, J-C. & Barba-Romero, S./MULTICRITERION DECISION IN MANAGEMENTAxsäter, S./ INVENTORY CONTROLWolkowicz, H., Saigal, R., Vandenberghe, L./ HANDBOOK OF SEMI-DEFINITE
PROGRAMMING: Theory, Algorithms, and ApplicationsHobbs, B. F. & Meier, P. / ENERGY DECISIONS AND THE ENVIRONMENT: A Guide
to the Use of Multicriteria MethodsDar-El, E./ HUMAN LEARNING: From Learning Curves to Learning OrganizationsArmstrong, J. S./ PRINCIPLES OF FORECASTING: A Handbook for Researchers and
PractitionersBalsamo, S., Personé, V., Onvural, R./ ANALYSIS OF QUEUEING NETWORKS WITH BLOCKINGBouyssou, D. et al/ EVALUATION AND DECISION MODELS: A Critical PerspectiveHanne, T./ INTELLIGENT STRATEGIES FOR META MULTIPLE CRITERIA DECISION MAKINGSaaty, T. & Vargas, L./ MODELS, METHODS, CONCEPTS & APPLICATIONS OF THE ANALYTIC
HIERARCHY PROCESSChatterjee, K. & Samuelson, W./ GAME THEORY AND BUSINESS APPLICATIONSHobbs, B. et al/ THE NEXT GENERATION OF ELECTRIC POWER UNIT COMMITMENT MODELSVanderbei, R.J./ LINEAR PROGRAMMING: Foundations and Extensions, 2nd Ed.Kimms, A./ MATHEMATICAL PROGRAMMING AND FINANCIAL OBJECTIVES FOR
SCHEDULING PROJECTSBaptiste, P., Le Pape, C. & Nuijten, W./ CONSTRAINT-BASED SCHEDULINGFeinberg, E. & Shwartz, A./ HANDBOOK OF MARKOV DECISION PROCESSES: Methods
and ApplicationsRamík, J. & Vlach, M. / GENERALIZED CONCAVITY IN FUZZY OPTIMIZATION
AND DECISION ANALYSISSong, J. & Yao, D. / SUPPLY CHAIN STRUCTURES: Coordination, Information and
OptimizationKozan, E. & Ohuchi, A./ OPERATIONS RESEARCH/ MANAGEMENT SCIENCE AT WORKBouyssou et al/ AIDING DECISIONS WITH MULTIPLE CRITERIA: Essays in
Honor of Bernard RoyCox, Louis Anthony, Jr./ RISK ANALYSIS: Foundations, Models and Methods
INTERNATIONAL SERIES INOPERATIONS RESEARCH & MANAGEMENT SCIENCEFrederick S. Hillier, Series Editor Stanford University
MODELING UNCERTAINTYAn Examination of Stochastic Theory,Methods, and Applications
Edited byMOSHE DRORUniversity of Arizona
PIERRE L’ECUYERUniversité de Montréal
FERENC SZIDAROVSZKYUniversity of Arizona
KLUWER ACADEMIC PUBLISHERSNEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: 0-306-48102-2Print ISBN: 0-7923-7463-0
©2005 Springer Science + Business Media, Inc.
Print ©2002 Kluwer Academic Publishers
All rights reserved
No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
Visit Springer's eBookstore at: http://ebooks.springerlink.comand the Springer Global Website Online at: http://www.springeronline.com
Dordrecht
Contents
Professor Sidney J. YakowitzD. S. Yakowitz
Preface
Contributing Authors
Part I
Stability of Single Class Queueing NetworksHarold J. Kushner
1
2
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IntroductionThe ModelStability: IntroductionPerturbed Liapunov FunctionsStability
3Sequential Optimization Under UncertaintyTze Leung Lai
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IntroductionBandit Theory2.1 Nearly optimal rules based on upper confidence bounds and
Gittins indicesA hypothesis testing approach and block experimentationApplications to machine learning, control and scheduling ofqueues
2.22.3
3 Adaptive Control of Markov Chains3.13.2
Parametric adaptive controlNonparametric adaptive control
4 Stochastic Approximation
4Exact Asymptotics for Large Deviation Probabilities, withApplications
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Iosif Pinelis1. Limit Theorems on the last negative sum and applications to non-
parametric bandit theory1.11.2
Condition (4)&(8): exponential and superexponential casesCondition (4)&(8): exponential (beyond (14)) and subexpo-nential casesThe conditional distribution of the initial segmentof the sequence of the partial sums givenApplication to Bandit Allocation AnalysisTest-times-only based strategyMultiple bandits and all-decision-times based strategy
1.3
1.41.4.11.4.2
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Large deviations in a space of trajectoriesAsymptotic equivalence of the tail of the sum of independent randomvectors and the tail of their maximum3.13.2
3.3
IntroductionExponential inequalities for probabilities of large deviationof sums of independent Banach space valued r.v.’sThe case of a fixed number of independent Banach space val-ued r.v.’s. Application to asymptotics of infinitely divisibleprobability distributions in Banach spacesTails decreasing no faster than power onesTails, decreasing faster than any power ones
Tails, decreasing no faster than
3.43.53.6
Part II
5Stochastic Modelling of Early HIV Immune Responses Under Treatment
by Protease InhibitorsWai-Yuan Tan and Zhihua Xiang
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IntroductionA Stochastic Model of Early HIV Pathogenesis Under Treatment bya Protease Inbihitor2.12.2
2.3
Modeling the Effects of Protease InhibitorsModeling the Net Flow of HIV From Lymphoid Tissues toPlasmaDerivation of Stochastic Differential Equations for The StateVariables
3
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Mean Values of
A State Space Model for the Early HIV Pathogenesis Under Treat-ment by Protease Inhibitors4.1
4.2
Estimation of
Estimation of and
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An Example Using Real DataSome Monte Carlo Studies
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Contents
6The impact of re-using hypodermic needlesB. Barnes and J. Gani
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IntroductionGeometric distribution with variable success probabilityValidity of the distributionMean and variance of IIntensity of epidemicReducing infectionThe spread of the Ebola virus in 1976Conclusions
7Nonparametric Frequency Detection and Optimal Coding in Molecular
BiologyDavid S. Stoffer
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IntroductionThe Spectral EnvelopeSequence AnalysesDiscussion
Part III
8An Efficient Stochastic Approximation Algorithm for Stochastic Saddle
Point ProblemsArkadi Nemirovski and Reuven Y. Rubinstein
1 Introduction1.1 Classical stochastic approximation
2 Stochastic saddle point problem2.12.1.12.1.22.22.32.4
2.5
The problemStochastic settingThe accuracy measureExamplesThe SASP algorithmRate of convergence and optimal setup: off-line choice ofthe stepsizesRate of convergence and optimal setup: on-line choice of thestepsizes
3 Discussion3.13.2
Comparison with Polyak’s algorithmOptimality issues
4 Numerical Results4.14.2
A Stochastic Minimax Steiner problemA simple queuing model
5 ConclusionsAppendix: A: Proof of Theorems 1 and 2
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Appendix: B: Proof of the Proposition 182
9Regression Models for Binary Time SeriesBenjamin Kedem, Konstantinos Fokianos
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IntroductionPartial Likelihood Inference2.12.22.32.4
Definition of Partial LikelihoodAn Assumption Regarding the CovariatesPartial Likelihood EstimationPrediction
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Goodness of FitLogistic Regression4.1 A Demonstration
5 Categorical Data
10Almost Sure Convergence Properties of Nadaraya-Watson Regression
EstimatesHarro Walk
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IntroductionResultsLemmas and Proofs
11Strategies for Sequential Prediction of Stationary Time SeriesLászló Györfi, Gábor Lugosi
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IntroductionUniversal prediction by partitioning estimatesUniversal prediction by generalized linear estimatesPrediction of Gaussian processes
Part IV
12The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously
Distributed Information LagCarl Chiarella and Ferenc Szidarovszky
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IntroductionNonlinear Oligopoly ModelsThe Dynamic Model with Lag StructureBifurcation Analysis in the General CaseThe Symmetric CaseSpecial Oligopoly ModelsConclusions
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Contents ix13A Differential Game of Debt Contract ValuationA. Haurie and F. Moresino
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IntroductionThe firm and the debt contractA stochastic gameEquivalent risk neutral valuation4.14.2
Debt and Equity valuations when bankrupcy is not consideredDebt and Equity valuations when liquidation may occur
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Debt and Equity valuations for Nash equilibrium strategiesLiquidation at fixed time periodsConclusion
14Huge Capacity Planning and Resource Pricing for Pioneering ProjectsDavid Porter
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IntroductionThe ModelResults3.13.23.3
Cost and Performance UncertaintyCost Uncertainty and FlexibilityPerformance Uncertainty and Flexibility
4 Conclusion
15Affordable Upgrades of Complex Systems: A Multilevel, Performance-
Based ApproachJames A. Reneke and Matthew J. Saltzman and Margaret M. Wiecek
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IntroductionMultilevel complex systems2.12.2
An illustrative exampleComputational models for the example
3 Multiple criteria decision making3.13.23.3
Generating candidate methodsChoosing a preferred selection of upgradesApplication to the example
4 Stochastic analysis4.14.2
Random systems and riskApplication to the example
5 ConclusionsAppendix: Stochastic linearization12
Origin of stochastic linearizationStochastic linearization for random surfaces
16On Successive Approximation of Optimal Control of Stochastic Dynamic
SystemsFei-Yue Wang, George N. Saridis
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IntroductionProblem StatementSub-Optimal Control of Nonlinear Stochastic Dynamic SystemsThe Infinite-time Stochastic Regulator ProblemProcedure for Iterative Design of Sub-optimal Controllers5.15.2
Exact Design ProcedureApproximate Design Procedures for the Regulator Problem
6 Closing Remarks by Fei-Yue Wang
17Stability of Random Iterative MappingsLászló Gerencsér
123
IntroductionPreliminary resultsThe proof of Theorem 1.1
Appendix
Part V
18’Unobserved’ Monte Carlo Methods for Adaptive AlgorithmsVictor Solo
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El SidIntroductionOn-line Binary ClassificationBinary Classification with Noisy Measurements of Classifying Variables-OfflineBinary Classification with Errors in Classifying Variables -OnlineConclusions
19Random Search Under Additive NoiseLuc Devroye and Adam Krzyzak
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Sid’s contributions to noisy optimizationFormulation of search problemRandom search: a brief overviewNoisy optimization by random search: a brief surveyOptimization and nonparametric estimationNoisy optimization: formulation of the problemPure random searchStrong convergence and strong stabilityMixed random searchStrategies for general additive noiseUniversal convergence
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Contents xi20Recent Advances in Randomized Quasi-Monte Carlo MethodsPierre L’Ecuyer and Christiane Lemieux
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IntroductionA Closer Look at Low-Dimensional ProjectionsMain Constructions3.13.23.2.13.2.23.2.33.2.43.33.43.53.6
Lattice RulesDigital NetsSobol’ SequencesGeneralized Faure SequencesNiederreiter SequencesPolynomial Lattice RulesConstructions Based on Small PRNGsHalton sequenceSequences of Korobov rulesImplementations
4 Measures of Quality4.14.2
Criteria for standard lattice rulesCriteria for digital nets
5 Randomizations5.15.25.35.45.5
Random shift modulo 1Digital shiftScramblingRandom Linear ScramblingOthers
6 Error and Variance Analysis6.16.26.2.16.2.2
Standard Lattices and Fourier ExpansionDigital Nets and Haar or Walsh ExpansionsScrambled-type estimatorsDigitally shifted estimators
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Transformations of the IntegrandRelated MethodsConclusions and Discussion
Appendix: Proofs
Part VI
21Singularly Perturbed Markov Chains and Applications to Large-Scale Sys-
tems under UncertaintyG. Yin, Q. Zhang, K. Yin and H. Yang
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IntroductionSingularly Perturbed Markov Chains2.12.2
Continuous-time CaseTime-scale Separation
3 Properties of the Singularly Perturbed Systems3.13.23.3
Asymptotic ExpansionOccupation MeasuresLarge Deviations and Exponential Bounds
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3.3.13.3.2
Large DeviationsExponential Bounds
4 Controlled Singularly Perturbed Markovian Systems4.14.2
Continuous-time Hybrid LQGDiscrete-time LQ
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Further RemarksAppendix: Mathematical Preliminaries6.16.26.3
Stochastic ProcessesMarkov chainsConnections of Singularly Perturbed Models: ContinuousTime vs. Discrete Time
22Risk–Sensitive Optimal Control in Communicating Average Markov
Decision ChainsRolando Cavazos–Cadena, Emmanuel Fernández–Gaucherand
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IntroductionThe Decision ModelMain ResultsBasic Technical PreliminariesAuxiliary Expected–Total Cost Problems: IAuxiliary Expected–Total Cost Problems: IIProof of Theorem 3.1Conclusions
Appendix: A: Proof of Theorem 4.1Appendix: B: Proof of Theorem 4.2
23Some Aspects of Statistical Inference in a Markovian and Mixing FrameworkGeorge G. Roussas
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IntroductionMarkovian Dependence2.12.2
Parametric Case - The Classical ApproachParametric Case - The Local Asymptotic Normality Approach
2.3 The Nonparametric Case3 Mixing
3.13.23.33.43.4.13.4.23.4.33.4.43.4.53.4.63.4.7
Introduction and DefinitionsCovariance InequalitiesMoment and Exponential Probability BoundsSome Estimation ProblemsEstimation of the Distribution Function or Survival FunctionEstimation of a Probability Density Function and its DerivativesEstimating the Hazard RateA Smooth Estimate of F andRecursive EstimationFixed Design RegressionStochastic Design Regression
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Contents xiii
Part VII
24Stochastic Ordering of Order Statistics IIPhilip J. Boland, Taizhong Hu, Moshe Shaked and J. George Shanthikumar
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IntroductionLikelihood Ratio Orders ComparisonsHazard and Reversed Hazard Rate Orders ComparisonsUsual Stochastic Order ComparisonsStochastic Comparisons of SpacingsDispersive Ordering of Order Statistics and SpacingsA Short Survey on Further Results
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25Vehicle Routing with Stochastic Demands: Models & Computational
MethodsMoshe Dror
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IntroductionAn SVRP Example and Simple Heuristic Results2.1 Chance Constrained Models
3 Modeling SVRP as a stochastic programming with recourse problem3.13.23.3
The modelThe branch-and-cut procedureComputation of a lower bound on and on Q(x)
4 Multi-stage model for the SVRP4.1 The multi-stage model
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Modeling SVRP as a Markov decision processSVRP routes with at most one failure – a more ‘practical’ approachThe Dror conjectureSummary
26Life in the Fast Lane: Yates’s Algorithm, Fast Fourier and Walsh TransformsPaul J. Sanchez, John S. Ramberg and Larry Head
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IntroductionLinear Models2.12.1.12.1.22.1.3
Factorial AnalysisDefinitions and BackgroundThe ModelThe Coefficient EstimatorWalsh AnalysisDefinitions and BackgroundThe ModelDiscrete Walsh TransformsFourier AnalysisDefinitions and BackgroundThe Model
2.22.2.12.2.22.2.32.32.3.12.3.2
3 An Example
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4 Fast Algorithms4.14.24.3
Yates’s Fast Factorial AlgorithmFast Walsh TransformsFast Fourier Transforms
5 ConclusionsAppendix: A: Table of Notation
27Uncertainty Bounds in Parameter Estimation with Limited DataJames C. Spall
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IntroductionProblem FormulationThree Examples of Appropriate Problem Settings3.1
3.23.3
Example 1: Parameter Estimation in Signal-Plus-Noise Modelwith Non-i.i.d. DataExample 2: Nonlinear Input-Output (Regression) ModelExample 3: Estimates of Serial Correlation for Time Series
4 Main Results4.14.24.3
Background and NotationOrder Result on Small-Sample ProbabilitiesThe Implied Constant of Bound
5 Application of Theorem for the MLE of Parameters in Signal-Plus-Noise Problem5.15.2
BackgroundTheorem Regularity Conditions and Calculation of ImpliedConstantNumerical Results5.3
6 Summary and ConclusionsAppendix: Theorem Regularity Conditions and Proof (Section 4)
28A Tutorial on Hierarchical Lossless Data CompressionJohn C. Kieffer
1 Introduction1.11.21.3
Pointer Tree RepresentationsData Flow Graph RepresentationsContext-Free Grammar Representations
2 Equivalences Between Structures2.12.2
Equivalence of Pointer Trees and Admissible GrammarsEquivalence of Admissible Grammars and Data Flow Graphs
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Design of Compact StructuresEncoding MethodologyPerformance Under Uncertainty
Part VIII
29Eureka! Bellman’s Principle of Optimality is valid!
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IntroductionRemediesThe Big FixThe Rest is MathematicsRefinementsNon-Markovian Objective functionsDiscussion
30Reflections on Statistical Methods for Complex Stochastic SystemsMarcel F. Neuts
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The Changed Statistical SceneMeasuring Teletraffic Data StreamsMonitoring Queueing Behavior
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Author Index 761
Preface
This volume titled MODELING UNCERTAINTY: An Examination of Stochas-tic Theory, Methods, and Applications, has been compiled by the friends andcolleagues of Sid Yakowitz in his honor as a token of love, appreciation, andsorrow for his untimely death. The first paper in the book is authored by Sid’swife – Diana Yakowitz – and in it Diana describes Sid the person, his drivefor knowledge and his fascination with mathematics, particularly with respectto uncertainty modelling and applications. This book is a collection of paperswith uncertainty as its central theme.
Fifty authors from all over the world collectively contributed 30 papers tothis volume. Each of these papers was reviewed and in the majority of casesthe original submission was revised before being accepted for publication inthe book. The papers cover a great variety of topics in probability, statistics,economics, stochastic optimization, control theory, regression analysis, simula-tion, stochastic programming, Markov decision process, application in the HIVcontext, and others. Some of the papers have a theoretical emphasis and othersfocus on applications. A number of papers have the flavor of survey work in aparticular area and in a few papers the authors present their personal view of atopic. This book has a considerable number of expository articles which shouldbe accessible to a nonexpert, say a graduate student in mathematics, statistics,engineering, and economics departments, or just anyone with some mathemat-ical background who is interested in a preliminary exposition of a particulartopic. A number of papers present the state of the art of a specific area orrepresent original contributions which advance the present state of knowledge.Thus, the book has something for almost anybody with an interest in stochasticsystems.
The editors have loosely grouped the chapters into 8 segments, accordingto some common mathematical thread. Since none of us (the co-editors) is anexpert in all the topics covered in this book, it is quite conceivable that the pa-pers could have been grouped differently. Part 1 starts with a paper on stabilityin queuing networks by H.J. Kushner. Part 1 also includes a queuing related
paper by T.L. Lai, and a paper by I. Pinelis on asymptotics for large deviationprobabilities. Part 2 groups together 3 papers related to HIV modelling. Thefirst paper in this group is by W.-Y. Tan and Z. Xiang about modelling earlyimmune responses, followed by a paper of B. Barnes and J. Gani on the impactof re-using hypodermic needs, and closes with a paper by D.S. Stoffer. Part 3groups together optimization and regression papers. It contains 4 papers startingwith a paper by A. Nemirovski and R.Y. Rubinstein about classical stochasticapproximation. The next paper is by B. Kedem and K. Fokianos on regressionmodels for binary time series, followed with a paper by H. Walk on properties ofNadarya - Watson regression estimates, and closing with a paper on sequentialpredictions of stationary time series by L. Györfi and G. Lugosi. Part 4’s 6 pa-pers are in the area of economics analysis starting with a nonlinear oligopoliespaper by C. Chiarella and F. Szidarovszky. The paper by A. Haurie and F.Moresino examines a differential game of debt contract valuation. Next comesa paper by D. Porter, followed by a paper about complex systems in relation toaffordable upgrades by J.A. Reneke, M.J. Saltzman, and M.M. Wiecek. The 5thpaper in this group, by F.-Y. Wang and G.N. Sardis, concerns optimal controlin stochastic dynamic systems, and the last paper is by L. Gerencsér is aboutstability of random iterative mappings. Part 5 loosely groups 3 papers startingwith a paper by V. Solo on Monte Carlo methods for adaptive algorithms, fol-lowed by a paper on random search with noise by L. Devroye and A. Krzyzak,and closes with a survey paper on randomized quasi-Monte Carlo methods byP. L’Ecuyer and C. Lemieux. Part 6 is a collection of 3 papers sharing a focuson Markov decision analysis. It starts with a paper by G. Yin, Q. Zhang, K.Yin, and H. Yang on singularly perturbed Markov chains. The second paper, onrisk sensitivity in average Markov decision chains, is by R. Cavazos–Cadenaand E. Fernández–Gaucherand. The 3rd paper, by G.G. Roussas, is on statis-tical inference in a Markovian framework. Part 7 includes a paper on orderstatistics by P.J. Boland, T. Hu, M. Shaked, and J.G. Shanthikumar, followedby a survey paper on routing with stochastic demands by M. Dror, a paper onfast Fourier and Walsh transforms by P.J. Sanchez, J.S. Ramberg, and L. Head,a paper by J.C. Spall on parameter estimation with limited data, and a tuto-rial paper on data compression by J.C. Kieffer. Part 8 contains 2 ‘reflections’papers. The first paper is by M. Sniedovich – an ex-student of Sid Yakowitz.It reexamines Bellman’s principle of optimality. The last paper in this volumeon statistical methods for complex stochastic systems is reserved to M.F. Neuts.
The efforts of many workers have gone into this volume, and would not havebeen possible without the collective work of all the authors and reviewers whoread the papers and commented constructively. We would like to take this op-portunity to thank the authors and the reviewers for their contributions. Thisbook would have required a more difficult ’endgame’ without Ray Brice’s ded-
xviii MODELING UNCERTAINTY
PREFACE xix
ication and painstaking attention for production details. We are very gratefulfor Ray’s help in this project. Paul Jablonka is the artist who contributed the artwork for the book’s jacket. He was a good friend to Sid and we appreciate hiscontribution. We would also like to thank Gary Folven, the editor of KluwerAcademic Publishers, for his initial and never fading support throughout thisproject. Thank you Gary !
Moshe Dror Pierre L’Ecuyer Ferenc Szidarovszky
Contributing Authors
B. BarnesSchool of Mathematical Sciences
Australian National University
Canberra, ACT 0200
Australia
Philip J. BolandDepartment of Statistics
University College Dublin
Belfield, Dublin 4
Ireland
Rolando Cavazos–CadenaDepartamento de Estadística y Cálculo
Universidad Auténoma Agraria Antonio Narro
Buenavista, Saltillo COAH 25315
MÉXICO
Carl ChiarellaSchool of Finance and Economics
University of Technology
Sydney
P.O. Box 123, Broadway, NSW 2007
Australia
Luc DevroyeSchool of Computer Science
McGill University
Montreal, Canada H3A 2K6
xxii MODELING UNCERTAINTY
Moshe DrorDepartment of Management Information Systems
The University of Arizona
Tucson, AZ 85721, USA
Emmanuel Fernández–GaucherandDepartment of Electrical & Computer Engineering
& Computer Science
University of Cincinnati
Cincinnati, OH 45221-0030
USA
Konstantinos FokianosDepartment of Mathematics & Statistics
University of Cyprus
P.O. Box 20537 Nikosia, 1678, Cyprus
J. GaniSchool of Mathematical Sciences
Australian National University
Canberra, ACT 0200
Australia
László GerencsérComputer and Automation Institute
Hungarian Academy of Sciences
H-1111, Budapest Kende u 13-17
Hungary
László GyörfiDepartment of Computer Science and Information Theory
Technical University of Budapest
1521 Stoczek u. 2,
Budapest, Hungary
A. HaurieUniversity of Geneva
Geneva Switzerland
Contributing Authors xxiii
Larry HeadSiemens Energy & Automation, Inc.
Tucson, AZ 85715
Taizhong HuDepartment of Statistics and Finance
University of Science and Technology
Hefei, Anhui 230026
People’s Republic of China
Benjamin KedemDepartment of Mathematics
University of Maryland
College Park, Maryland 20742, USA
John C. KiefferECE Department
University of Minnesota
Minneapolis, MN 55455
Department of Computer Science
Concordia University
Montreal, Canada H3G 1M8
Harold J. KushnerApplied Mathematics Dept.
Lefschetz Center for Dynamical Systems
Brown University
Providence RI 02912
Tze Leung LaiStanford University
Stanford, California
Adam Krzyzak
xxiv MODELING UNCERTAINTY
Pierre L’EcuyerDépartement d’Informatique et de Recherche Opérationnelle
Université de Montréal, C.P. 6128, Succ. Centre-Ville
Montréal, H3C 3J7, Canada
Christiane LemieuxDepartment of Mathematics and Statistics
University of Calgary, 2500 University Drive N.W.
Calgary, T2N 1N4, Canada
Gábor LugosiDepartment of Economics,
Pompeu Fabra University
Ramon Trias Fargas 25-27,
08005 Barcelona, Spain
F. MoresinoCambridge University
United Kingdom
Arkadi NemirovskiFaculty of Industrial Engineering and Management
Technion—Israel Institute of Technology
Haifa 32000, Israel
Marcel F. NeutsDepartment of Systems and Industrial Engineering
The University of Arizona
Tucson, AZ 85721, U.S.A.
Iosif PinelisDepartment of Mathematical Sciences
Michigan Technological University
Houghton, Michigan 49931
Contributing Authors xxv
David PorterCollage of Arts and Sciences
George Mason University
John S. RambergSystems and Industrial Engineering
University of Arizona
Tucson, AZ 85721
James A. RenekeDept. of Mathematical Sciences
Clemson University
Clemson SC 29634-0975
George G. RoussasUniversity of California, Davis
Reuven Y. RubinsteinFaculty of Industrial Engineering and Management
Technion—Israel Institute of Technology
Haifa 32000, Israel
Matthew J. SaltzmanDept. of Mathematical Sciences
Clemson University
Clemson SC 29634-0975
Paul J. SanchezOperations Research Department
Naval Postgraduate School
Monterey, CA 93943
George N. SaridisDepartment of Electrical, Computer and Systems Engineering
Rensselaer Polytechnic Institute
Troy, New York 12180
xxvi MODELING UNCERTAINTY
Moshe ShakedDepartment of Mathematics
University of Arizona
Tucson, Arizona 85721
USA
J. George ShanthikumarIndustrial Engineering & Operations Research
University of California
Berkeley, California 94720
USA
Moshe SniedovichDepartment of Mathematics and Statistics
The University of Melbourne
Parkville VIC 3052, Australia
Victor SoloSchool of Electrical Engineering and Telecommunications
University of New South Wales
Sydney NSW 2052, Australia
James C. SpallThe Johns Hopkins University
Applied Physics Laboratory
Laurel, MD 20723-6099
David S. StofferDepartment of Statistics
University of Pittsburgh
Pittsburgh, PA 15260
Ferenc SzidarovszkyDepartment of Systems and Industrial Engineering
University of Arizona
Tucson, Arizona, 85721-0020, USA
Contributing Authors xxvii
Wai-Yuan TanDepartment of Mathematical Sciences
The University of Memphis
Memphis, TN 38152-6429
Harro WalkMathematisches Institut A
Universität Stuttgart
Pfaffenwaldring 57, D-70569
Stuttgart, Germany
Fei-Yue WangDepartment of Systems and Industrial Engineering
University of Arizona
Tucson, Arizona 87521
Margaret M. WiecekDept. of Mathematical Sciences
Clemson University
Clemson SC 29634-0975
Zhihua XiangOrganon Inc.
375 Mt. Pleasant Avenue
West Orange, NJ 07052
D. S. YakowitzTucson, Arizona
H.YangDepartment of Wood and Paper Science
University of Minnesota
St. Paul, MN 55108
xxviii MODELING UNCERTAINTY
G. YinDepartment of Mathematics
Wayne State University
Detroit, MI 48202
K. YinDepartment of Wood and Paper Science
University of Minnesota
St. Paul, MN 55108
[email protected], [email protected]
Q. ZhangDepartment of Mathematics
University of Georgia
Athens, GA 30602
This book is dedicated to thememory of Sid Yakowitz.
Chapter 1
PROFESSOR SIDNEY J. YAKOWITZ
D. S. YakowitzTucson, Arizona
Sidney Jesse Yakowitz was born in San Francisco, California on March8, 1937 and died in Eugene, Oregon on September 1, 1999. Sid’s parents,Morris and MaryVee, were chemists with the Food and Drug Administrationand encouraged Sid to be a life-long learner. He attended Stanford Universityand after briefly toying with the idea of medicine, settled into engineering (“Isaved hundreds of lives with that decision!”). Sid graduated from Stanford witha B.S in Electrical Engineering in 1960.
His first job out of Stanford was as a design engineer with the Universityof California’s Lawrence Radiation Laboratory (LRL) at Berkeley. Sid wasunhappy after college but claimed that he learned the secret to happiness fromhis office mate at LRL, Jim Sherwood, who told him he was being paid to becreative. Sid decided that “Good engineering design is a synonym for ‘invent-ing’.”
For graduate school, Sid chose Arizona State University. By this time, hisbattle since childhood with acute asthma made a dry desert climate a manda-tory consideration. In graduate school he flourished. He received his M.S. inElectrical Engineering in 1965, an M.A. in Mathematics in 1966, and Ph.D. inElectrical Engineering in 1967. His new formula for happiness in his work ledhim to consider each topic or problem that he approached as an opportunity to“invent”.
In 1966 Sid was hired as an Assistant Professor in the newly founded De-partment of Systems and Industrial Engineering at the University of Arizona inTucson. This department remained his “home” for 33 years with the exceptionof brief sabbaticals and leaves such as a National Academy of Science Post-doctoral Fellowship at the Naval Postgraduate School in Monterey, Californiain 1970-1971.
In 1969 Sid’s book Mathematics of Adaptive Control Processes (Yakowitz,1969) was published as a part of Richard Bellman’s Elsevier book series. Thisbook was essentially his Ph.D. dissertation and was the first of four published
