Exploratory Data Analysis Using Fisher Information PDF
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Exploratory Data Analysis Using Fisher Information B. Roy Frieden and Robert A. Gatenby (Eds) Exploratory Data Analysis Using Fisher Information ~ Springer B.RoyFrieden, BS,MS,PhD Robert A.Gatenby,BSE,MD College ofOptical Sciences Radiology Department University ofArizona Arizona Health Sciences Center Tucson Tucson USA USA Cover image:DNA nebula orDNAmolecule? See Chap.5,Sec.5.1.7.Imagecourtesyof NASNJPL-Caltech,and withthanks alsotoProfessorMarkMorris,UCLA. BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongress Control Number:2006927790 ISBN-IO: 1-84628-506-2 Printedonacid-free paper ISBN-13:978-1-84628-506-6 ©Springer-VerlagLondon Limited 2007 Apart from anyfair dealing for thepurposesof research or private study,orcriticismorreview, as permittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced, storedortransmitted,inanyformorbyanymeans,withthepriorpermissioninwritingofthepublishers, or in the case of reprographic reproduction inaccordance with theterms of licences issued bythe CopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbesentto thepublishers. Theuseofregisterednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceof aspecificstatement,thatsuchnamesareexempt fromtherelevant lawsandregulationsandtherefore freeforgeneral use. The publishermakes norepresentation,expressorimplied,with regard totheaccuracy oftheinfor mation containedinthisbookandcannot accept anylegalresponsibilityorliability foranyerrors or omissionsthatmaybemade. 9 8 7 6 5 4 321 SpringerScience+BusinessMedia springer.com Contents ContributorDetails... .. vii 1 IntroductiontoFisherInformation:Its Origin,Uses,andPredictions 1 1.1 MathematicalTools.......................................................... 3 1.2 ATutorialonFisherInformation.... . 8 1.3 IntroductiontoSourceFisherInformationJ. 21 lA ExtremePhysicalInformation(EPI).. .. 23 1.5 GettingtheSourceInformationJforaGivenScenario............... 32 1.6 InformationGame............................................................ 34 1.7 PredictionsoftheEPIApproach.......................................... 38 2 FinancialEconomics from FisherInformation. 42 2.1 ConstructingProbabilityDensityFunctionsonPrice Fluctuation..................................................................... 42 2.2 YieldCurveStaticsandDynamics........................................ 50 2.3 InformationandInvestment , . 64 3 GrowthCharacteristicsofOrganisms........................................ 74 3.1 InformationinLivingSystems:ASurvey............................... 74 3.2 ApplicationsofITandEPItoCarcinogenesis 94 3.3 AppendixA:DerivationofEPIPowerLawSolution. 115 4 InformationandThermalPhysics ,. 119 4.1 ConnectionsBetweenThermalandInformationPhysics 120 4.2 HamiltonianSystems........................................................ 123 4.3 ThePlaceofAFisherThermalPhysics.................................. 131 404 ModemApproachestoStatisticalMechanics.... 134 4.5 FisherThermodynamics... 138 4.6 TheGradApproachinTenSteps.......................................... 144 4.7 ConnectingExcitedSolutionsoftheFisher-SWE toNonequilibriumThermodynamics.. 145 v vi Contents 5 ParallelInformationPhenomenaofBiologyand Astrophysics 155 5.1 CorrespondingQuarter-PowerLawsofCosmologyandBiology... 155 5.2 QuantumBasisforSystemsExhibitingPopulationGrowth.......... 172 6 EncryptionofCovert InformationThroughaFisherGame............ 181 6.1 Summary....................................................................... 181 6.2 EmbeddingCovertInformationinaStatisticalDistribution 191 6.3 InferenceoftheHostDistributionUsingFisherInformation........ 194 6.4 ImplementationofEncryptionandDecryptionProcedures.......... 203 6.5 ExtensionoftheEncryptionStrategy..................................... 214 6.6 SummaryofConcepts....................................................... 215 7 ApplicationsofFisherInformationtothe ManagementofSustainable EnvironmentalSystems........................................................... 217 7.1 Summary....................................................................... 217 7.2 Introduction.................................................................... 218 7.3 FisherInformationTheory.................................................. 219 7.4 ProbabilityLawonStateVariables....................................... 222 7.5 EvaluatingtheInformation................................................. 224 7.6 DynamicOrder................................................................ 225 7.7 DynamicRegimesandFisherInformation 226 7.8 EvaluationofFisherInformation............................ 227 7.9 ApplicationstoModelSystems............................................ 229 7.10 ApplicationstoRealSystems.............................................. 237 7.11 Summary....................................................................... 243 8 FisherInformationinEcologicalSystems................................... 245 8.1 PredictingSusceptibilitytoPopulationCataclysm..................... 245 8.2 FindingtheMassOccurrenceLawForLivingCreatures............. 256 8.3 DerivationofPowerLawsofNonlivingandLivingSystems........ 267 9 Sociohistory: AnInformationTheory ofSocialChange................. 285 9.1 Summary........................... 285 9.2 SocialCybernetics............................................................ 292 9.3 DevelopingaFormalTheoryofSociohistory 296 9.4 SocioculturalDynamics 307 9.5 TheParadigmofSociohistory.............................................. 309 9.6 ExploringtheDynamicofCulturalDisposition........................ 321 9.7 TheSocioculturalPropositionsofEPI.................................... 325 9.8 AnIllustrativeApplicationofEPItoSocioculturalDynamics....... 325 9.9 ACaseIllustration:PostcolonialIran..................................... 330 9.10 Overview....................................................................... 334 References............................................................................... 337 Index 357 Contributor Details H. Cabezas HeribertoCabezasistheChiefof theSustainableEnvironmentsBranch,amul tidisciplinaryresearchgroupofapproximately20scientistsandengineersatthe NationalRiskManagementResearchLaboratory,OfficeofResearchandDevelop ment(ORD),USEnvironmental ProtectionAgency.Dr.CabezasservesasChair oftheEnvironmental DivisionattheAmericanInstituteofChemicalEngineers. Heservesashislaboratory'sdesignatedrepresentativetotheCouncilforChemical Research.Dr.CabezaswastherecipientoftheSustainableTechnologyDivision 1997IndividualAchievementAward,the1998EPAScienceAchievementAward inEngineering,andthe2003ORDDiversityLeadershipAward.Hereceivedthe PhDinchemicalengineeringfromtheUniversityofFloridain1985intheareaof thermodynamicsandstatisticalmechanics.Hisareasofresearchinterestinclude complex sustainable systems,chemicalprocess design forpollutionprevention, designof environmentally benignsubstitute-solvents, and thermodynamics. His publicationsincludeover40peer-reviewedtechnicalpublications,manyconfer ence proceedings, guest editorship of the Journal ofChromatography and the journalResources, Conservation and Recycling, various trade publications, in vited lecturesatnationalandinternationalconferences,presentationsatnational andinternationalconferences,andinvitedresearchseminarsatacademic,private, andgovernmentinstitutions.Dr.CabezasisamemberoftheAmericanInstitute of ChemicalEngineers and the AmericanAssociationfor the Advancementof Science(AAAs). Affiliationand contactdetails: Dr.HeribertoCabezas USEnvironmentalProtectionAgency 26WestMartinLutherKingDrive Cincinnati,OH45268 E-mail:[email protected] J.L.D'Anna JosephD'AnnaisManagingDirectorandHeadofEquity-FundDerivativesStruc turingfortheAmericasatRabobankInternational,NewYork. Formerly,hewas vii viii ContributorDetails aSeniorFinancialEngineerinSociete Generale'sEquity Derivatives group, also servingasChiefInvestmentOfficerofCatalystRe,SG'sreinsurancesubsidiary.He joined SG via Constellation Financial Management (CFM), a structured finance boutiqueacquired by SG in 2003.At CFM he was Managing Directorof Strate gic Capital Raising and Alternative Risk Transfer, where he directed the design andplacementof$1.3 billion innotes backed bymutual fund andannuity deriva tives.AtBankofAmerica,heanalyzedfinancialmarketdata, validated derivative models, andhelped setbankwidestandards.HeisalsoanNASDregistered repre sentative andCFACharterholder.Joe holds BachelorofSciencedegrees inmath andphysics from theUniversity ofRedlands andaPhDinphysics fromUCSanta Barbara. Affiliationandcontactdetails: Dr.Joseph L.D'Anna ManagingDirector, Head ofEquity-FundDerivatives Structuring North America RabobankInternational,Inc. 245Park Avenue,37th floor,NY 10167 E-mail: Joseph.D'Annats'Rabobank.com B.D.Fath Brian Fath is an Assistant Professor in the Department of Biological Sciences at Towson University in Towson, Maryland. He teaches courses in ecosystem ecology, environmental biology, human ecology, and networks, and has taught shortcourses inecologicalmanagementandmodelinginPortugal,Denmark, and Croatia. His research isinthe area ofecological network analysis, sustainability, andintegratedassessment. Hehaspublishedmore than45papers inreferredjour nals, conferences,and book chapters.Hehas asummerappointmentasa visiting research scientist in the Dynamic Systems Program at the International Institute of Applied Systems Analysis in Laxenburg, Austria, where he has organized a series of workshops and supervised student summerresearch. He iscurrently an associate editor for the internationaljournal Ecological Modelling and Systems Ecology, andcoordinatingeditor foraforthcoming EncyclopediaofEcology. Affiliationandcontactdetails: Professor Brian D.Fath Biology Department TowsonUniversity Towson,MD 21252 E-mail:[email protected] B.R.Frieden Roy Frieden is an Emeritus Professor in the College of Optics, University of Arizona,Tucson.Heconsultsforgovernmentagenciesinstatisticaloptics(NASA, James Webb 2nd generation space telescope) and in scientific uses of Fisherin formation.The latter include the monitoring of ecologies for the Environmental ProtectionAgency,aswellastheanalysis offunctional andcancerousgrowth for ContributorDetails IX theUniversity ofArizona Medical Center.Other suchuses oftheinformationare listed inSection 1.7ofthis book, andinclude the parallel behaviorofbiological, cosmological, and social systems as information transducers, and the invention of optimal capital investment programs ineconomics. Past research successes in opticshavebeentheinventionoflaserbeamshaping techniques(currentlyusedin laser fusion energy research), theproposed useofe.m. stealth technology for the USnavy,three-dimensionalimaging theory,maximumentropy imagerestoration, andimagery whose resolution much-exceedsthediffraction limit.The authorhas publishedwell over 100peer-reviewedpapers in scientificjournals aswell as20 invited chapters and 5 books. He is a fellow of the AAAS, Optical Society of America, and SPIE. Affiliation and contactdetails: ProfessorB.RoyFrieden College ofOptics, University ofArizona Tucson, AZ85721 E-mail: [email protected] R.A.Gatenby RobertGatenby isaProfessorofradiology andappliedmathematicsattheUniver sityofArizona, andhasservedasChairoftheRadiologyDepartmentsinceJuly I, 2005. His research interests arefocused on integrating mathematicalmodels and empirical techniques for purposes of understanding tumor invasion and carcino genesis.Nonlinearcellularandmicroenvironmentaldynamicsdominate thesepro cesses. Dr.Gatenby received the BSE in engineering from Princeton University, and an MD from the University of Pennsylvania.He completedhis residency in radiology atthe Hospital ofthe University ofPennsylvania. His interest intumor biology began during his early career while working at the Fox Chase Cancer Center in Philadelphia. At the University of Arizona, Dr. Gatenby works with an eclectic group of researchers at the interface of mathematics and medicine. This includes young physiciansandlifescientistswho areinterestedintheuseof mathematical modeling techniques, as well as applied mathematicians, theoreti calphysicists, aerospace engineers,andoptical scientists who wishtoapply their skills tobiology. Affiliationand contactdetails: Dr.Robert A.Gatenby Chair,DepartmentofRadiology University Medical Center University ofArizona Tucson, AZ85726 E-mail: [email protected] R.J. Hawkins RaymondJ.Hawkins isExecutiveVicePresident, InterestRateRiskMasagement, at Countrywide Bank, NAThe bank is a member of the Countrywide Financial x ContributorDetails Corporation family of companies. Dr. Hawkins is also an Adjunct Professor in theCollegeofOpticalSciencesofthe UniversityofArizona. AtCountrywidehe provides oversightof the bank's strategiesthat address interestrate risk asit im pacts investments,loan portfolios,time deposits,escrow deposits, and otherbank activities. Heenteredthefinancial servicesprofessionin 1993inthefixed-income derivatives group at SalomonBrothers. Since that time, Hawkinshas held a vari etyofpositionswith organizationsincludingBankofAmerica,BearSteams,and Barclay's Global Investors. These were as a strategist, specializing in risk man agement and securities valuation. Prior tojoining Countrywide Bank he served asManagingPartner, DirectorofDerivativesTradingandResearchforMulsanne Capital Management. At the University of Arizona, Dr. Hawkins leverages his earlier work in guided-wave electromagnetics and integrated photonics in a re search program that centers on applications of information theory and statistical physics to the emerging field of econophysics.Priorto 1993 Hawkins served as ateam leaderand researcherin computationalphotonics at Lawrence Livermore NationalLaboratory. Dr.Hawkins wasformally educatedatColumbiaUniversity inthecity ofNewYork,beginningwithColumbiaCollegeandending with adoc torate for workdone incondensedmatterphysics.HeholdsaCharteredFinancial Analystdesignation,and haspublished extensivelyinphysics,econometrics,and econophysics. Affiliation andcontactdetails: Dr.RaymondJ.Hawkins ExecutiveVicePresident InterestRate Risk Management CountrywideBank 225 West HillcrestDrive, MS TO-20 ThousandOaks, CA 91360 E-mail:[email protected] A.L.Mayer Audrey MayerisaseniorresearcherattheUniversityofTampere, Finland,where she is working on two issues:applying ecologicallybased indices to sustainable forestmanagement,andmeasuringimpactsonbiodiversityofglobaltradeinforest products.Priortothisappointment,shewasanecologistattheUSEnvironmental ProtectionAgency(OfficeofResearchandDevelopment,National RiskManage mentResearchLaboratory),workinginmultidisciplinarygroupsintheSustainable Environments Branch on theoretical and appliedsustainabilitytools, particularly usingconceptsfromdynamicregimes theory.Shereceived thePhDinecologyand evolutionarybiologyfrom theUniversityofTennessee, Knoxville,andcompleted postdoctoralpositionsattheUniversityofCincinnatiandtheUSEPA.Herresearch spans several areas, including multidisciplinary sustainability indices influenced by informationtheory, managingimpacts ofimpervious surface on aquatic com munitiesat the watershedscale, and bird conservation,particularlyland use/land covereffects atmultiplespatial scales on terrestrialbird communities.
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