Exploratory Data Analysis Using Fisher Information

375 Pages·2007·8.677 MB·English

by  Professor B. Roy Frieden (auth.), B. Roy Frieden BS, MS, PhD, Robert A. Gatenby BSE, MD (eds.)

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:[e-mail]
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:[e-mail]
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: [e-mail]
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: [e-mail]
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:[e-mail]
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.