StatisticaSinica17(2007),1259-1260

Algebraic Statistics: A New Bridge Between Statistics and Mathematics

Applicationsof algebra in statisticshavea longhistory.However, the classicalapplicationsmainly involve linear algebra techniques such as those alreadyused inmultivariatestatistics. It isonlyduring thepastdecade thatcomputationalmethodsfromalgebraicgeometryandcommutativealgebrahave found theirway intostatistics.ThisdevelopmentoriginatedwithworkonMarkovchainMonteCarloalgorithms forexactinference incontingency tableanalysis,which represents thebest explored statisticalapplicationofcomputationalalgebra.However,manyother fieldsofapplicationhaveemergedandacommunityofresearcherswithalgebraicinterestshasbeguntoformundertheumbrellaof“algebraicstatistics”.

Throughaseriesofeightarticles,thisspecialissuehighlightsthediversityofthisyounganddevelopingfieldofalgebraicstatistics.ThearticlesareprecededbyaneditorialnotebySteveFienbergwhoshareshisviewsofthefield.Theplanforthisspecialissueoriginatedat the2005WorkshoponAlgebraicStatisticsandComputationalBiology,whichwasheldat theClayMathematicsInstitute(Fordetailsof theworkshop,pleasevisit thewebsiteathttp://www.claymath.org/programs/cmiworkshops/ascb/).Whilethreeofthearticlesdiscussapplicationsincomputationalbiology,thegeneralscopeofthisspecialissueisbroaderthanthatoftheClayWorkshop.Therepresentedstatisticaltopicsareindeeddiverseandincludecontingencytableanalysis,experimentaldesign,foundationsofalgebraicstatistics,graphicalmodels,andmaximumlikelihoodestimation.

Wehope that thisspecial issuewill stimulate interest inalgebraicstatisticsamongstatisticians, which brings with it exciting new opportunities for interdisciplinarycollaborationsbetweenmathematiciansandstatisticians.

—Mathias Drton1, Seth Sullivant2, Chun-Houh Chen3, Vanja Dukic1 and Jun Liu2

Guest Editors

1UniversityofChicago2HarvardUniversity3AcademiaSinica

Highlights

1260 HIGHLIGHTS

StephenE.FienbergisMauriceFalk

UniversityProfessorofStatisticsandSocial

ScienceatCarnegieMellonUniversity,

withappointments in theDepartmentsof

Statistics,MachineLearning,andCyLab.

He has served as Dean of the College

of Humanities and Social Sciences at

CarnegieMellonandasVicePresident

forAcademicAffairsatYorkUniversity,

in Toronto, Canada, as well as on the

faculties of the University of Chicago

and theUniversityofMinnesota.Hewas

foundingco-editorofChanceandservedastheCoordinatingandApplicationsEditorofthe

JournaloftheAmericanStatisticalAssociation.Heiscurrentlyoneofthefoundingeditors

of theAnnalsofAppliedStatisticsandisco-founderof thenewonlineJournalofPrivacy

andConfidentiality,basedinCyLab.HehasbeenVicePresidentoftheAmericanStatistical

AssociationandPresidentof theInstituteofMathematicalStatisticsandtheInternational

SocietyforBayesianAnalysis.Hisresearchincludesthedevelopmentofstatisticalmethods,

especially tools forcategoricaldataanalysis.Hisworkonconfidentialityanddisclosure

limitationaddressesissuesrelatedtorespondentprivacyinbothsurveysandcensusesand

especially tocategoricaldataanalysis.Fienbergis theauthororeditorofover20books

and300papersandrelatedpublications.His twobooksoncategoricaldataanalysisare

CitationClassics.HeisamemberoftheU.S.NationalAcademyofSciences,andafellowof

theRoyalSocietyofCanada,theAmericanAcademyofArtsandSciences,andtheAmerican

AcademyofPoliticalandSocialScience.