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区间分析及其在参数估计中的应用 Title:IntervalAnalysisandItsApplicationinParameterEstimation Abstract: Intervalanalysisisamathematicaltoolthatallowsforthecalculationofrigorousboundsonthevaluesoffunctionsandthesolutionsetsofequationsorsystemsofequations.Thispaperaimstoprovideanoverviewofintervalanalysisanddiscussitspracticalapplicationsinparameterestimation.Thepaperwillexploretheadvantagesofintervalanalysisinprovidingrobustandreliableparameterestimatesinthepresenceofuncertaintiesandvariationsindata.Additionally,thelimitationsandchallengesofintervalanalysiswillbediscussed,alongwithpotentialavenuesforfurtherresearchanddevelopment. 1.Introduction: Parameterestimationisafundamentaltaskinmanyscientificandengineeringdisciplines.Itinvolvesthedeterminationofunknownparametersfromobserveddata,withthegoalofcharacterizingtheunderlyingphenomenaormodelsthatgeneratedthedata.However,inpractice,dataoftencontainuncertaintiesanderrorsthatcanaffecttheaccuracyandreliabilityofparameterestimates.Intervalanalysisoffersapowerfulapproachtoaddressthesechallengesbyprovidingrigorousboundsonparametervalues. 2.PrinciplesofIntervalAnalysis: Intervalanalysisisbasedonthemathematicsofintervals,whicharesetsofrealnumbers.Anintervalconsistsofallthenumbersbetweenalowerbound(infimum)andanupperbound(supremum).Thebasicoperationsofintervalarithmetic,suchasaddition,subtraction,multiplication,anddivision,aredefinedinsuchawaythattheypreservetheorderandguaranteethecorrectnessofthecomputedbounds.Byperformingintervalcomputations,itispossibletoobtainrigorousestimatesoffunctionsandsolutionstoequations. 3.ApplicationsofIntervalAnalysisinParameterEstimation: 3.1UncertaintyQuantification: Intervalanalysisallowsforthequantificationofuncertaintiesinparameterestimationbyprovidingconfidenceintervals,whichrepresenttherangeofpossibleparametervaluesconsistentwiththeavailabledata.Theseintervalscanaccountforbothmeasurementerrorsandmodeluncertainties,providingacomprehensiverepresentationoftheposterioruncertainty. 3.2RobustParameterEstimation: In