What is what:intervals,fuzzysets,random variables,impreciseprobabilitiesepistemicuncertainty
Michael Beer 1 / 15 What is what: intervals, fuzzy sets, random variables, imprecise probabilities epistemic uncertainty
VagueandimpreciseinformationSOMEOUESTIONSHow precisewill it be?Anyconcernordoubt?modeling,quantification,processing,evaluation,interpretation?2/15MichaelBeer
Michael Beer 2 / 15 How precise will it be ? modeling, quantification, processing, evaluation, interpretation ? Any concern or doubt ? SOME QUESTIONS Vague and imprecise information
VagueandimpreciseinformationCHALLENGEstatistical analysis ofIs it safe ?impreciseand raredataF(x)set of plausiblemodelsreliabilityanalysis2p'一一Is the[Pr,I, Pr,]imprecisionreliabilityanalysisreflectedinPstill reliable?EffectsonP?SensitivityofP,toimprecision?3/15MichaelBeer
Michael Beer 3 / 15 CHALLENGE of imprecise and rare data Is the reliability analysis still reliable ? statistical analysis Is it safe ? Effects on Pf ? reliability analysis F(x) model Pf ~ ~ set of plausible s [Pf,l, Pf,r] imprecision reflected in Pf Sensitivity of Pf to imprecision ? epistemic uncertainty Vague and imprecise information
Vagueand impreciseinformationCHALLENGINGCASESSummaryofexamplesimprecisemeasurementsexpertassessment/experiencemeasurement/observationlinguisticassessmentsunderdubious conditionshighplausiblerangemediumXlowimprecisesampleelementsX.smallsamples.incompleteprobabilisticobservationswhichcannotbeelicitationexerciseseparated clearlyconditional probabilities observedvague/dubiousprobabilisticinformationunder unclear conditions.only marginals of a joint distributionchanging environmental conditionsavailablewithoutcopulamixtureof informationfrom different sourcesand with different characteristicsclassificationand mathematical modeling?Michael Beer4/15
Michael Beer 4 / 15 CHALLENGING CASES Summary of examples mixture of information from different sources and with different characteristics classification and mathematical modeling ? • imprecise sample elements • small samples • changing environmental conditions incomplete probabilistic elicitation exercise • vague / dubious probabilistic information • • imprecise measurements x plausible range measurement / observation under dubious conditions • observations which cannot be separated clearly • conditional probabilities observed under unclear conditions • only marginals of a joint distribution available without copula • low medium high • linguistic assessments x • expert assessment / experience Vague and imprecise information
VagueandimpreciseinformationCLASSIFICATIONANDMODELINGAccording to sourcesaleatory uncertainty·epistemic uncertainty》irreducible uncertainty》reducible uncertainty》propertyofthesystem》propertyoftheanalyst》fluctuations/variability》lackofknowledgeorperceptioncollection of all problematic cases,stochasticcharacteristicsinconsistencyofinformationtraditionalno specific modelprobabilistic modelsAccording to information contentuncertaintyimprecision》probabilisticinformation》non-probabilisticcharacteristicstraditionaland subjectiveset-theoreticalmodelsprobabilistic modelsInviewof thepurpose of theanalysisaveraged results, value ranges, worst case, etc.?MichaelBeer5/15
Michael Beer 5 / 15 CLASSIFICATION AND MODELING » reducible uncertainty » property of the analyst » lack of knowledge or perception According to sources • aleatory uncertainty » irreducible uncertainty » property of the system » fluctuations / variability stochastic characteristics • epistemic uncertainty collection of all problematic cases, inconsistency of information » non-probabilistic characteristics According to information content • uncertainty » probabilistic information traditional and subjective probabilistic models • imprecision set-theoretical models traditional no specific model probabilistic models In view of the purpose of the analysis • averaged results, value ranges, worst case, etc. ? Vague and imprecise information