A Probabilistic Characterization of Simulation Model Uncertainties

Transcription

1 A Proalstc Charactrzaton of Sulaton Modl Uncrtants Vctor Ontvros Mohaad Modarrs Cntr for Rsk and Rlalty Unvrsty of Maryland 1

2 Introducton Thr s uncrtanty n odl prdctons as wll as uncrtanty n xprnts Th uncrtanty n th xprnt and uncrtanty n th odl prdctons ar consdrd ndpndnt Any coparson twn th rsults of xprnt and odl prdctons ay usd to stat uncrtanty of th ral valu of ntrst Th odl uncrtanty s th only uncrtanty that should consdrd whn th dstruton of ral valu gvn a odl prdcton s statd. Thr dffrnt odl rrors ar prsntd: th addtv rror prcntag rror odl and ultplcatv rror odl Th ultplcatv rror odl shows a ttr agrnt

3 Addtv Error Modl: Assuptons Th addtv rror of th rsults of xprnt copard to th ral valus of ntrst s a norally dstrutd rando nur wth gvn an and standard dvaton Th addtv rror of odl prdctons copard to th ral valus of ntrst s also a norally dstrutd rando nur Error twn odl and xprnt can now assssd 3

4 Addtv Error Modl = + E ; E ~ N s Modl Prdcton Rsult of Exprnt = + E ; E ~ N s whr : : Ral Quantty : Rsult of xprnt : Modl prdcton : Man and SD of xprntal addtv rror : Man and SD of odl addtv rror E ~ s + s N 4

5 Ptfalls Error plottd twn odl prdcton and xprntal asurnts ust dntcally dstrutd whch s not always tru as thy ay ncras at hghr rangs. Th ntroducd addtv rror can ngatv zro or postv Th E whch s th addtv rror twn odl prdcton and xprnt can ngatv postv or zro. Ths lts th chocs of lklhood functon for ths rando varal to noral dstruton. Whn th data s wdly scattrd th noral dstruton assupton rsults n ngatv lowr ounds wth no anngful physcal ntrprtaton 5

6 Prcntag Error Modl: Assuptons Th prcntag rror of th rsults of xprnt copard to th ral valus of ntrst s a norally dstrutd rando nur wth gvn an and standard dvaton Th prcntag rror of odl prdctons copard to th ral valus of ntrst s a norally dstrutd rando nur Th prcntag rror of odl prdctons copard to th rsults of xprnt s a functon of th two rando varals ntroducd arlr. Th dstruton of ths rando nur wll usd to rprsnt th lklhood of data 6

7 Prcntag Error Modl Modl Prdcton Rsult of Exprnt whr : : Ral Quantty : Rsult of xprnt :Modl prdcton :Man and SD of xprntal prcntag rror : Man and SD of odl prcntag rror = E = E = E ; ; E E ~ N ~ N 1 E E E = E + 1 : Man and SD prcntag rrorof Exprnt copard to odl Indpndncy of E E } ~ N E 3 4 Approxaton! 7

8 Ptfalls Th ntroducd prcntag rror can ngatv zro or postv. Ths ascally forcs th noral dstruton assupton for prcntag rrors E & E. Th E whch s th prcntag rror twn odl prdcton and xprnt can ngatv postv or zro. Ths lts th chocs of lklhood functon for ths rando varal to noral dstruton. Th xact dstruton of E can not analytcally drvd Whn th data s wdly scattrd th noral dstruton assupton rsults n ngatv lowr ounds wth no anngful physcal ntrprtaton 8

9 Multplcatv Error: Assuptons Th odl prdcton rsult of xprnt and ral valu of ntrst hav th sa sgn all postv or all ngatv Th rato of ral valu and xprntal rsults s a rando varal wth lognoral dstruton for whch confdnc ounds ar known Th rato of ral valu and odl prdcton s a rando varal wth lognoral dstruton wth paratrs to dtrnd Th rato of odl prdctons and rsults of xprnt s a functon of th two rando varals ntroducd arlr. Th dstruton of ths rando varal s lognoral and wll usd to rprsnt th lklhood of data Havng th aov assuptons th dstruton of ral quantty of ntrst gvn a odl prdcton wll a lognoral dstruton 9

10 Multplcatv Error Modl Modl Prdcton Rsult of Exprnt = = = t Indpndncy of t ~ whr : : Ral Quantty : Rsult of xprnt : Modl prdcton :Th rror factor for odl prdctons : Man and SD of xprntal rror factor :Th rror factor for xprntal data : Man and SD of odl rror factor LN = = ; ; + ~ LN ~ LN 10

11 11 Multplcatv Error: Baysan Postror n LN LN f f L whr d d L f L f f π ln ~ ~ prdcton odl gvn as followng : as statd wll of dstruton th as such prdcton odl Gvn a Paratrs Postror Jont Dstruton of : Paratrs Pror Jont Dstruton of : 1 : 3 0 ln = + = = + =

12 Exapl IVE Radant Hat lux Baysan Approach 1

13 Proalty of Excdanc: HGL Tpratur Excdanc Proalty Excdanc fro 18C Excdanc fro 330C Prdctd HGL Pak Tpratur ºC 13

14 Conclusons Th rror statd y coparng xprnts and odl prdctons s not th uncrtanty of th odl. It s rathr a conaton of xprntal and odl uncrtants. Th dstruton of th ral valu of ntrst gvn a odl prdcton dpnds only on th uncrtanty of th odl. Th Baysan frawork allows dffrnt wghts and xprt judgnts to latr consdrd whn dalng wth non-hoognous populaton of xprnts or odl prdctons Postrors fro Baysan analyss can usd as pror to updatd y nw data ponts whn co avalal Multplcatv rror odl provds good rsults 14