To Estimate or to Predict

Transcription

1 Raer Schwabe o Esmae or o Predc Implcaos o he esg or Lear Mxed Models

2 o Esmae or o Predc - Implcaos o he esg or Lear Mxed Models Raer Schwabe, Marya Prus raer.schwabe@ovgu.de suppored by SKAVOE Germa ederal Msry o Educao ad Research INI Cambrdge 0, AEW0 Augus 9, 0

3 Oule Prologue: Shor roduco. Model escrpo. Esmao ad Predco 3. Opmal esg 4. A Smple Example 5. Oulook

4 Prologue: Shor roduco Example: Pharmacokecs measure he cocerao o a drug s.o. s blood over me e e

5 Example: Pharmacokecs observaos j j j j esmae respose curve, AUC area uder he curve, c max maxmal cocerao ec. opmal me pos o measuremes,...,?

6 Radom coeces each dvdual has s ow curve populao parameers ypcal curve dvdual parameers dvdual curves

7 . Model escrpo lear mea respose j j j j radom error observao j=,..., explaaory varable j Var..d. j regresso ucos,..., p,..., p parameer

8 Bu! each dvdual has s ow respose curve = = ocodo degus = 3 = 4 dvdual resposes ollow a commo model

9 Herarchcal model dvdual level dvdual parameer j j j dvdual =,..., replcao j=,...,m explaaory varable j ~ error N 0, populao level populao parameer ~N p, depede

10 Idvdual observaoal vecor ε b ε ε I m Cov m m m dvdual desg marx b 0 b b Cov, E, dvdual eec

11 Idvdual covarace srucure ε b dvdual covarace marx m I Cov observaos are correlaed m m m I Cov e.g. radom ercep equal correlaos

12 Sgle group desgs all dvduals a he same expermeal segs m m Cov j ull observaoal vecor j I m V I b ε Cov I V

13 . Esmao ad Predco esmao o populao parameer ad populao respose uco predco o dvdual eecs b, dvdual parameers ad dvdual respose ucos

14 Esmao BLUE: bes lear ubased esmaor o populao parameer does o requre he kowledge o WLS=OLS BLUE: bes lear ubased esmaor o populao respose uco

15 Covarace o he esmaors Cov Var covarace decomposes addvely o» covarace he model whou radom eecs» dsperso o he dvdual parameer 0

16 Predco regular BLUP: bes lear ubased predcor o dvdual eec b b predcor o dvdual respose uco Hederso 959 predcor o dvdual parameer b OLS,

17 MSE o he predcors regular I,..., Cov Var MSE or predco: weghed average o» Bayesa covarace» covarace he model whou radom eecs

18 Predco regular, kow predcor o dvdual parameer MSE o he predcor I,..., Cov Gladz, Plz 98 MSE = Bayesa covarace

19 Predco geeral predcor o dvdual respose uco predcor o dvdual parameer,ols BLUP: bes lear ubased predcor o dvdual eec b b

20 MSE o he predcors geeral I,..., Cov Var MSE or predco: weghed average o» covarace he model whou radom eecs» ad

21 3. Opmal esg exac desg,..., am: choose,, rom desg rego o mmse Cov or Var resp. o mmse Cov esmao or Var predco

22 IMSE crero mmse he Iegraed Mea Squared Error or he respose uco d race d E esmao d race d E predco

23 IMSE crero or esmao d race d race lear cosa! opmal desgs or esmao he model whou radom eecs rema opmal or esmao he model wh radom eecs d race IMSE whou radom eecs

24 IMSE crero or predco lear d race d race d race IMSE whou radom eecs Bayesa IMSE IMSE or predco: weghed average o» Bayesa IMSE crero» IMSE crero he model whou radom eecs

25 Radom ercep radom blocks parallel dvdual curves j j j IMSE or predco m race cosa opmal desgs or esmao he model whou radom eecs rema opmal or predco he model wh radom eecs IMSE whou radom eecs d

26 4. A Smple example dvdual respose: smple lear regresso o =[0,] j j j 0 j dvdual parameer ~ N,, ~ N, depede dvdual curves guea owls = = = 3 = 4

27 IMSE opmal desgs opmal segs a = 0 or = m m» m observaos a = m m IMSE opmal proporos small m observaos a = small large predco / esmao m / m / m m m = 00, m =

28 Ececy ececy o he equ-replcaed desg m = m/.0 ececy = 00, m = 0 small Bayesa opmal desg m = m sgular ececy = 0

29 5. Oulook opmal desgs may deped o dsperso marx» may badly perorm, s msspeced» averaged or mmax crera oher crera, G are more sesve o predco o dvdual eecs b» may resul sgular desgs o-lear respose?...

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