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Combining measurements with deterministic model outputs: predicting ground-level ozone Liu, Zhong 2007

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oe isc mo a auseey ee sceo asis ueecaces  aes gimesay as a su oamesagiesey ee comeemes   wiis asie  make e emeey ese eia e eicaooecoaisSuceemes caee e s oiu- ouuo a ssiy suggesoimacoseis use ie aemeey eseO oe mosima as oe isc mo is aa yie e same ouu wiiu ais w ey a cae"isc"Uike sscamoey  aem  cau e ameamic ocesses ago e emeoies e come oe equao asc sucmics caeac sooimssie a e e1use omecamocay wi  ocomicacomcoa sw i mesIis esiswe a iesie isc mo useic-ma a eieaseso eme i e M (gioCma Mo sciCaya ea (1995 AeemeeMAQSI(Muisca AiQua Simuoaomois sciOaa Im (199e cmicaa mo(CcaeGEOS-CM (Goa EaOei Sysm-Cmisy wcmoe uy o esis suggesie cue ew oAQS (-oAme AiQua Sasas a meoesma ocy  ckgu ( (Gaeea (Mo -i aue ous io oGEOS-CM mo ca u a/www-asaa/cmisy/ogeos/ e  a se- e AQSis e o coeoawou oaiiewe  aogec soues oo iAmecae ca measus   mocause emo aas iAmeca is u o wcis om oeacesemee moy mamauy o coeoie Yeowso (WYis o5 (s io meimosmo om 199  (gu 3-a iGaeea (is ocoeois w ecomwi uaaasIe E Gaeea ( e cue isc mo esma eis 15-35 Mooe isc mo cageuseoc sucas esmas oe acooe o e ome icaa om e sasec o  e oseomw o we ao e isc moouu as moouu simiciisc mo simu e o aiuoogces wiceaisoowe e measumes a oaiaeacmo- sooe sceSo we caocom e moouu wie measumes cysswe caemi wee iscoeoeemoouu a e cameasumesIe issuccoeo we cause sscamo  com e measumeswi moouu  ace eeco Iaio we caaocaa isc moouu ec e o coeoEas (19a Se(19 sesi e iscmoouu  usi sscamo Sacks ea (19amae eeme ouu wi scsc ocesses a cose iues oimi some o oe ouuo a e (use ayesiamo com e io e iu eea eueaiies oe moouumsay ea (use meicmeo  esma e me oeiaequao ia iisc mowe e come oe isc mo sucasMAQSIsomemes may sus woi oose eiaequao -cySo we simy eae isc mo as ack sWe3oy cus oe moouu wiouai i oe eiaequao iose isc moKasiaa a Cmeis ( g ea (as misc moouu imeogicaa eieasciee coes usi aoscaeo a assquas asis omeasumesa mo ouu; mooey emi e coeoeemeasumes om mo so a isc mo ouuGuo a Wae(19ass ese issues wiia sscaame-woOicuiesis e wo oees ea (a eesa e ( iwce yesiamei (mois use com measumes a mo ouuw sc eiisic eese comogigs e scies a simieseee ese  moca use ece emeoiesa caa e isc mo  usi  measu-mes a mo ouu  ae igy "yesiamei"was ose o a e (  aicousio omw oiis esise yesiamei (moscicay  e moose ees a e ( Aeyesiamois ose Sao a Guei (w ke ees a e( s a "ue ueyi ocess" iis scicay coeewi ia a uses a uamoe oeeeue ueyi ocess a e i( Wik a i(ao  auw  use yesiamo  com ioaoom e souese  mois i oa yesiaamewowcees us  com measumes a mo ouu om moao isc mois eeiooe  mo imoouu om mo ao isc mo is oiescauseusuay aeeme oisc mo is useiweaecase ea (uses a yesiamoagi aac commoouu om isc mo ie iacoio  gia mo accu weaecas e yesiaeeme mei (Mmocao aaea  aaacAuge  moca use com measumes wimoouuiwas sigas a samowccao emcoeoaea imoseieaocmac eo  use Kasiaa a Cmeis ( e uy mea-sumes a moouu oe o coeoieas aceUSAwcs  so mau-coeo Iis siae   aaea wca sammoWik aCssie (1999 Wik a y (1999 Wik ea ( Wik (s osesammo seoous aacs sucasmic kaae keesescaasis oyesiae-camo Guias ea (os a sime weugssioaacwcees us  a e  wi mcoeoWe ee is gssioaac a mo maemacay gousyesiasammo ewe ee is yesiasa5mmo a muia moe soe esis is oaas owsCegis e moscicaoeCe3 eses e MCMC aom  e  mo As aoc we e co e ime-me e  mouee sceosWe ao i a sciooe co iCe3We se  mowi a comeisimuos iCe Ie simuoswe iesga eecoa caaooae oe  moious sceiosAs aaea  e  mo Ce5 a Ceesee yesiasammo iua a muia casesCe7 summas a e casa saecosus e moa ua/muia yesiasammoCescicay scusses w we caa e isc mo usi e  a yesiasammoe  soue e ases iCe7 a a e o  use Kasiaa aCmeis ( Ce9 eses aacaoe M mooe m  use e ea ( Ce1eses amic M mowcees e M  a sammois esis cos wi Ce11 iwcwe scuss some  -seacs iassessi ocaa isc mo useicmacoeieasesCeSaCoae a MeiMois ceeses some ckgu kwe oe so aso sacoae suceieses e scica-o oe  moose ees a e ( ees ea ( ees a e (1 oa EsmaooeogmSuose we  a aeom ocess  {s  s  E  wcisoeeacao {s i i = 1  oa geogic gio c   i a si iege e om ocess { is as seco oe7so iisases a  sE((s +  s =  s +  =  sCos +  s = C(w  C(  is a coae o Ioewose coeoeeses ao cao s oy oeige oseo Iaio e a seco oemomes oe om ocess  sa e same a  s oi C( = C (I  w IA I is e o   e coae o C(  is caeisoocAeima quai useisasscse ogmis  esacoae eeo caoWe s +   s = -y(7(  i kwas e ogme cssicaesmaoe ogm ose Mae(19isoai usi e meoomomese esmais1 7( ^ (sis i  I (1w e sum is o   =  { (i i 5  i s   i   a I1is e mosemes i   Auguiase is cs-sicaesmais gy aec ouie e  e squa iesummao wki a Cssie (19eseea mo sesma;11(   I 1E (1  (5^1/7 +   (om ouooe ogmiis caa7( =  wemo gey  7(   may aoweas  ---+   iwccase   ise caeggeeec Mae(19 O oe soues oe ggeeecis measume eoa commoy measumes a assume e gu u  s us some measume eo e ok  Cssie(1993gis mo i aue ggeeece coae ooy e  eu e coae maiigees is si  a symmeicIe ok Si(1999 ceseom scies ae si  coae o a osewca ueas oga measusO com-moy usecoae oose Ma (19s e owiCo =   _  (  ( 1/1/1(11/IG(  1/ 1/ i e se eea o caocoeeewe 9 = (a    a e  si  me eses e ae oomocess  s w    e  e  me is w se coe-ocases wse   iases a  e  smooi  me9co e smooss oe coae o is e moesseoo III as sc Aamowi a Sgu(197Macoae o  e aaage oeCeaicices oesmooi mece i sime we kwcoae oeme s = 1/gis e so-caeeoiacoae oC  ( =  1 a e(-1/ i1    iI = O(3e  gge meis    Iis oious ae coae o -a a oy suie so om es cause we assumee coae  C(  is oy a ooe se    we imacasesiis asoe  assume seco oesoIce yeae so oem s ceia suiaamou oaeioO oe eaiesa mosima  is e  Samoa Gu (199w oaia semi- meic esma oe sosacoae o ai e ogigeogicamaio ae e eaweaaomeoesoameasumes  gi aemcaesma oe ogmaseous mioie coe ogeosscsemew cayso aooa sce - me ocess is aieas (1995199ciums aoem wi a mo wiows meoas es gea (1999wi a coooaacaugese meo may -qui  om a e momo sis   eecOe1so  i ciok a Scis( ca ea( ciok a Scis( e oGea ea (coi e so oem a muia caseees aSmi (ose a css oso samo useieesea ( ees a e ( ees a e ( isaacs aeas oy om i ciumiooe eica measumes as weom i sime iuieasy  ues uoas we as e ease wi wcica imemee Moi aue coooaaca eseeie  secoA Css oso SaMoCaea Cssie (gis aeee summa oe cooosesamo wccome mo ce cause oieYagm (19saa so saocess {sca weass= K (s u ( ^ (w  K(su is a keeosasi  K (s u M   a W(is a owamoo e coae ooe ocess  {s  isC ((s  1 (   =  K (s  1  u (s   uu11 ese a so saocesswe camo  eieassumi e keeo K(su oe owamooocess W(i ocao s gea (1999use e coooaacwi a say e keeo ese so o-cessais(s= K   (u ((5wse coae oisC(si  (  =  K (siu   ( uugea (1999use Gaussiakeeoso ae sui so ocess s a Gaussiacoae oi om gea (1999 ees a Smi (assumee keeois co a cooes so ocess as oose owamooocessis secosws w we cause e aoacoees a Smi ( moe so ocess ii is aacassumes e ese aa mocao ouoeaeieeso om ocesses ae aysicameaeiese oy s us  couce oeaeso ocess so ey  e  a ysicameae oeeso ocess is eseeas a weigeage ocooooese  ocessesEac om ocess s iowcoae me wc om o  ocess (cao 1ae e weig aac eacoe so ocesses ie seaooe oeeso ocess s oi caoSo e coae oe ocess eea o cao s oyoeise   ao oeicaoe sois secogisa iaccou oe so mooees a Smi (We i i ee us  ice e iMCMC aom use is moiSeco3Suose e  so ocesses a   i = 1  K wiCos  3(s  = i ^ ee oeeocess  s caesseas(S = Ei (s(si= i = 1w=11iwcw  is e weig aac so ocess  e aequaoca eee aieg aci e weig wi a keeoas ows = K(s9( w  K(  s is a keeo Soe weig o ocess  e (s s oe caoee cee  a  s e sacoae mecoe  so ocess {  is  9(si oi ceecao s ais w ese  soocesses a cae"cay so"13Sie e coae ee e( (   a  o ( (  isCo ((    (   =  Ce(   e coae ee    a    ie so ocess   ca esseas a cooooe cacoae  Ce((  C( ( i    =  K(   s(   so((   s ^ (e ocess  {}  is so cause e coae ee  i a    s oe cao  1 e keeoca a oe   K(u=  1 - K (3 K ia ga owi ieg1ees a e (usee owi keeo3Ko(u= 1 u 1(1 uwi u = (u 1u a ige a + = ma a} a scaequai ais keeois csecause iis easy  com ais a comcsuowe oekeeo ca useaswee cice okeeois as ima as e wime   wcca a si scaequai suecceaisico eiiis seco Ao iSeco asimuois caieou emi e eecoe cices oe1wi  oecoa meesmaoOucice oe keeoimies aa giiocao 1 a  oy e caso ocess wse ceecao s is wiicis wi ogi  1  a us   wi  aeecoeicoaeIe  ees a Smi ( e ieg( is a-ma aage e ceecao  sm m = 1  M  oose so ocesses a cseas is oa gugoema e keeieg( is eaceMCM(  ;  9=  m-i  E  K(  - 77K-( - 7c (   ( -   (7m=Ie so mo e me 9 oe  so o-cesses is a ooi ceecao s is oca smoo iaees a Smi (assume aai "A" (asisoae mo9  is oceecao  s e sois a is oa gugoe ma emee eiacoae o wi so mee  si a  a e15e   e "A" s wou o- i  = a +  i^ i^E3 ^ 1= a +  i +  + E;9 = ^  (a ^  c^ (A =^n i  7 c71i ( E(7 --M(  E(  71 Ie a mo  1 a   a e m ois ie aa icaco scAs we7-  c3 a maieec oceecaos i a  o a e maieec oe ceecaos i a  o  a 7 a  c  Isscs sigmaiis a maiais useiceaisscamo sucas Amo Icoai iicaaes (os a saiicas egumem e sigmai si a  s a meioo( 1(1 +  i +  e emes ie comoe maia a 1com  k E [  i + 1]oy e emes om ws  1 E  [(k    +1 (k 1  i a 1com  k  E  +   i + ] oy e emesom ws  1 E  [(k  1 1  1 + 1(k  i  i ]  a 1A e oeemes ie sigmaia Iis ecamo  a a   mig we  aiosi-oee me wou   i    c3 c;  a  y  77 771is "A" mois ee cause ies assume a meicoo a  a   oe scewe e a assumiooa  a   cou  a oem cause ese o me su aays siAaea is  moem wi g-asiowceu cs a  s  a siSeco3 es aaom i is so mo3 KgiKgi is a ceageosscaaac saieooiei-e seia me gi i Mae(19ioGKgea Sou Aicami eie Kgie sauiaseec(Uweigs e aie oeao iac-coae wi e se eee cao w ey a ma aaoe se   ieo ese Uweigs a oai mimi e ae oe ieooeoassumi e sacoae is so a kw Gimeasumes oa om eY = (Y(s i   Y(s   acao  (s i  s   e quesois w ece om ae Y aa w si s oe simesKgi aoac oi Kgiassumes  E(Y o= = i = 1   eieoe a so isY(so= ^ wiY ( s i= 117 i e weig oY(s suec e coai  Ei 1 i  = 1Oi-ousYs ois auiaseesmaoY(  So mimi e MSE(measqua eo oY  we oy e mimi i aeaE = E [(Y(s oY (so ]=  7(  so E^ wiy(sii1-   Ewe-y(sis oi KgiuaKgi assumes e meaoe ocesss ooeaes sucas e cooisCo-Kgi is a mui-a eeiooKgiIacce   e sacoae oisesmaemcay  (1o(I simici a ease ocom-os ma Kgi  ee a e a ae oisiaow iis acaee Kgi meois aie ie ckage"geo  i a gg ( awe use  imemee meoiousimuoses a  ases iis esisyesiaMei MoAugKgi is easy  imemeKgi es oa kwogm com i weigsose esmame as  So e ue uceaiy iieoois uesma e simuos iSeco1 moas asaaageMo imagce  om a isc mowi  o1coaescas osooae mic sca owcmeasumes amaemee isc AQM seiis esis ouuiuy o coeo aa sookm e mismaoscas a  a e -caa e simu wcom iwi e  ieoo W is cou   iaac sowi Kgiiis sig awi aissue ia ameawayIcos Kgie  mo a se eesa e ( ees ea ( as we as ees a e( is sig  a Icoms measumes a iscmoouu ia yesiaamewo aees caaooiisc moouu a saecoi ieoo mos ocesses wi ses omismascas ugaueyi ue ocess  {s  s E  } caee "u"  i emeiooe mai Ie cao s  oy s i a e =   w ie caoao s ai e =  3e uyi ue (ocessi ueaemusie  esma e measume ocess  {s s  E  a e iisc moouuocess   {} i e gce mas  we ao esi e ese oisc moouuo-cess {s  s E  seocao  s Ocouee  coeuaocess {s es acay es I ose  e moouwi e u ae mic- scae ei i eseaoasaiego {s e u us sees as e commosis 19ocesses {s a {se yesia  mos e owi maemacas= s+ e(ss= (s+ s =   - sss= a(s+ s(s+ s( = ^  a(ss +  i31 ^113 1 ssis= s ^ (9Ie a mo e measumes eoa moouueoa ie-e oeacoe e measume eo e(s  a iee aiicay si  a asio c e  e moouueo s  a iee a iicay siwi a masio  ag e say coesias  meaa coae maiE(w   is e coae mec- e mocao is     a  (  a ieg o sa  s ogce    We oy oee ao oocess a  ameasuso a gces moouue meaoe ue ueyi ocess is  (s =  s3 w  sis a ooe coois acaos a is e coesicoeicie c We use miaoaugoeo caao  use e miaoca ge sucas 1u 3 ascessae coae maiE ( is coucwi some coaeo  a me c   (See e eous secoaiscussioocoae o iso a socases uguis esiswe use e eoiacoae o(3 we e sowa we  a ocause eiee MaGaussiaoeoiacoae o I mo(9measume  s is moas e u  s us measume eo e(sa moouu s  as s mes a muiica caaomes us ai caaome a(s a om eo sIge we caassume ae caaome a o oe caoo s me  s a  a(s ie moscicao  ke ioaccou eia wi sc caosimiciwe assumea a   a cos ugue sois ceoaie simuosie  asiswe assume a is aooe coois oe cao s  a   s mai coe aso kee  co is aa es osce mucmo a ees a e (suggesa we use a Moe Cao meo ama e ieg imo(9 emewe cou same is  s wiigce    om w o we ca ese is"sami is"  suisem om soe    ca aoma e age oe es oocess eaae samiis wii ( 1Ce3Imemeaooe yesiaMei Mois ceeses e i ow  e  mo(9 usi eGis sami aom ose Gea a Smi (199 wecoie  mowi so sacoae sucewesw w  e mowi so sacoae sucWe ao i aeeio e mo(9 com measumeswi moouu om aeeme oisc mois cao eses w  ioo ie mMCMC io e mo ywe gi a sciooe ckage we  imeme e  moie sceos3 yesiaMei iSo Casee yesiagm ima seeks e sosiooa euw gie  as a sciooeiueaiyese ukw i e om eoaes ( t coeicie c/3eue ueyi ocess    caaome a  a coae m-ec   We use c   s ao oe ue ueyiocess ae so a sami is wiigcesIwe  so a m gcese meioo  is + m    e meiooe measumes   a moouu   a a m sc= {     ese a e w   is e coa maiimo(9 usi e a o e i siooa e uwa aie  ca comseas ows13  a = k I  o(I  a o e Q (1/ ^ AOE ^  a    c  E3(1 3(a( 1(1 3(  agi   a   a ieeI(3 1 E(  ss emuia ai wi meac e a coae maiEWe ke e coms o (   ae(7   iee iosi-oais o - aa=  a e (a c( ^ e maices A o a A1   ^  Ao =^   ^1 ^   ^ /  (ma/A=^  ^ ^ 1- 1           ^ ^ ^  ^  1^ 1^   /  mmImaiA o e com  aii maia a oee-mes a a ImaiA 1e emes iw i a -I   om com+ 1 + (i 1   + 1 + i   a a oeemes a a We ge(3 usi e amao(1E 1 -/ is e coaemaiomeasume eoc e = [e(s i  e(s i   E=  o-  ecoae maio = [S( i    (1  a  E3 = E( e coaemaio  w  I  is e ii maie i oe i coiosio(         a a   aisk   a  a  ae aa e  [ k  i  E1+ (k  a  1 E ^ a   i +  ( i  E (  e= e {-- 1 [  (A  Ei k +  1( a+ E 1/(  E--1 A+   a i + i  E  +   (Ai -1 A + A 1     1 + C^ (3w  i= 3  is e meaco a  C s e oes wiouAs is we kw e aiosiois couga  e asami sio e  coiosioo  coiooa e oeuwme a aie  is ao a awimeac a ae maiESoe  coiosioo  musp (139a  1a  ce -- 1  - 1-  (3wa a E ?  ma e s coai   a  i(3a (3 we ii e qui   a E e  coiosioo  as e owi1(13 a a  ^ M (;---1E^(AEA AiE-1A1 E  = E (AE +  1( a+ E ^ (3Ie io  we  /3M(   ewe cou cim e coiosioo /3 wou (   oeme   ^ (3w  3-^ x --  a  =  E31 -1 /3  e oooacim w owsGiE3 1  13  is iee ooemeSo e coiosioo/3 is  E3a  O E31( 3 1a e{ [( E31(  + ( 3   1 -1 (3  }-We ca e meaa ae o  EA aaacoya Smi (197; Smi (1973e eoiacoae o e o coms  a  a  o  a iee wi iee gamma a gamma iosiosce iee gamma sios e i o1^ 1^ e-  a7=   a -ya - ^ a a 7 i e s a sca mesce  coiosoi oo   gie oe-aes a e  is1   a 1E 3e [- (  - (3  ^ (3w    is e ioi    Ige we   E3 = a g( Cw  C is e Eucase maieee so a samiis a  g(  is e sacoeoo ee  coiosioo  ca weas1 113   (1  9(C -1  e  ( 3(ag(C 1(1(3om (3e cougacy oe iee gamma as a iocomesaaWi aeoiacoeosuce sacoeomaiis  g( C=  e(/ a so (3ca weas^p(  a a -  1 11e i ^ e ^ +^  (e -c -1 (13] us e  coiosioo a  ao s aiee gamma wime= + 1   (^ c 3  (e _1 ( M-  we  es  a sa  coiosio i us use Meos-s aom ose ss (197  same om (3wi  a  Ia e a  a   iee gamma io wi me (s=a  ca=1/A 1a (s=a ca=1/A sce  coiosio oa  a    comeoI (a      IG (s = a  + m/ sca = (A 1 + -1 A-1 ^wi A = (- a -  1 (- a - ^  ac    IG (s =  a +  sca = (A  +  -17 1wi  -y = (- Ao  (-  A i e ioa  7 M(  yies e  coiosiooe caaome a  asa A1  E  M(w =(A i (E ( 1 Ai  +  - 1aC =^ (E ( 1^  +1We  1   acomc e same meioas  (33 yesiaMei isoCasee eous secoeses e  coiosio oa eme a so ue ueyi ocess sio e coiosio a e same e so case ee e sacoae me  (a  a   Imo(e io e"maieec" (a  c3 a a  c3  a iee muia asio wi mea   o a  ees a Smi (ose e so mo( wiougi muciaui e mo Iis seco we  e coiosioo a a  o-  a  77aose we  Y  e sigmaiimo(e me associawi e  sii  a c  o a  7 w ose associawi e  e  i    a    cause e  coiosiooe meassociawi e  si  a agous  ose associawi e  eswe oy gi e ooe  coiosio omeassociawi e e Iao   eses a e oeme as we as e aie e  coiosiooa  is e owi( - 111a  I E IE (7 ^ e ^ [( E(c  -1 (] }e{1 ^ 1-E(711(c ^ 1-}3w E (c  e sacoae maio  a E(7- 77 is e sacoae oe c a  e  so ocessesIe so casee  coiosioo o  is  ea sasio cessi use oe Meos-s aom  uao  as a ockSie    s a aiowi mea a ae mai  u  i coiosioisM(  -1  = Y E (a  77-1 Y +   1= Y E(  1  +  1 a e  coiosioo a is777 oc ^ 715E( ? MI -1  e [  (c Yi ( o-7/- (c 1 7 /5  OuGis sami aom musi Meos-s s  sam-e om e  coiosio wey cao scieia cse3 MCMC Aom same om e sosiooe me ie  mo(9 we use e Gis sami aom ose Gea a Smi31(199 as imemee ees a e (  we cose someaia iaes    as e(   13(1 e e Gis sami isimemeeie owi e sges Sge 1 Gia e oeme a e aie aio oe ue ueyi ocess  {s  a uaasoa   sami is wiieacoe m gcesIis sgeaom same o  is ge usi (3 Sge    =  (a  is uagi /3 a   oaiiSge 1Secogia   is ua (3 Ua  /3 a  a  is easycause ei   coiosio a muia aaiee gamma scwe e  coiosioo  es  a cseso we   use Meos-saom  ua i Sge 3 Iis sgec 7 a a  a easi uagia eoeme sie ei   coiosio a eieaoiee gammaSoiis easy  ua eme a Gis sami aom is ay iicae soa so casese oy ee i ie ua o  iSge 33 Saecois secoiicas w e  moca use ecaooe ueyi ocess auosis usi e aie     u  ao oe ue ueyi ocess ae uoisis oies i e ieoooce eai ie sosioo  u  g  9 i ao oe ue uei ocess amo so a sami is wiigcesOee a E( 9= 9 a E( u=  us e coiomeaaae o  u I  g /3  aE( u  9 =  mu + Eug E9 1 ( 9  mg  a u  g  = E u E ugE9 1E9ue coae maio u is Ea e coae maiee ua   9 is  E  Egu   e ase o E" Ie  mo(9 we   s =  s+  e(s  Soe coiomeaa ae oku  99  aE(k u  g  =  u Eu g E   (g ^ 0,  a u  g  1 ^ = E u E u9E9 1E9uiwce meiooe ii mai I  is e moso  ec33e maisioo ku  isku   =  ^ (3iwc ss a e oeme sucas   9 a   aca amak  I g  kuiw c/ i (i = 1  is e i- MCMC same oa e me3 Eeio Eemeseous seco coie oem ocom measumes ommo sis ma wi a si iume wi ouuom soisc mo Ic e  moca eee com om eemes omeasu iumes a oisc mosimici we coie case osa si measu iume amuie isc mo auge eeio ioo muiemeasu iumes wi  oious ee mo(9 suose  k   k  a ouuom aeeme o isc mo eu a siusacoae maisuose  oaeee mo sis a sami is wiieacgce a e e isc mosimiciwe3assume e mosami is wiieacgce is e same a e isc mo augeeio e m issaigaWe ao assume eacisc mos moouuom gcesee meioo  is  m    As i(3 ei sosioca comseas ows k 11    1 1 7^     Ce 11  1  =     (7    i 1 ai    o-1o -e o-  aa   9i=i=  CI  (k   ( i  (  a i  iAi a(1 E(eae(  ( 3 i= 1isc moi s caaome a i a  i  moouueoae me as i e coae maiomeasume eoe is E  = o - I  a e coae maioe moouueocS ioe i- isc mois E i = a i /e meioomaiA o is( + m    a aomaiA i (i = 1   is m (m e com omaiA o  aii maia e maiemes a a  w   omaiA i (i = 1  s emes omcom+1+(i-1m+(11+(i-1m+a a oeemes a e i oe coiosioo (  1    gi35(Q7  aia ^    Ce    q  iS k  1 ^ 1    a " a  1 ^  c(I   e - -1 [( -  A   E1 (-  A 1 i a-  i Ai  ( -^ E-1 ( - /1= e^ [- (A  A;-  1(  a i +  E-1 i=i( E  +^ i ( i  ai  1Ai + iE -1  i=-1(^+   A 1 iii  ^ 1E 1Ai + E -1   + Ci= 1(3  a  E i e meaa ae o  C e oes wiou ke (3 e  coiosioo  is e owi I oeme a a  ^ EE 1 1 c 1A +^ i iq E1Ai + E -1 i=1=^ E A 1(  a i + E -1 / i=i3e iosioo(a i  i  i ^ 1   isai    M (ei coiosiois(ai^ i  Ei M  ( iw(= ^(Ei1 ( 1(A +  1aC 1  (E1-1 ^(Ai   +  1i 3 ie mMCMCeous seco assume a kwge ie miaesei emeao ss Ioewose coeicie cskwmeio Ge(1995oses e ie mMCMC aow e meioo  auwme e  mowe  k   /3  meioa   k = (O   e ie mMCMCaows  k  w e meiooa oeme a  e37oec same om e i sosioo k  a   k  ais k k i   ace a we  e  i coiosioo k  a   k  Gi  a coiosioisk 97kI oc   71kk= k 71k( 71k1k(kk i e iosiooe meio k  a  77k (k e iosioo   gi k Suose iay e meioo/3 is   ee  ios o ssie ouomes  k iase e mesio o (a "ocase i o (a "a" e ooa " o"a" is 1/ e mscme ca qui aiawe make e a cice cause we " o"a" equayAecosi eie" o"a"we acce/ce mwio a/(1 a e scicaooai eiwIwece m ewe sy wi e cue meio   oeiseemeio k wi  eie +1  o 1 Ie same io e suas e me  gi k  as ie meiocaseusi e us oiGe(1995 e acceae oes o" a "a" a e owi" mom e eous meio k =   a w mesio k= +1 we e ose o e coeicie  1 7E oe coaae coeicie/3 7 w is ose a osasiowi i  q( cause A ie  is oseiee3ooecoeicies e coaoai om  Soe w coeicie cis 13= (13a e acceaeo o k= + 1 isk(Okk   1-a =  mi  ok o(e"a" mom e eous meio k =   a w mesio k= 1 we e  o coeicie om e coeiciec We cose   e scoeicie oe c /3 easois awe aae e coas om weoeoe coos  goea usuay e goeoe cooisa mo ke   iigca aweosAgai e cois 1 a e acceae o o k= 1 isa = mi 1 e(  (k (  }k(31k(k 3Aecosi meio k we ua a oeme  usi Gissami as ie meiocaseISeco3we couca simu-o see w we e ie mMCMC wos wiooio e  moe scussioa sws w  use e ie mMCMC agom  cose e meioo /3aaom caao  usecose e meioocoeicies oe ai caao a(s  Iwe39 a(s= Y(s a Y (si e miaooe cooiacao s ewe cause ie mMCMC  cose e mesioocoeicies O a e iaom is  simi e awie mMCMC is ae cose e meioo   ecue sowa es i e ie mMCMC  cose emeioocoeicies O a we a ai  ioo aio esowa ie a3 yesiaMei MoSowaWe w a  moogm i  e e Coam ( e ogm is oi a/eiua/mei/meicoi e co e s-o  mois ie c "mcmc" a e co so moioo e ie mMCMC is ie c "m-cmc"e co e so  mowi  aie oisooe suic "g" ic "mcmc" is use g e ogmsac is e  "simu" simu e mea-sumes a moouu "mcmc"e maio imeme eMCMC aom"ua"ous o  same me omei coiosioe sciooe maio"mei" i "mcmc" is e owiee3 a ckages "MASS"Usagemei(mmamcamciaeegeomoAumes mosami is ieacgce oe moouu samccoois oe sami is a e mo s-oIsu  a (m + m mai e mws a e coois oe sami is igcese smws a e coois oe mo so samc coois oe uoso w e measu-mes a   ec  moMCMC io ie Gis sami i e "-i ooe Gis sami a e measumes c ee moouuc gege oe miao-e mea s=si  a e owi oio a aowee meais assumeco acss sce1 e meais assume  a oemiaoe coos s= Qo +  / 1 + 13e meais assume  a seco oemiaoecooisA(s= Oo + 91s1 + + sQ+   5s1s como a si wi e me oe coeoo eoio a o oe owi e o"eoiae(1   is e se a  o  is e eme"Gaussiae( /  is e se a  o  is e eme"Ma"[( 1(] -1  ("IG( is e smooi -mea  Ku (  s e moesseooe iki ooee o"mei" wi  a soe owi oec "ssomeaoe coeicie cQ "ss "sosa aooe coeicie c "essomeaoe sacoeoc9 "ess "sosa aooe sacoeoc O "ecosomeaoe saeco "eq1"5% quai oe sosiooe sae-co "eq95% quai oe sosiooe saeco "aessomeaoe ai a muiica mea a   "aess "sosa aooe ai a mui-ica me a a   "sigmaessomeaoe measume eoae -meo "sigmaess "sosa aooe measume eoae meo "sigmaessomeaoe moouueoae -me  "sigmaess "sosa aooe moouueoae me ce sciooous o i "ua" is e owi "ua(" ge MCMC same om e  coiosioo e aumes ois oiye ao oe ue ueyi ocess  {s  amo-so a sami is wiigces e coa maiamoso a sami iswiigcesiomea iomeaoe coeicie c iosoeiee oe ioae maioe coeiciecsigmaoeiee oe sacoae maioue uei ocess { "uae(" ge MCMC same om e  coiosiooe aumes ois oie sia oe ue ueyi ocessee es oe coae me  e  om e e-ous MCMC iosee Eucase maieea e caoi moso a sami is wiigces momoso a sami is wiigcescomo o oe e ssie cices e coae -o "eoia"Gaussia a "ma" "uasigma("ge MCMC same om e  coiosiooo a  e e aumes ois oia e measumes cee moouucmosami is ieacgce oe moou  momoso a sami is wiigces; m mogcesaai as mea;  muiica as me A maiA  as sciSeco3 "uaa"e MCMC same om e  coios-iooa a   e aumes ois oiesame as ie o"uasigma("soemAsigma e ouueoae me ysame as ie o"uasigma("mA same as ie ouasigma( "ua("ge MCMC same om e  coios-ioo   e aumes ois oi e coa maiamoso a sami iswiigcesa e same as ie o"uasigma("sigma sigmaee ouueoae me 1 a mea-sume eoae meo - sigma3oeiee oe sacoae maioue uyi ocess {ie mMCMC is use  e ae secoia yesiaamewoIis o simi e swise gssioicssicaamewoA e o i"ua" a e same as ie  moscaIe o"mei("we  sci e"ge"wcis esma e ie mMCMCe o"me(" oy s e meiooe coeicie ie meaoueyi ue ocessMo i oe sowa ca u iu(Ces e yesiaMeiMois ceeses aeei simuos oe  mouea e osceos aassess e meow ccki e co o We giwi e so  mo o isc moao measu iumeewe mo o e case wi aeemeoisc moWe i a simuos aioos aie mMCMC io e  mo Iaio ses a  seoeissues sucas w e esmaoocoae meca imo emosi you a e eecocosiwi  iso  mo1 A Si isc Mois simuo wcassumes a so ue ueyi ocesss ooses is e MCMC aom imemei e mo Secoicoms e eco oKgi wi ose oe moSimuoSeisIe simuo we   mosis a 1 umosiswse ses a   ec e moaie gcesiases om  5uge sequee  1 3 5  ceoucomoe we oy  o sami i wiieacgcee coois oe aie/uie so a samiis wiigces a geu o[-55] [-55]gu1 c e cao osis (moa umo a samiiseaccomoosis a sami iswe ge 5iee seoe measumes a moouu accoi e  mo(9e measumes geae 1 ueasuso wi useie MCMC eco o As e mogces iaseswe iesga ces iecoaccucy a cogeo e ecoiea aous c  (95%9%7% %I 9we e meaoe ue ueyi ocess E [s  = s= A+ 31s1 + /3 ^ (1s1s  i e coois ocao sWe assume  {s  s aeo-iacoae sucAe same mewe gi  13 a ioasiowi mea  = (111a agocoae maiwiagoemes (111 e coae me  a  a   iee iosio;  a  s aiee gamma iosiowi s =  sca =  w   s a gamma iosiowis = 3sca =  e caaome a a    ie aiosio wi mea k a =  /  = 1 a aesa a = 1 1  1e om aes    a a  iicaaiee iee gamma sio wi s = 3 a sca = 1Usi e MCMC aom  same om e i sosi-ooa mewe ke 1Gis sami io (e 1i "-i wcis eug eu coeee as swig-u 3 a gu  ais u sie comomes a a cessi a esees oio wou  gay miesco oousimuose sowa useious is aieoi (/eiua/mei/meicoi   ee ie-e caooouisSimuosuses 1a 3 ese esmaosus e me-e eses e SS (sum osquaecoeoe 1ueasusoOusus a e owi ooeao-^ -^ ^ ^ cooigu 1cao o1 ( mo 1   ec sis ais sameom u 5gcesMosis (s sis wises   ec +1e is om gces 3-1is311- is -3is531-5is e esmaooa  a  /3 a  cse  eiue es seogu  wcsws e ue ueyi ocess esus e  ecoie case o5gceswe casee e eco a qui cse  e ue es e esmas oe coae me  9 =  (a  a asoygoo we e  e  me  os mucmo icu esma ae  si  me a e sosioigu55 sws     wi se e a a sigca aoie SS om o simuse ae e sws aai mo gces cases e age SSe  mo e age is como5ieese Ieac e SS es cessa case ia mocsoas e moces iaseswe aoom ecasi e ie SS may s e  e samiaoeee gese e 5 sws e SSoai usi e ue es oe me ie ecIs oaaaagee SS eis eces aays case mocay as e mogces iases(See se a  eme e sws ae emcacoge o e  e-ccomes cse  e miwwe  a asoy emoces (aas1weais e case wwe socessusi gie uci o iosesiaoKgi coge o s ou  mucsmaeaae  ecew simu a aiae om e isc mo(so ae o meo com"ao asu wou  aicisieas is we kwKgi uesmas e ueaiy ii saeco51gus 3a 5 sw e MCMC sames om sosi-o oa   a  a   ie case o5gcesom ese eguswe casee e Maocicoees aea w ioe 1Esmas oa a   wi e m omoouuaiee ue es a a = 5 a  =  5Com 5 a eages oe somea a sa aoe ages acomoe 5segeie simuosSie ise is e esmas ome a a    e is  uassocia e m iis eEacoese me is a scamoces a s  s 51 1  1 51 1 5  5 1 5 3 5  5 5 55  5 Imo Coae meEsmase 3 sws aauge someao  ge cse e uee as e mogces iases om  5 e sos aomai  e ewi 5gcesamaywe  e  iuicie sami is icse omi  o aeIoewoswe   eugioaoaue sma scaocess a e accu esma e ogm e5e  Esmas oe coeicies /3 = (/3 /3/3wi e m- omoouu aiee ue es a   = 5  1 = 9a /3  = 3 Com 7 a e ages osomea a s aoe ages a comoe 5segeie simuosSie is e is e esmas ome/3/3 e is  uassocia e m iis eEacoese me is a scamoces  s (31 s 35   1 13 75  131 11 77  13    133    135    13/3131 131 1313131acoecwe cay oua sma simuos wi  mosis a 5sami is igces as ie eous simuo w-e icos e eous casewe coe  sami is ia sma giogi [-] [-]Ee a-ao we ge ese  iecise e same way as ie eoussimuo e 7 sws e sus e esma oe coaemeom aewe casee ae sa eooesma  is cesigca comwi e su ie 3eai suo  oucoec53e 3Esmas oe coae me i=  (a  wi em omoouu aiee ue es a  a =  1  =  5Com 5 a e ages osomea a sa aoe ages a comoe 5segeie simuosSie is e is e esmas ome  a a    e is uassocia e m iis eEacoese me isa scamoces Q s  s 1  1 1 1 31  1 1 35 9  13 33 31 3 1 33  175 1  5 3CosioOusimuosus i  ses a weaksses ie  moSes e  mocaesma e caaome oe moouu wegia asoe momo sis agces Ige iasi e mogces imos saec-oaccucy aumosis Esmas oe coeicies oe ocess meaa  goo50ue es- - - ieoo meiI^ I ^ ^ ^  ^ 1umosisgu  Saeco 1 umosis  usi  moie case o5gces e  ecgis mucmo asc esmas oe ecoueaiy aes e cssicaKgi aacWeaksses e  moes esma e coae me (o a  we is oeisa eo uess aaciae mosami is a  cse  o ae (As seeseeom eeous seco i a mosucis io cse omies case eisa eo suiay55Gis sami io^  ^  ^  ^  ^ 1Gis sami iogu 3MCMC Gis same oe ai a muiica ca-aomea a    scie case o5gcese cue  mo(9es i mioaoe o uo se Kasiaa a Cmeis(  e ameasumes a moouua uy wca my coe Eei e  mo emaceom sce - me es wou  sieas iwou ee -iay gase   oweacss me as we as sceO osuceeio is e mic M mowe ese iCe15Gis sami ioGis sami ioGis sami iogu  MCMC Gis same ocoeicies ie case o5gcese comoeimse e  momi i ac-caaesms om e e ie a e mesiosacoae maices e mes ieacGis samiio eme mo sis a 1 gces wisami is ieaca  a sacoae maiwi + 1 = ws a comMCMC es o a"ee yesia as mig i  sugges i  egaeo57Gis sami ioiacCO1^ i^ i^  ^  ^  ^  ^ 1Gis sami ioigu 5MCMC Gis same ocoae me   =  (a  ie case o5gcesEeme SesSimuoseisis secoeses a simuos iusa e use oM mo com measumes wi moouu om mo ao iisc mo make is simuos cse e a caseweusecao om a sese Kasiaa a Cmeis (g ea (a emeasumes come om mo sis("so"a mo ouuom isc moIc we use5  ^  ^  ^  ^ 10--a _o  -I^ i^ ^ I^ 1 ^  ^  ^  ^ 1Gis sami iocisIcaCOGis sami iogu  MCMC Gis same oeoae    a o - ie caseo5gcesoy a sueoese so a gces iousimuo wi 5moisis eaas so a 1 umosissimiciwe assume oy o isc mo iousimuos yieiouui gces a eacoem s o sami isgu 7sws e cao oe sis (mouo a e samiis wiigcese meaoe ue ueyi om ocess   is a mia-591^ i-1 ^ -9 ^ - ^ -7gu 7cao o15sis (5mo 1   ec a gcesSoA; sis wi sis   ec +; gcescsEacgce s o sami is ii e as is ei igesy-ase  igesooe cooisE [s  =  /-s =  +131s1 + + /33+ + s1  i e coois agecao s is seco gemiameaooe coois is o ge geemeao(1useie eous simuo is mo comicacice i us  see w we e M mowos  maewcomicae meaoIis simuo we ge 15 iee seIay weie1io oe MCMC aom u ii coeeMucesus oaiaewe eeee moio 1wi a "-i oo1 Ie case oeeme iscmoe a mo me ie M mo e come oM moquis a muceMaoci accoeeeSimuosuse gis e esmaes e me a e 9eSS (sum osquaecoeoe 1 uosoese sussuggese owi cosio Esmas oe ai a muiica ases  iisc mo a qui accu (e  e esma oe  si  me a  is  cse  e ue ew aoe  e  me  is  we e ue ees e wiii 9 c iea Esmas oo - 5 is asoy accuwe e esma oa ieee e ue e  qui a mai e M mogis eeco aKgimeasuSScause e caaome a esma wemea ieec ae moouus  ace ee-coIsummae M moseems  wo qui we wwe  moao isc moauge esma oag i is  cse e ue e3 ie me so caseis simuoioes  so a 5gcesEacgce soy o sami i  ce e comoe A so(mo sisas we as sami is a geu o[-55] [-55]e meaooe ueyi ue ocess isE [s  =  s = /3o + /31s1wi ue me = (1153 e ue me oeeoiacoae oa  a =  1 a  =  5e caaome a a = 5 a  =  5e aes oe measumeeoa moouueoa c e =  a     scWesimu 15 iee seigu sws e MCMC oa sgm oe meio ke 1sws e esmaosusey aus  make e owioeao e Maoci k coees  e ue meio k =  (gu e esmas o o 1 e ue es oous me a wiie yesiaceiea ee ose ooa     Gis sami io                ^ 5^ meioo 7 gu  e ueo e meio k oe coeicie  3as a -ooe moMCMC ioe weo sgm oesoMCMC sames o kyesiaMei isoCaseIEquao( e wi  s   cse ese e so ocess  coooo so ocessesA mimaquime    eu e si ss oe coae maiYei  is sma eo cao wi   iau wcs-o ocesses cee eeeme coae eeese ocao wi  Soi  is o sma eo ma s wi aeaie coae maioe so ocesssui imecaoems wis coae maiis iee ea e keooe so ocessOe oei  is o ge coae eeo caocou ao  o sma cause e keeois o aa  M  i(7is g eug Iacce  M  cao cseo g causeoe comoe is simuoses e eecoi  ima ies cuses osaecoeoas we as oeaccucy oe a a   esmase 11 a 1ese e ecoa esmaosuseysw aas  as   is o sma e SS a esmas oa a   a mucewe we cse  is o gsaymo aice e ue wiuse simu e eSS is mucgge Aoe sa eooesma oa a   amucggewi sma   (% oe ue   ae esma wi agge   I  is cseo smasayss a oe ue wiuse simue ee MCMC aom wi "cs causee coae maicomes siu So as a coea sagywecomme cosi a e    e iis camea oe seeeo is caae es oe ago acss egio acice o  is ss ke  oce a w ocom osie sacoae mai a imo mecay see  SS (Sum osquaecoeooKgi a e mowi e mogcesSie e  is simu eis  uassocia e m iis ese Ki Oces ces 1ces  ces 3ces 5ces1 11711 7 753 5 5 71 1  3 7  7393 3 1 115 17 95  7 119 773 737 73 73  75 1 3 97 73  1 1359 593 9 5 5 53 517 15  1 7 7   1 91 939   799 1159 1 591 9 577 1 51 11 1 1177 1 1 911 311 19 53 575 5 553 5131 17 1 9 91 93 7713 1 717 793 1  5 591 1951 1 133 137 1 15 1915 1 9 7 7  71 7 151 13 1 1179 17 9517 19   77 73 79 5791 17 9 3 911 797 7319 1131 73 797 73 1 9  993  3   79 731 97 19 13 15511 1313 19 13  959  791 7  13 5 739     11 77 7579 3   11 99 919 3 7  7 1 11 119 1175 17 91  3511 1137 1173 1 1119 1 1353 75 73 733  7 117  5 13 75 7 73 15 135 1339 1 117 93 731 1575 1173 117313 1 11 93 1 13 17 935 9 93 533 1 1 15 1 1 1113 13 1 939 1 77 77 335 153 3 77 75 719 7 73 1713 75 73 759   5137 1 1 779 799 7 73 15 5 71    39 75 173 171 1 1799 15 13 15 1 119 1957 91 1 1 93 1 1 9  1 13 757 731 733    19333  1  7 75 13 7 7 759 797 793 7 11 79 9 7 75 7  15 1 95791 9 91 7 39 137 1391 11 1 11 939 15 3 77 7 9 9  13 7 7 5 9 55 1137 11 953 5  795 733mea 17 93 9 1   77e 5e SS we ue es oe me (a  Q   ause aiswe use e coiomeaoe uie measumesseoe aie measumes  ecae 1 uie s-oSie e  is simu e is  uassocia e miis ese ces 1ces  ces 3ces 5ces1 715  571  7 7  7 9 3793 91   7 59  3 9 55 595 1    5 537 53 5  517 9 799 717   751 7   79 51 51 5 5 5311 7 71 55 5 111 59 55 3 5 11 959 9 75 1 5913 3 1 57 5 5531 91  5  51515 9 9  3 1 57 5 59 57 717  9 5 7 1 5 5 1 3 51319 7 775 7 57  77 7 1 551 51 1 997 1 711 51 7 757 595  533 53 5 1 1 9 7 5  1  77 3  591  9  7  5 1137 11 79 733 5 1 57  5 5 9 9 5 59 553 3 3 595  931 9    733 9 597 57  33 9  7 53 3 737  5 53 35 773 1   5553   7 7 3937 577 5 5 511 5313 579 537 55 5 739 1 5 1 713 791 795 75   571 93 93 551 555 7 7 5 599 5 3 713 713 737 5 517 71 71 71  9  577 5 5 1  9 1 75 7 7 715 71 513 5 9 5   39 9 55 519 7 5 1 75  55 mea 735  1 57 5e  Coge o oe ce ieae simuos iSeco1wi  mosis a u 5gces ec1 umosise comis e micogeo oe ce ieakgi ce ces 1ces  ces 3ces 5ces95% 37  91 9% 9% 973% 959 37 59     91%   73 79 7% 7% 7    7%   71% 1% 33 57 57 5% 55 59% 1%  3% 39 39 37 e 7Esmas a seo mosis a 5sami ise a  sami is icse omi  o ae e agesa como5se ue es a  a =  1a  =  5Sie is e is e esmas ome  a  a    e is  uassocia e m iis eagesomeaagesosa^ 97^ ^ ^ 7e  meesmas ie simuos oeemes o-isc mo iSeco Com 3-gi e ages osomea a sa ao  a  i =  1 e caaome- oe moouuo isc mo aoi a  a a eaes oo moouueoocessese ages a como15 se Sie is e is e esmas omee is uassocia e m iis eEacoese me isa scame ue e mea sa 5 9 i 5 5 a    3 39 Q 1 11  5 73 91  5 1 59/1 9 9 17  3 3 1    1 11  1 31 ae  33 13-   Q (5  51 91e 9SS oe  moa Kgi ie simuoomui-isc moWe  5mosis a 1 uoose a  gces eacoem  o sami is iiSiee  is simu e is  uassocia e m iis eseKgi 1 7 333 7 7993 9 59 5 95 5  1 7397 5 559 551 9 9 5791 793 5711 1 1  5913 979 51 3 515 9 5mea 5 57e 1 Esmas ie so case usi ie m mo e "esmas" a "sa eo a ages oaiom 15iee se Sie is e is e esmas omeeis  uassocia e m iis eEacoese meis a scame ue e Esma Sa Eok  9 a 5 5 51 5  a 1 1  5 9 i  1 9 7A 1 1  5 51 1 3 3 U(539571e 11SSs wi e cices o  iso  moCom gi e SSs e os oe ue wigea e  oe csewiie so  moSie e  is simu e is  uassocia e m iis ese 17 13 1 5 1 79 7   173 39 31 9 3 513 3 3 7 59  3 3 3 3 5 11 79  5 173   1 31 717 37 37 5 19 5 15 13 7  39 9 3  59 1331  5 9 73 11  35 37 51 31 39  5 59 713 13  5 57 31 37 39 31 9 715 75 7 77 7 mea   77 9 797e 1 Esmas oa a   i es o  iso mo Com 5 gi e ages osomea a saaoe ages a comoe 15 se geiesimuose ue es a a = 5a  =  5 Sie is eis e esmas omee is  uassocia e miis eEacoese me is a sca(ue /(cse a s  s17 5 33  13 53 3  1 51 31  5 5 3 5  51 13 7 573Ce5A w UaSamMoe  mocaoawi mcoeoie  oaaea  e  mo we coia gssiomo e sois ceis oaas owsSeco5 ews a o-sagssiomo Seco5 eses aac eeiooe o-sagssiomo seoe e sus seeiSeco5Seco5  mo gous a sammoia yesiaamewoe  asis sus a cosio a iSeco75 o-Sagssiois secoews e o-sagssiomoose Guiasea ( e so acoeoeee uy measumesa moouuaeacsomakes suca moseem  gu5 sws ose coeo   ggea5 amossoii a aoeee measumes a moouu7e moie o-sagssiooce oseGuias ea (s e measumes {}  e moouu{M(}  = c+aM(+   1  ^ (5wi aucoesia  = -1  + e ^ (5gOO 3 ^  ^  ^ ^  aos coeocoeicies eemeasumes a moouugu 5sgm oaos coeocoeicies eeuymeasumes a moouue 7soe sia e aucoeomoi sas e owi75{ 1 imo1= i;mi (imo ^ iagssiomo11e= ^ aim( ^ E ^ (5i=i =   ^ 11e mo (5 (5a (5a e same a sow ecoeicies a soscic e measumes a moouua ae uy omsooa us ey  a soau-gssi suc{  } is aA ocess ie    = C ^ -i  + Ew e     (7  iee a iicaye augssi -me a  i    Ma auo omico  c simiciSomecoais a cessa oe es oe me ois moioae momai soemeocesses ie A1mowi  i 1 a soAssumi e {  }  aA1augssi suc os comosimici ae ssieeee oasmWe ao  ieaA suc e {  }e cassus  imoa us  use A1ugu7is esisowi Guias ea ( we mo(5 usigeassquas as ose ea (199   i aA1ocessIe moouucaus e msuc oemeasumes  we emo(5wou  eug we mosoe mee measumes wi s  some msuc ae moouui  cauais  saye sia {e  } wi  meaSoe seco sis  mo(5 e coas iis moa iicao oe 1uWe ao ieiicao oe  ue cassus  imoSoiowemewe cose iicao oe 1ue sia oe A1ocess  {}E  (7iee aiicayMo (5-5a esequeiay a ieeese omo cae use case measumesSuose aeacso e ai  a measumes a moouumes  =1   mes  = +1 + oy e moouuis aie ae goais  case measume  a me o  somo (5-5a e oaiesma   a 1 = 1 1e caso O is ee owiO = a + 77w11 t =  - +^ d-rn  ( ^ (5t =+ 1+Auge o-sgssioa is easy  imemeis osaaages ies i a sacoeoeesoWe mo (5-5aeacsoieeus wecaoy case measume so a measumes ie s aeesma e quisi coeiciesIoewosicaoow se acss sce  cas es oso wious  ei  om igo wi a s Secoe o-sgssiooce oy gis i cas wioua iicaooeiueaiies ass e saaage oe o-sgssio we cosia sime ac aacwcKges meesmas (Ca  i acss sce  gees em aso wioumeasumesAeaii e e oouac aac we ass e seco s-aaage  eei i a yesiasammo e es eyesiacia ae eacomes ae iceogacomee ce ec iea oe casasaecocae oaiom eiMCMC sosamesacoie comocos75 o-sagssiowi Kgiis secoeses aac aacwcis ae  oy case measumes ao say ece measumes aose -cao wiousc measumes we mo (5a (5ae so wi measumesee esmas ome a ca a i =   11a ieoacao wioumeasumes Kgi as sciSeco(3 We uses e eoiao(3 moe sacoaeMo comecices oe sacoae owi  coii woAe cao wioumeasumes wi moouu we e Kgi ieoes oe me a c a a i =  11ewe caug ese me io u (5 oaisaeco oe measumes5 A yesiaecaSamMoe ac aacie eous secois "se-coc" causei mo (5-5 geesmas {a i ig eisacoeo eiuses Kgi  ieo e esmam-ees ae cao wioumeasumes assumi me ae so a say coe79Aesaaage oe ac aacis aii  omeasus oe ueaiies associawi e cas oecoKasse ea (use a simio-sgssiomo ieo1coeo owes EuIis  e auo a agssiomowi 1as e semo ouua oee aes as co-asee sia a ieousi Kgie aaciKasse ea (s e same weakss as e ac aace-seeie eous seco aisiassumes e sia a sayiee  e mo usi oi assqua meoa euses Kgi  ieo e sia aoecaoMoo emouseiKasse ea (es i mcoeocause e  a yeay ages o1coeo a  mucmcoeo esicy saki e acaacie eous secoa aoKasse ea ( yie sammois secoeses a yesiae-casammoaassumes me ae so imo (5a (5a say coeGaussiaocessese yesiasammos e owi maemaca a8 C8M8,  =  1 ^ ( 1 ^ 7 ^ +  711 ^ Ca = (a i c a    M( a E a c = (c1 cm M(1 1 Ec= (7171 1= (711 ^ 71 ^M(/ 71E 71 (   M(  EE  iee a iicaymes  = 1   asis s = si s=  ( 1- = (1- Ea = a a e(/A a E= o -c e(/AE =  (77 e(/A  i = 1 1= (y/- 17 i = 1 ^ 1EE e e(/A ^ (5i e momo sis   e mou a    eEucase maieesoc  a  c a  E7 meio Imo(5  s  s caoa    mee me-coas ame   a  i  = ee   mo1= i wi  = 1i = 1 ese me-coas a e same as eiicao  m(  i(5 Aeacme    e sia aecao a ao say coe e sacoeois isooca scie aeoiacoeoo Aeaccao s esia    aA1me sees wi meaWe make e owi assumio is yesiasammo e measumes a moouua ay  e augssi me  is co acss soSeco11 s mo scussioauis assumio e msacoeois seea ocess  {si msais see ie coeoca weasocosaa mcoeooaisemcoeoes ce osce a e sacoe-omai e same omeSeco11 scuss  wo ase is assumio e sacoeoeemeasumes ae so ca ei e moouua e sacoeoeee coeicies a siaSeco7 ses is assumioiou asisWe use e Gis sami aom ose Gea a Smi(199  e yesiasammo(5 e key  makeGis sami wo eicie is  w mo(5imaiais Aa+Mc+ = 7 1+  + -y i +  Ea   M(/-aEac t  M( c E c -y   M(i yi ^ i = 11E    M(  I1 Ee ^ (5I1  i aii maiwi meio (1  ( 1a E  ise sacoae maiosia    acss sce aeacme  e measume cis as  = ( O1O O a e c   as  = (  ^    emeasumes a aaeie oeocao a eieoeomeSoe measumes om e cao ae sameme a   eacoe ais w we gee Kckeocsuc e ae maiosia  E imo(5 e mai oe moouuis   MM 1  M =  MM1  - MIe mai M e ws om  ( + 1     a agomaiomeio =1   e emes ieacagomaia e measumes om e cao ame    e maiA s e same suc as  M We ^ 1A =^1 ^ ^ ^   Ie mai A e ws om  (1 + 1     aiimaiomeio = 1 e mai  s meio  1  Aeacw ii =  1  1  e eme acomi is    a e eme acomi + is 1A e oeemes ie mai  a e mai 1 is1^    o^  11 1  =  1^     ^   1is mais meio  1  e ws om  (1 + 1   (=1 -  aii maiomeiooy  mo1= 1A e oeemes ie mai  a  e maices(i =  1  e same meio as mai 1mai (i =  1e ws om  (1 + 1     (= 1    aii maiomeio 77oy   mo1= iA e oeemes ie mai  a = Aa Mc  a  =  17i  ee i oc =   is e owiOc  EE a  IEEE 11e[- Aa - Mc- ^ (Ii  E -1- [ -  Aa - Mc- 1](5e iees aue mecas a eco a seoeiMaoCiMoe Cao (MCMCsames ge eGis sami aomaaom as imemeeis iwe cose some aia iaes a e mee ieaciooe aome me a ua ge aom same om eicoiosio gie  a oemees om e eous io comoeicieyeacoe mec  ac  a -y  -y i is uaas a ockcomesswe se coiosio eacoe meom (5 (5 e ioa  coiosio o a  aaiaEa   M (EaaiaEaMA E E M( aEaEa =^ + A(/ _i  E   -i  ]  1a = Ea [A  (  i E E -  7(- Mc-A  (I i  EE -1 + Ea   ]  ^ (5e ioa  coiosio oc ac  e  Ec   M(  EcEc M, M,  E E t M ^ Ec Ei - + M i E E-1 ]  1c =  Ec [M i  E -1 - Aa-M i +  (5e ioa  coiosio o ^ i = 1 1 a7i1I- 7o E "M(  E- yi-y i^ E  M, A     t M Gu i  E  =^ (i1  EE1= E 7 i -1  EE1  (0  Aa -  Mc-+  (5e ioa  coiosio o a a  uaasio wi e owi sgao ^ ao  /uaoEaa ^ aof = [ ci +  E 11]-1ao =  [a E 11 + 1I   o ^ (511 i a comeiowi a e emes a 1 o a  3eioa coioae o ae  coiosio o c(i = 1  1 a aossame as (51oy aci  a Ea wi cEa -y a K coesie ioa  coiosio oaa  iee gammasio wi e owi s( oa1 ^ (aa 1 e  (  ^ 1   7?c  ia 3a Aa[ ^ (c  -ai ^pCa = a + = [1/Q + - 1 a (e(/A a -1  (a  a ^ (5We cao a couga ioe meA aso i coiosioes  a csewe we A a  a ac(/A a-1e -1  (a  a  (e(/ a  1 a  ^ (53 oaia om same om e a siooA we  use e Meos-s aom ose Meos ea (1953a ss (197e coiosio oa c Aa o -1yi(i = 1 1 a  simi c a a  a We oy e ace  awi  c  a y  Ec  coesi i(5 a (53e ioa coiosio oaa  iee gammasio wi e owi si "  I a CAEi- (c ^ e ^ /31G1  1a = a +1(3 = [11 + (e(e(/AE-1e=11Ca /  C (C -a-1  e(5E i e sia cae cao ame    As wi  a we use Meos-ss aom  oaia om same oA  We9Ao" ^ ic( AE -1  1 (e(e(  AE i e} (55 ua    i oi assqua (Oesma gioem-e is useiaoa om same om i coiosioWe  is i comosimicii a couga io  is  icu w i i oi assqua esmaois easye maiasois ae ae oe coiosioo  is sma eug  eaas  cause oe e same si ( 1 e O esma o  is ^   5 i  i7iS-1=^=^E(5w   is e mai o  imo(5a  3 = ee  mo1=   w  i  = 1AeacioiGis samie casoecois oaiiai waye casoecoisO = a+  c M  + 1  =    _i  + ^ 7i + Ei=1E is a om same geom M( E E ^ (5791M  i e comeasumes om a e so ame   c  e sia ame    O e casoecoame  Aoseso w e sc measumes a aie u me    a  =  + I - +   a e casAose so w e is sc measume a = 1   a e ecoe meaose so wioumeasumes ca say ec emees aso wi measumeye ce ieaoe casoecois oai ki e quais oa eiMCMC sames9CeMuia SamMo e  moiCea e yesiasammoiCe5 a ua moaise ses iese moa ua aeswe iaccee mo so caco e coeo omo ao uIis ao ssiee isc mo  ge muia ouuemeGmia Mass (sc e Ui oWasmesoscas-e eeme cas sysm oe cic es issysm cage m a sea suace essu ae samemee muia gssiooem s eseeei  owa k (19 Mee a k (19 owa k (19Cs ea ( eIgeo-sscsa we kwoieoa muia saocess is e so-caeco-Kgi aacsc Wackeage(199Co-Kgi is a muia eeiooe Kgiaac we ke Kgico-Kgi is  a samowc93cao e mcoeoia ameawaye moce  omuia u ecois Maia aGoo (1993 owea (199;  a k (1997 Suea (199;k ea ( Sci a Gea ( Gea ea ( ece ie oks   a k ( ee ea (o eee summaes oous muia mo useie s-asscswe ma omuia mo ose assumee ses a my ieeIsome casesis assumioiscause e  s emoy oyeay ageso e is mucmcoeoIoecasessome emi asis se  mo e mcoeo usi e muiamois ceeses a muia mowcis aeeiooe ua sammooseiCe5Iioos saa mcoeo is muia mois i iayesiaamewo ioe ea e ueaiy oe cas asaecoe sois ceis oaas owsSeco1 eses e i oe muia sammo Secoeses e MCMC aom  is muia sammo91 Muia SamMois secoeses e moscicao a  coiosi-o oa e me e imeme e MCMC aomAme   a so s e mos e owi    = /3 M + 1  = i+ + C =1  =1  E t M( E  iee a iicay ^ (1  q  1 i e measumes co q us a  M a  (+1  1e coiee  a   moouu  q usIis cessa a = q e coa   is a comeiomwccai m oeaes i  casoecemeasumeseme  cai m wcis  casoece o coeoe mai E is ecoae maio q use so-caeco-gioomaiigeo-sscse au-gssiocoeicie mai  is omeio  q  qe coeicies O s a  ye  aeaccao s  a maices omeioq  (+  1a  q m scEaceme oe mai /3  a -y95a say coeacss soaiswe ( 13i 1       M(AiEs= aQi e( Ai=  1 7  7 q  =   7 ("Y i7 ^ i  "  y7= ^ e(/ii = 1q= 1m ^ (Saocesses {   } (i = 1  q =      a {-y   }  (i = 1  q=1  ma assume  eoiasacoeoowe ese saocesses   1 a   1  iee iosioWe use e Gis sami aom  mo (1a(We w mo(1ia mai  make e MCMC aommo eiciee mai is e owi= M  + =-ycc t  M(OI  EE (3e meiooii mai I  i  11 e mea-sumes c   e scki c  O (= 1-  Ioewos O = (7   q1   7 1   q1  17  wc9is e measumes o q us so ame    Imo(3 we  e coeicies c=^  ^  ^   1 i1  - 1^   i3  1  1q  a= (71 71 ^  7i 7   m 1   q   e coeicie=  1 q= 1 k = 1-  is e eeco moouuoe i- measume aso k  a  iok is e iee oei- measume aso k Iiiewe caaae e emes oc  Q a y iaia oee aso  e scic oea is awe caeasi w e coae maioe coeiciesa  7  ia ock ago swie  seco Imo(3 e moouu M  is maiomeio   (+  1 ecoa mai  is omeio   m e maiomeasu-me  M  is e scki e maices  M  = 1   wsEacmai M  is omeio     (+  1a iis e scki emaices  m i i  = 1  wsm i i a agoock maiomeio  q  (+  1 e w c oe agoomai m 1is (Mo  ^  ^   M  1    M1 =  1 coesi e ieeM1    i  1  coas aso1 ame    emai  s e same suc as M ee ai meio a o (1  m97e i oo  is e owiy   EE oc II E -1e  (1 [ M/3(I E -1 [M 13 y]MCMC Aom use e Gis sami aomwe e  e  coosio oa e mee keoooeme 13y  E a   is (e ioa  coiosi-o oa e owi13 E  M( o EO o  E     E 7M(i E [E i  m  (/ E i A -]  1i  = E[E i is M  (I  ^ ( y e iomea  o is e scki c=  (u   u oi = 1 q  a  =      e emesic  o   a iicacause we assume e iomeaoA o ise same aeacso e ioae o[3 is E= ag(E    E   E q  EacmaiEo i is e sacoae maioc      7 39cause e saocesses ocoeicies  3  a iee oeacoeso E is a agoock maio   (+  1ockse ioa  coiosio o-y a e owi711 1 yE-y M(u- E-y-y1/17E 7   O  EE -yM(7E7Ey 1 (I Ei] -1y =E7 [E-1 7 +  (/  E  ( M /e iomeaa ae o ^  e same suc as ose o e oy ee is ae meiooe coeicie mai-y kso k  is o q m e meio o 13 is  q  (+ 1A q q  si  maiW is sai  a Wis siowi ges oeem ii i ois oe (W= [  q (/]  1 1W - q-1  e [A -1 Wq ( ^ (q-1171(i 1 = oo  - e-  ^ (5a si  q  q maiA(A -1 Wi e ace omaiA -1 WW = E -1  ss e ecisiomaiie i o99(e ioa  coiosio oW aW  -  Wis(AWe -- Wis(A A = (A -1  + " -17; = +  1 ^ (e    q mai -    =    a  s = 1   Eacsia ce  is omeio q ua e au-gssiocoeicie mai   we use oi assquas esmaoiaosami om i  coiosioIGis sami aomi ua eacmeock i  coiosio as a iis seco AeacioiGis samie casoecois oaiiai waye casoecoisO = m +  s1 =   3i +  ca is a om same geom M( E E ^ (7Aose so w e sc measumes a aie u me  O =  + 1- +   a e casAose so we is  sc measumes O = 1  a e eco1e me aose so wioumeasumes ca sayec e mees aso wi measumesye ce ieaoe casoecois oai ki equais oa eiMCMC samesSeco7 eses aacaooe yesiamuia sammoa moas i use1Ce7cas a SaecoO oe ima oses oisc mo is  ece e-me ey eseis ceeses saecosus sciCe eicoies  e e makiosuceco a cas  e sammooseiCe5Ie sois ce we use e  "eco   saeco w "cas    ses7 yesiaMei Moecoe  comes om o souesgiosuace o coeomea-sumes a moouu om a isc moAQM (aiquamoa osc iooe MAQSI(Muisca AiQuaSimuoaomo is AQM sysm s escii Wea uyou(199e AQM moouuis seogces wi sookm  e measumes a om e AiQua1Sysm (AQSmo o e measumes a moou a uy coeo si om May 15  Seem111995oa 1-y o e seeses 375 mo so ieAQS o a 3 gces ie AQM ouu e measumes amoouu a seoe suosaismeasumes aseoi es w moouu a gce ages osceIaio e moouu a seoe U (CooiUsameme sae measumes ocameIg is meee wou su iocoeoeemeasumes a moouue  secosws e cessi  ausis scyis ses ea Kasiaa a Cmeis (g ea ( as we as g ea (a e coms e aocoeocoeicies eequais (1 5 75 a 9 oe measumes a AQM moouu iage e eo  ao a e coeoeemeasumes a moouuaecomsi e uy mesees io susees oe me scasey acsimicosioae AQM moouueses e measume eaeme scasweiesma e coeoeemeasumes a moouu e a asis igs e ma sacoeoie us a some ueaiy aueiMoocooasis es  ie assessme oe mocaao1(ai a muiicasie e coeois  oiaauee aaoomeasume scasy ouieses me ie ge oaassociaoeemeasumes a moouu measu e coeo eiec e o auocaoese c mo a w  asis usie emi  asise eous secois ouae measumes a seocame w e moouu a seoGM(GeicMeameSo we ause moouu  e camee ses 119ys aee ausegu 7 sws e aoeee measumes a moouue measume seesuike ae moouu missiesemea e measumes om so553 (iWis-coisa missi awi e missi eswe coseose so a  mo a1 u omissi measumesSecowe use e  umea  ie missi esemeie missi es occua1 ewe use e age oe aiees a1e y   iese missi esAeaus e me sas a ig e so wi mo a1 miss-i measumeswe  measumes a so a moouu1^ 5^ 1 ^ 15so 7gu 7Scaeo a aocoeo eemeasumes oso97 a moouu ce 7e y-as sse moouu ogce 7 a e as ss e mea-sumes aso97e so97 is ii gce 7Oee ae coeoeemeasumes a moouu is 71o375 gces o5u (119 ys Iese 375 gcese a 7gces wccoaio a oy o so  ee us ueee  omo-measume coeoisaecoom w oe  aays wi cus oe 7gces wi 7soii e gcesAuge measumes a moouu aaie  e 119 y o we oy cus oe 3ys owe o coeois aa ge  gmse o coeoag a eay ie moi is mucwea e ygu 7 sws e  si--si uy o omeasuo  aso315 a simuo e agce 5e so315 is ii gce 5e oeea simuo a aa ak  e u om1 17gu 7 sws e sgms oe mo-measumecoeoaa  u a ae useogus 7 a 7we cus oe asis oumeasumes a moouusieoeise e o  soues a qui ssimi Moo  iesoai ie u oui ao om w o e uagemeasumes omoouu is ao e as e "i age"We a   a e uyi a week age o coeao e secume o Kasiaa a Cmeis( o ea (cus eiasis osimii ageIicu o ea (use e emcaogoo(EO meo a iicom asis (A  com e 1o iicoms oe measume a moouue simuo  ae 7gces a measumes a so a use e  mo(9 e measumes aemai 3so a useas oese 3so acae"umo" sis om w o gu 7 ma e gcesa mo/umo siscao s i a  we use e Eu-case oeii a    e se eeem as e owi s s 1 =  ( 1 S1  + (S1 s  (7s11 1 1s 1  a s e s ocao Ic e mo accu u  cau e se ikm eeo cao is e owiss i s = 1111 s 1   + cos  (s1/57 s  (7e ses cauom Equao (7a (7a oiocause oe cosi  iEquao(7 we e  eooe ses eee 7so we  is smagu 7 swsaau9 oe  eo a wii1Aeasous use e Equao(7  e se eeso is eusage oKgi ickage "geo  i a gg ( ackage  e se  usi Equao (7  com e sus10 - 1-o    o  ^6  - ^^E   7^-7- I 1 ^ I  11     ^ 11 1CCcaaCo ao -(00_o ^ 1^ ^ 3^  -c -.11111111111111115^ ^ 7^ ^ 9^ 111 113 115 117 119    -1- o -9-^ uC(ia o^ 1^ ^ 3^ ^ 5^ ^ 7^ ^ 9^ 111 113 115 117 119    ugu 7e ueis e  si--si uy o omea-sumes aso315e weis e  si--siuy o omoouu (simuo igce 5e so315 es ii gce 51Oo0Ca0C O-^ - ^  ^ ^  ^  ^ coeoosce a  u--CC --     coeoosce u 117gu 7sgms ocoeoosce aeacu e uesgm is a e  ue wesgm is e uymece e maey emo-measume coeo e u 1171oKgi a oeaacswe sck  aooe seom w oWe com e sus osaecoeeo com aoacs a KgiIc we  o e io oKgiKgi usi measumes a Kgi usi moouue S(omeasqua ecoeo measus e ec oaeAme    wccou  u y oweekwe  e S S = ^ ( O i  (7i e moumo sis   ec  e measu-me asoi a O i  e ecoAsis ouy e 3ys om  1   3 1995we  uy measu-mes a moouu ae i ume o(117secasisWe a e  moa Kgi  eacuseewe se age S e  moa Kgi ie 7e ages a comoe ugu 7 swse ooe S ee eee  moa Kgi usioy measumes us e coeoeemeasumes a moouu osceWe oee owi oeao aue asis11i-i-1-75i-9 -7i^ 1-1 ^ -95gu 7cao o aie so7gces a 3uiesoAaie socgces+uie so  ec e as is e i igesy-ase iges1110    1 1 eo ieagesgu 7Cumu o oe  eo ieages eee se usi u 7 a u 711ouy  e 7 sws aoagee  ecs e smaesS amo a e com ecoaacs e  ecseems maiy eaKgi usi oye measumese S e  ecis 15aKgi usi measumes13 As swie  secoe  eces muceaaiooKgi ieasis oi age  Kgi usi moouu s e ggesSii  esi ocaa e moouu gu 7 sws aige saeco  mo keoueos Kgi usi measumes we coeoeemeasumes a moouu is g e is o uawce  ecois mucwoe aKgie asoisae esmaooae   is ge aau is aoa some i o wi e uy wcmay ooe aso aees a e (use e week age ieiasis e coge o o 9 ec ieais wcis iy goo1130oo 0^ ^         coo r^ ^   o    1 oe% ^   e     13     o  eauc" ( 9o  ^ o     ^ ^ ^  1 ^  0I^ I^ Io_o_cU0ccc^CSw  a- I(/ECC  ^  ^  ^  ^ sacoeoeeoeaoa ouugu 7uy S (omeasqua ecoeo eeeeKgi usi measumes a  us e coeoosce eemeasumes a moouuis a e a ie oese ces e  mooKgi11Asis oui Age is secoeses ouasis oi u(117measumesa moouu agesWe wou make e owi oeaoauouasis oi age  e 7 sws ai agese  mos e smaesS amo a com ecoaacse S oe  mois smaeaKgi usi measumes o1ouoe 3yse age S Kgi usi moouuis e gges swi e e caa e moouu gu 7 cois e iui ausie su aigeeecooae oe  moimos as e coeoeemeasumes a moouu iasesWe coe-oeee  e  moos suiay eaKgi omosys Iimemei we assume e ai caaomea(s is a miaooe coois acao s ais a(s= ( a  We use e ie mMCMC  cose ege oe miao e ie mMCMC casame e meiooO a om i sosio Seco3 scs is ie mMCMC ii a 3yse sosiooO a es ee1  3Sowe ca115assume  a(s is a aooe coois acao s ais a(s=  ao +a i si +a ss 1  i e i a  iges acao s  assumi a is a aocoois acao s we gea smaeS a assumi a is a coacss e sceI (9 we assume ae muiica caaome is co acss soe mo asc is assumio eewi  e  ecs oae agaiKgiIese eacsois caia gceso e moouu agce ca eaas e moouuae soiie gceusaeacgce    we caausiy esma   -( e    (7(w    =    ss  is e iego {s  oe gce  cause we oy  o sami i ieacgceis iegis s s aise measume ae soii gce  Aeoai    om e a uwe cacom esami ae o{} a e ao meaee o{}eegces  measuoueasusogu 7a gu 7 sw o o(Kgi S -  Sus a e ao meaee  sce 3ys iom ese o we casee ae  ecois11eaKgi w a e ao meaee o a smais i is eeccause e  ecois ewe moassumio a mo se e coge o oe 9 ce e  ecois3%wcis iy gooAsis oweek Age ees a e (a week age SO  measumes amoouu iUSAe aie/uie so a gces useie asis oweek age  is e same as ie asis oiage we wi ages oeme scase ecoo e  moa Kgi a eec imo cause oea oe  sioa smaeaooe age oe eme scae imome oe  ecoao esie eoae oisc moe eme sca as Kasiaa a Cmeis ( g ea (a e7 eses ae S oe  moKgi wi oy measu-mesKgi wi measume 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kmgu 7 oose us coeoe asiaom mo513S amo a e com aacs cas a s-ay eco case meaS oe yesiasammois au1 smaeae cas ome moouue S oe ac aacis sgggeae yesiasammo Ieco susiKgi s e ggesS cause we  ieo- sis usi measumes om oy 15 soe Soe yesiasammois au1 smaeaeac aaca e moouu Sousi mo(5 caia e moouu seems wo ace e-cas a ecoe coge oes oe iea e yesiasammoa iy we caa meae ueaiies ie cas a eco a ccqui weAugiagi oe sise yesiasammoaces e smaesS a Siis ao maiyeae ac aacicas aeiasigca cosicomome a imo i om e mo-mee 7 sws ae yesiasammos smaeS aac aaca9 ou15 soe7 a 7 sw ae yesiasammos smaeS aac aaca ou soSocogi e cossae maoe yesiasa135mmoes ie gqua osaeco a ii we caace ec iea e 7 sws e someaoe au-gssi me   as g as 91wcsugges so au-gssioiesia {  } Ame    e sia cosce is e  a e asiua cis e  = E E  e gu 7sws e emcasacooe asia om e yesiasammo5 io iesi seWe casee aeew i osoe asia   mucsacoeo e a oy o i oso wse aisia s  sacoeoga5e asocou  e simime oe asia wca cau e sammo7 Muia SamMoecoa casis secoeses e sus oai e muia sammo(1a (  e o uo sciSeco7We use e measumes a moouu om e same 7soa gces as iSeco7We  119 ys ouy measumes13a moouuOeacywe ke e uy me age omeasumes a moouu om 1 17 a e g meage om e suOeacywe  e y- a gmeages omeasumes as a sese y- a gmeages omoouu a e coas  M  imo(1 We use e e  ys a15 so  e e muia sammo ewe case measumes ie  39 ys ae 15 so a say ece measumes ae mai sis e  ysImo(1 we assume e sia {  } aeacsi  aA1ocess wcs a  meawi coas{  }Ie acaooua mo(5 e coas { s  } aiicao  i e 1uoci oe measumeswe e y- a gme age measumes a oa i scaa ey   sucso oci as e uy measumesWe useiicao as iSeco5  i e 7-y ocioe measumeswe e cas oeco a imoSo we sassume -y  = imo(1wwe  e  asisWes i e coa mai  ie muia mo(1ecomess a e oe mo We ea e casaecosus  S a S  (7a 7e7 eses e esmaosus e me   o a EAaea  usi e muia mo(1 is  a e uamo(5 e y- a gme age  se iusa137e oe muia mo we com e S a Soese o aacse 7 eses e comsosuse 7 a e 7 aus  e owi cosio e someao/    is sigca e om  is swse moouu a iec a cas ymemeasumes e somea o/1  a  i3 3 a sigca eom cause e o  ag a mucweae y-meis sws e gme measumes a mucmo icu ecocasom e moouu e someaoE 11 E  Ioewose aooyme measumes a muceae g-me measumesis is susi  us cause e ocoeo a mucgae yme e coeicies oe au-gssi mai  a sigca  om  we e au-gssiois as so as ieua casee esmaooe au-gssi meiua case is 91 w imuia case e me a eae asois ae measumes a oauysca ie ua asis a i ages imuiaasis13e 7 sws ae muia mocas a eco smaeS a S ae ua mo y- a gme measumesSo iis wousi muiasammo(1 ace ecas a ec-o oe y- a gme measumes i measumeagggase coge oes 9 ecoa casce ia a 3% a 3% scis sws e ueaies oe eco a cas a keio accou asoywe  e mo139e 7somea a sa ao ome a   a 5 C17 7  c5 QE AeAa C 7  17 Ac a    Sie is e is e esmas omee is  uassocia e m iis eEacoese me is a scamea s mea sa 157  a 1 ci 3  c 3 o 9 15 a3  39A 35  c3 35 Aa 7  a 193 3a 33  c 37 cc 33 13 a5 17 9 91  c5  1e 7e comgis e ieces o15 so w e umeasumes a aiee secoi a com ae S (squa ooe measqua caseo oe  umeasumes -cas e yesiasammoac aaca moouue mowe iicase aacas e smaesS iawe uoem om com iis e is so sam ac moouu1 1 1  19 9 3133 133 1 1 11 1 5 151 171 13 15 151 1517 193   191 19 199 1 137 171 11 157 1111 1 17 11 157 159 15913 195 1 151 157 13 115 171 153 171mea 157 157 1571e 7S auaugesis 1-35Com yesiasammo com3ac aac com moouu;com5Kgi wi measumese mowe iicase aacas e smaesS ieacwe uoem om com 5 iis e is si sam a-c mo Kgi1 11 13 13 151 11 1 13 1753 139  131 13 5 117 17 5 1975 1  199  117 115 115 97 159  19 155  19 13 175 9 191 17 5 11 17 1 131 3111 151 1 119 3591 15 17 15 13 153 5 117 3711 175 157 1 15 1 119 155 171 171 191 1 17117 199 177 135 191 115 15 115 719 1 1 17 133 153 115 15 17 1 13 1 179 11 1  111 1 15 1 111 13 9 175 117 19 15 153 157  1 13 133  111 19 15 3 1 19 197  1  197 1 3113 1 17 13 331 19 17  3 1 1 1 31933 1 9 1 3953 191 159 159 535 1 17 1 31e 7S auaugesis 3Com yesiasammo com3ac aac com moouu;com5Kgi wi measumese mowe iicase aacas e smaesS ieacwe uoem om com 5 iis e is si sam ac mo Kgi3 135  1 35337 1  13 3393 171 15 131 39 1  7  135 1 199 191 13 1  157 133 17 1 177 199 1 199 3 199 1 179  15 157 179 1 13 135 135 31 13 13 151  11 15 191 19 15  195 15 139 155 13 1351 11 11 1 1315 11 1 1 13953 179 1 19 15 13 177 1 13755 15 157 17 1515 11 171 13 57 13 191 9 95 17 19 171 559 111 17 197  1 13 13 1 1 13 115 193 7 1  1 177 15 15 199mea 1 113 15 1e 7someaa sa ao oe me   a Eo a /11 a e mea oiees; /11 a e meaocoeicies oy- a gme moouu oe ymemeasumes; s  a io 3e meaocoeicies oy- a gmemoouu oe gme measumesSie is e is eesmas omee is  uassocia e m iiseEacoese me is a scamea s mea si 17 3   A     1    17 / 13 17 17     1 E1 1319 -/3 11 1 E1 133 -E1 133 E 537 -e 7Age oS a S yesiamuia sammo(1(com a  a ua sammo(5(com 3 a 5 e age oS is o sisa e age oS is o15 soe uoe m iis e is S Smuia ua muia uaymegme1715111119199151911CeCaaooiscmoCe1 scs e o cy  ckgu ( aw icao measu aicuy es use oisc moouu iee  we aouue   caaeu e isc moouueses e  Caaoe   seoe measumesis ceei w wecause e  mo(9a yesiasammo(5caa isc mo a ieses aeme ioi moouu oo coeoAs iCe7we cus oe uyme age measumesa moouu 7gces a so  e 3ys om 1   3 1995e caamoouuagce    usi mois( 1(ss/ ^ (1e muiica caaome  is assumeco acss sce1a  a(s=  ac+ aisi + a  w s 1 a s  a e i a ocao s ees a e (ug-ie someao a(sa   io (1 oaie caamoouui e ug-iaacuse ees a e ( wecaa e moouuusi e  mocyIeaciooe Gis samiwe use u (1 cau e caamoouu so awe gee emcasioecaao ecaamoouu usi e yesiasammoisa +  c ( iusa e ocaa e moouu we com ie 1 e S e caaa uaamoouue 3ys owcous cusesAs e i  asis iSeco7e  aie is e measumes a so a moouu aa e 7gcese caamoouuae mai3so a use ece measumes eAs aemegu 1 sws e ooe measumes us e uaaacaamoouuy 1 e  a yesiasammo caamoouu a iiao gusws e scaeo o mocaamoouu usuaamoouu a gu 3 sws scaeo oyesiasammocaamoouu us uaamo1ouuom e caaosus e moouu we  eowi cosio gu a 3 amaeees eecaaauaamoouu cause ma is a om e so wi iee a s 1 e 1 sws aoage e yesiasammocaamoouu  e smaesS ae ua-aos a  caamoouu ao  smae-S auaaosAecaao e meaS sece 1%  mo  yesiasammo Ouoa e 3ys  a yesiasammocaamoouu  smaeSs auaaos  ysSo iis cia caa e moouu  usi eie oyesiasammo gu 1 sws a  a yesiasamca-amoouu a cse e measumes ae ua-aos amosso gu sws e sgms osomea ocaao-me  ao a aa   ie 3yse somea o  eom 9  imosoe ys1_C 7  aOC  coaCOOCO   CoOOCCa-5_CcCu0measumesmoouu caaouusamcaaouu^ 5^ 1^ 15^  ^  ^ 33sisgu 1Measumes us e uaaa caamoouo3gces oy  e so sws e measumes ii egcese ea ss a e uaaa caamoouu sc1e 1S ouaaa caamoouu e e-coomeasumes ae 3socom1y 1-3 comS ouaamoouu com3S o caamoouu com S oyesiasammoca-amoouu e mwi a iicas e "wie iawe uoe m om com iis e is y moouu  sam1 3 15 139 19 1 1173 1 7 7 1 139 15  1 15 7 159 17 11 135 13 15 1 119 1 1 151 1 119 111 19 1 91 171 119 1513 157 1 1551 3 157 15 9  91 1 17 117 15 117 1191 159 155 13319 13 1 79 1 119 13 19 3 137 17 117 9 1 117  157 1 93 7 135 13 1 1  11 159 99 1 19 175 135 13 113 153 15 171 119mea 1 11 13913^  ^ 5^  ^ 7^ 3^ ^ 5^  ^ 7^  ^ 9uaamoouu i3^ ^ 5^  ^ 7^3^  ^ 5^  ^ 7^  ^ 9uaamoouu igu  Scaeo ouaamoouu us  caamoouue sos  iee a s 1e o a ys  7a  om e ue  e weg coei--gsequee153^  ^ 5^  ^ 7   7 -3^  ^ 53^  ^ 5^  ^ 7^  ^ 9^ 3^ ^ 5^ ^ 7  ^ 9^lr d tp ppbv ^ uaamoouu igu 3Scaeo ouaamoouu us yesiasammocaamoouue sos  iece a s 1e o a ys  7a  om e ue e weg i--g sequee1515 1 15a  -1 -5 ^ a 1- -3 -  1 ^ 1 ^ a gu  sgms osomea o a  a a  a    e 3ys owce cue s cuses o15Ce9Acaooe yesiaEeme Mei Mois ceeses e sus oai e M mo commeasumes a moouu om aeeme oisc moSeco3 gis a cicaico e M mo iisce we ese e aioimocao ea ic-uacaowe assSeco9 ices e ieeacaoa Seco9 eses e sus a cosio9  scioceoe  iaeiooy  e weaecasao e ueaiies oe cas Ueaiy is aea a we esiscoe isscacommueme usi a agssiomo sscia oy ece se seoe aie ey ao gi a ec ieae ecee ea (ose aia  osc cas a ey  aea153seua wei (/oascom/   gi sucosc case cic esaaIyesiamoiis saiga use e MCMC sames om e soec sio gi aosc cas Iis seco we gi aeme ousi e Mmo com measumes wi moouu om mo aoisc mo  gi saeco a eice ieais osewe woa om e MU ocwei(/wwwwase/MU/ is seis measu-mes a moouuoe sea m ie cic esaae me oe measumes a moouu a aie a1coecu u  a- e moouu age e Ui oWasmesosca s-e eemesysm e cic es wcs esc GmiaMass ( is sysm is a -memmui-asis eeme coisi oe  oe geosyaa S UioCeeAosec seaMesosca mo(MM5 Eacoe MM5 mois ma wi e iacoioe wisc moouua aie ogceswe emiasis s e  ieo e moouu  e cao omo soSo is se eacsos o measumea  "ag moouu e me ea (mois se usi yesiamoagi oe  moouu  make e -uaacasoe m we15moe same se usi eeme   comsoe momo so es om 311  aeueacu we cau e aocoeocoeicieseemeasume a eacoe  moouu osceuswe  1 coeocoeicies eacoe  iacoiogu 9 sws e sgms oese coeocoeiciesCaye coeocoeicies a ea7 amosue socoeomakes e acaooe M moa asoe cice com e measumes a moouu9  AsisIouse moso es om u-ua we cose asueo15so wc measumes a moouu aieaeacu We use e M mo com measumes om 3so a moouu a 15so  ece m ae mai 1 soWe a e M mo e measumesa moouuaeacuayUike e o  aiSeco7e moouu om a aie acaoaeieooa e   we  es  e coois oe gcesesSo iis asiswe  e e coe ogces a e coiosio(3 e e some smamocaoAssume awe  m so ia measumes155^ I  -7 ^ ^  ^ mo13 ^  ^  ^  ^ ^  ^  ^ 1mo^  ^ ^ mo3(CC7 C^ ^  ^ ^  ^ ^  ^  ^  ^ momo5gu 9sgms o1 uaos coeocoeicies -eemeasume a moouuosce 1-5 a e s-gms moouuom  e MM5 iacoioa aie asoa sueoe m sowe e moouu a aie aa m soc  is e aooeue ueyi ocess ae m soc  ki  (i = 1 5 eao oe moouuocess om i- isc moaem soa c   e aooe measume ocess aesoSimi e om (3e coiosioo (   1     gi(  a    a  1   c  ag1 ag is eowi15 ^ 1/3   a   a      C1      e ^  [(A  E i 1^A ^ + E ( i _ _    Ei (k i  i  i i=i+ (  ii   E -1  ( = e  1    E  1+ ^   k i + E - ei=i(k E  +^ i kiE 1 + iE-1  i=i+  E 11 +^1771 +  E-1  i-iw  =  5 a A o is as1  ^ ^ ^  ^ A  =^  ^ 1^ ^  ^ e com oA o  aii maia e semes oAo a (9157e iosioo (ai i  i = 1   is/ a  M( e  coiosioo(a i  i isai^I E i   M( w 1 = a( 1= 1 +  i 1 1 i w  E  is a agomaiwi meio m me agoemesa   e ae omoouueooisc moiWe assume eacai caaomea is a aooe coois ocao s aiswe a5 = a(+ a 1s1 + as1  i e i a  ocao s we aei e M mo we scoae coeicies a  a a  a15sigcaSo we assume  e caaome a a   acos acss scewe e caaome s ee e isc moaiswe   se ome aa    gu 9 a gu 9 sw e sgms oe someaoa a   e moEacsgm sws e someaoa a   1 u ece m ae 1 sowe  e com  saaacsMKgi wimeasumes a agi oe  moouugu 9 sws esgm oe S oese e aacs oe 1 uea asis a us  e owi is e meaSs oe ecoaacs o1 u a9(M 3(agi e  moouuwi equaweigsa 1(Kgi wi measume e M mos e sma-esmeaS w e Kgi s e es Oe 1ue M moaces smaeS aKgi aeaco77 ue coge o oe M 9 ce ia e ecois %wcaugasoesuggese M sg uesma e ueaiies oeco IKgiwe use e measumes aoy 3so  ec1soSoiis susi aKgi es ece mea-sumes  we gie si oe aie Auge meaSs eeM a moagi ouu is 159csegu 9 sws ae siooM Ss is mo skeweaoSs om simy agi moouuAo M caesma e caaome eacoe mo gu 9 a 9 sw ae somea o i a ie ia[915] a [ ] sc mosue e oe measumes is om  313 So oewioucaao e moouu ese e measume  weis coiis wi e so coeoeemeasume amoouu swigu 9 gu 9 eses a ooe S ee eeKgia e M mous e meacoeocoeicie eemeasume a moouu e meacoeocoeicie isas e meao coeocoeicies eemeasu-me a  moouu e osws ae soeecoeoeemeasume a moouue eme-i eco comwi Kgi summae M mogis e ssaecomeasu Se M moao ec ecoueaiy asoyweSowi a sma momeasumes a e momoouuwe cacom e measumes a moouu  aceesaeco e moouu  iecocause o1e so coeo eemeasume a moouu--1 ^ ^ 1^ ^ 3^ - ^ -  ^ ^ 1^ ^ 3^  ^ 5a omo1 ^ a omo- ^ ^ 1^ a omo3-CC - ocaC 7C -a-1 ^ 1^  ^ 3^ - ^ - ^ ^ 1^  ^ 3^  ^ 5^ d  ^ a omo5gu 9sgms osomeaoa 1-5 a e sgmsoa moouuom  e MM5 iacoio19 ^ 95 ^ 1^ 15^ ^  ^ 9 ^ 5 ^1^ 15^  ^5 ^ 1^ 1omo1 ^ omo^ omo3;-9 ^ 95 ^ 1^ 15omo5 ^  ^ 9 ^ 95 ^ 1^ 15^ 1omo5gu 9sgms osomeao    1-5 a e sgmso  moouuom  e MM5 iacoio1c^ 5^ M S i3^ ^ moage S i1Kgi S igu 9S sgms oeco  Mmoagi wiequaweig a Kgi wi measumes oy10 c9  q    o^  c o ^^ ^  ^   ^ ^ ^ ^    ^ ^  o^ o00^ 5 ^  ^ 7 ^  ^ 9age coeoeemoouu a measumesgu 9e as eses e meacoeocoeicies eemeasume a moouu ie meaoe  coeocoei-cies eee measume a  moouu1Ce1mic yesiaEemeMei Mo e  moiSecoa i eeio e M moiSeco3 a  samoSo we e ee em  sammoIsome casesa sime eeiois aie wiouecomees ioeicc e msuc sucas iAomicaamoSeco11 eses a cisiomaki oema i soo Seco1ese a EM (mic yesiaeememei mowccacase  wi sc   usie soooacisiomaki oem11 Gos oemyai a Go(19ose a cisiomaki mo comoo om e eese ia is moogiy som a oem ie ok  Go(197We ese ouoooGos oem a sw w  couca mic M mo1 usi i cosioeom 11 (Gos eom Eacoe K ees s s/owiosioa ceaimeWa  7  e iosiowcee i assig  W e ecu s s/ooauW om e oooe K ees a as/ioW isaweigeage oe  7  Soe ecu ioW isw= ^ Gi7 (w ^ ( = 1cE i i= 1^ i=1oe K ees a e ecu oee geee e oa om ae wse coiosiowW = w is (we sosiooe ecu wi agai a weigeageoe soe K eesooe soee i isw=  7(w(w (w  i (  is e maisioee ia is i ( = (w-i(ww 1e soe ecu is e7 (w1 =(w(wai7(w (wai( i(I ( w ^ ((w  ^ (11i=1  i (  is e maisioee iais i (  =  ( (w  (wwe maisioe ecu is   = E 1  a (w(wwSoe soe ecu is agaia weigeage oso(w i = IK e  K  eese uaweig ee iaeoei  =  is =  ce I  e uaweig eacee s os/maisioo 1mic yesiaEeme Meicascas o coeo iuaaas s come mo amo ima ic aaso sucas e sa ooe keasmacse cas ca oous me scas sucas uy oie sois secoeses w  couca EM mo1uy cas we e same mo caao  use caseage i o coeoe M mo we  uy measumes a moouu om   isc moe ue ueyi ocess   ame a   a   1    / 9 e ^  a  As iGosoeme meis W ^ (a  a    a e1 11  7 ag e measumes   acss sce aeacuis e   ie GosoemWe use e  K umeasumes a moouu  e Mmo om wcwe oaie sosio oe meW eacoe  K uese  K sosio wi  iosio W e  u So we  7;  (w was iGos oemWe ke e weigs a(i = 1 K oeiosio   equa 1/KSuose we   K + 1  uymeasumes a  K + uy moouue goais  casemeasume au K +   Aeoei e measumes a K + 1u we oaie uasio 71 -1(w(i = 1 K a eicoesi weigs a i So  e  K  sio W a eiweigs ce micay aee measumes come aie eu e ec sioomeasumes au K +  is eowi kK+  = a i ( 1 K +W  +   - 17(1 (WW  (11w   ss a e measumes a moouu aiee keooW is   (W  1  k  use e cocsioom Gos oemwe    is keooWe kw om a  a  1i  k  iee asiogiW a    ose asio a e owik  w   m(A    ii 1( ^M(ai1  i A o -  ^ (13i = 1 e maiA  a A 1 A  a e same as ie M mo  e coiosiok1W 1     we e oaie i sioo   1 k  (w  wcis a muia asio simiciwe suss e coioo(Wie owi equao1E( = E(E(=^ ^ E E(  1A   +o- 9-AEio + c/E( i = E(E( i 1= ai+  i Ai ^ i ^ E(I E(  i1a i +  i i  += 1  EA (  /^Co  i ^ E(E(k E(k(i AEAco i^ = E(E(i";1 E( i (=1  i (1ee i sioo(  1i     giW is e owi/  M(/17w/ Aoa11 + Ai    i   A a1E E11We   oo = k E 11  ise scki  1   com comee coiosioo(k i  k is muiaawi mea1a ae E   EoiEioUouwe   cses eieo7   (wso we  ama em  a Moe Cao meo so wo wi e imeme is EM mo we e Moe Cao aimaoa e imemeaoois mowi ese some cees/1171Ce11scussioa  Wois ceeses some scussioa ia woSeco11 scusses e  mo(9a Seco11 eses some wo eei e yesiasammo(511 yesiaMei Moe mei moose ees a e (as we asees ea (assumes e ese oa ue ueyi ocesswcsees as a sis owc "me" e measume a moouuocessesis mei aacis a ia a isome seeicaawi e cameasumes a moouuocesses e suosweis ue ueyi ocess ao esessome cees imakes e mocomicaa comoyeeiWwe coi ee e  moio a samowe i oa aacsimi e M (mic amo use Wesa iso(1997a ea ea ( Massumes e coeicies ia amomicay ei ome17emewe caassume ame    e coeicie  O IO_i   _1Ecause e coeicies a coeomeso e se is ao coomewe e assumioois ue ueyi ocesseses aoc  e eeiooe  moio a mic wcioos e mcoeo Secoiis icu  e e ua mei moio a muia oemewecaouse e aacoSci a Gea (w ose a co-oy eicie co-giooaac Iseems ae ggesois ue ueyi ocess is  ass e eiasuosissue esee measumes a moouuic eme-ogicaa eieawo oeuses some emi asis ieo e moouuoo mo sis a eeaeieos as i seEmes i Kasiaa a Cmei-s ( g ea (a o ea ( Iwe aycaig e eiasuos issueee gssioaacseemsmo aea a easie imemeIaaac e ses ae measumes om e mo sis a e coa is e moouuieo ose sis o oecaoOcoue we  uquam omoouu a measumesa  a sa missi e oemWe eie missi -ses ocoasIe mei mo(9 we assume e meaoe ue ueyiocess is a oooy e cooiswe we kw aoe173aes  eec oe u augwe   eiiomaoaie iouacao ese aes i mmiwi sea so o Wioue ioaoo eseaese ae oe sasia  c(s imo(9ca ea eco seoe ue ueyi ocess cou  iquesowe wwe gss measumes oe moouuaasoaioaois cau ie moouuSo e suisia ecoy e  amoouui  caue gssiomoscussea s e owi (s= a(s+ (s+ s  (11Ie a mo e sia e(sa say coewi coaemaiE couc coeoo sucas MaGaussiaoeoia is amo(11is muceasie wi weme a wioue ue ueyi ocessMoo iis icu  ee e mo(11 ioo muia se amcoeomuia mo we caow e ia om Sci a Gea( ey comse e muia moio seieeua mois comsioees e como  se-queiaa ss me coumiIoe ee e mo(11ioo mcoeo we  o iaoioe 17cice is  use Me oecice is  assume e sia  c(sacoeomeWe caassume AoeAA (Au-gssimo agemoe sia ome    Iwe use e micamo e sui samis easy  cause mosoeeo a sus e mic amoca ae cy usi e seco oio e coae maiosia     is aKckeocosacoae maia e mcoaemai is comicaKckeocoo maices may esesome comoceese a o oio a  seoe assumioae saa mcoeoa seeaisaeacme    e sacoeomai e same a aeacs-o s e mcoeomai e same oaas e samesuc11 yesiaSamMoe yesiasammo5 s a momioe coeicies a c 7  osce maico omee ea (ao make is oeaoaueiyesiaagi moa ey iesga w  e sc osu  i eimo e sake ocaswe suuse e mosce sc  we ao ea asoy  -o  eug  e mo As scusseiSeco11175o ssie soois  use e M  aowi e coeicies ee ime e ma sacoeomay omay  seeGi (scusses a css osee so co-ae o sce-me Iis ssie  ioois css osee o io e mo5Aeway moe see samcoeois  eaugssi me  imo5  osceSimie coeicies a c ywe caao assume   ae so asay coe e augssi coeicies a aays ieiea(-11 so we cause uaasio  moemaisaugssi coeicie acaowe (    ci E -- [- 1    i   1]w  I  ss e iicao aisis iicais 1ia e s acao a ie iea(-11 oeise iis e a co  c makes su e iegoe muiaai o  1 Mo5 assumes e say coesia a sois assumiooso cou   i a so mo say usi e ceaSamoGuo (SAGmeooSamoa Guo (199e maiia is awe17cae o-sagssiomo(5 (5a (5ewe a e SamoGuo meo e sacoaee esia  a e coois om e ogigeogicaa (G-a e ea (a Aee aao we cause e w coois oe aa e yesiasammo5 oagaiwi e oe esmaSG coaeWe caao ioo oeso ocess mo aacs io e sammo We  aea ssome e sucaacs ae e oSeco1 a gii oSeco177iogyAamowiMa Sgu IA(197 ok oMaemaca-o eeS Cai  a GeaA(  ecaMo aAsis Sa Caa /CyaiMa Go M(19 Oimai oecouaoe AmecaSscaAssociao  i    ( ysicasscamo igeoysics uaoGeoysicasea 1 -91 G iGa ie G(199 me Sees Asis-cas a Co 3 Eo  eyow   a k  (19 Ai muia e gssioe Aa oSscs    -717ow   a k  (19 Muia gssiosiage es-maowi uwcoae mai  ScaiauaoSscs99-5ow    a k  (199Muia saieoa eosu  aius e CaauaoSscs 9-5Cae Ca Cssie ( some cs icooosesamo ocees oe 5Sessiooe IeaoSscaIs uga omiCayaiseGiguM e G a Sckse Ga Mca (1995 sciooe caagiocma mo  Wa Aia Soiuo  7-Cssie A(1993  Sscs Sa Wiy-IecieeCsE C Ca Ko ( ae secoa coaesecoimuia gssiomo cica SAMSIGo M(197 Oimasscacisio McGw-EasA(19 A omeic case sSes oe siooses imies19-19aac1  omeics179oAM co uYaosca M iie  a Q( a isuace o ckgu oe ussImicao aiqua cy uaoGeoysicaseaoAM co Mau  a Mai   ( Acaooemcaogoo  ea o simuowi gioa gmo uaoGeoysicaseaeesMa eA( Mooa saieo-o com oeao wi ouu om mecamo ayesiamei cica  3 me oSscsUsi oWaseesMa eA( Moeaoa saieo-o yesiacomoooeao wi ouu om mecamo omeics   3eesMa Smi ( A w css oo samo uaoe AmecaSscaAssociao i eweeesM Guo a Ce  ( Sscaassessmeomecamo cica   CSEGae wisgseWa Aee C( Aiqua c-a o a ocmicaos (seco eeaewame iii cica UEieaocoAgey1GeaAa SmiA(199Sami-seaacs  caumaiies uaoAmecaSscaAssociao  399GeaA SciA eeSa SiaC( oa muia ocess mo ugsay i cogio-o(wi scussio s 13 1-5Gi ( eeso coae o sce-me  uaoe AmecaSscaAssociao 9759Ge  (1995 ie mmaocimoe cao comoa yesiamoio  omeika   711-73Gmi E a MassC( Iasus oa mesosca s-eeeme cas sysm oe cic es  Weaecas17 195GuiasS aoG Wues a owA( Sscaagsc a coecooa cmisy-a moe ecoocomo Aosec Cmisy a ysics    5-537Guo a Wae A(19 Oe eaoogeoysicamoe Geoysicauaoe yaAsomicaSocie  91 1-as (1995 caecooa so-mocess wi aacao wesua sio  uaoe AmecaSscaAssociao 9  11-11991as (199Sscaassessme oso-mu esa meogicaa mo Aosec Eie  3 15-19ssW(197Moe cao sami meo usi maocia eiacao omeika  5797-1wki a Cssie (19 skgi-a osa  uaoe IeaoAssociaoMaemacaGeogy  1 3-1g Swa a Ke (1999 so samoiyesiaSscs  7-7gC oS KasiaaoW SisaG MaMcy (a Ea e oae ogiosca o-cmicamo sysms ii-o eco AosEi3575-gC oS KasiaaKaosG emckC oWO uA Mcy a AK(Eae oae ogiosca ocmicamo sysmsi-meogicaeco AosEi  3559-7eaG Sao a Sou  ( A so-mmomeco ci o  uaoe yaSscasocie  531-1Kasiaa a CmeisW( Seasomo ogioo uoie eas uss Geoysse  15 -1Kasse  Koemei   A kkeA   M Sca Mma Ca Si A( Sscamai o1coeoowes eu usi secoa ioaoom siomoa mos sai oeao Scsc Eieaseaask Assessme (SEA  1-19 a k (1997 Ieoowi ueaisacoaeuaoyaSscs Socie 59 5-51  a k  (  SscaAsis oEieaSce-me ocess Siey a SmiA(197yes esma e amouaoe yaSscaSocieSees (Meogicau ( yesiamei mosowa i ieo  cca me oSscse Ui oisComaMaiaK a GooC (1993  Muia EieaSscsSamasis omuia eieamo-  EeeSciee isMa (19 Saao  cica   MeeeaS Skogsksi1Mae G(19 ai geossque aqueeme i Memois au  cs Geogiques eMiesMae G(19 ai  geossque aquee cicaMemois  au  cs Geogiques eMiesMeosseA seM e Aa e E(1953 Equaoos cauo  scom macs  uaoCmicaysics   17-1ca  WikCa y ( Muisoomo o sacoae o SscaMoiAIeoua   315-331Oa Ma ImC(199Muisca aiqua simuoa (maqsi soue co cumeaoa o  cicaEieaogmsMC-Ca Suom CeeciokCa Scis M( o coae ogaussiaocess gssio  i S  Saua  Sco (eAaes iuIoaoocessi Sysms 1  MIessCam-ieMAciokCa Scis M( Samoi usi a w cssoo coae o Eieics  17 3-51o a eA( Iee isc simuomoe yesiamei aac  uaoAmecaSscaAssociao 95 115e Co am (   A uage a Eie SscaCom uaoSscaComeaAusiaIS 3-91--eAE Giaoui a kowskiM(Usi yesiamoagi  caa caseemes MoyWeaeew  133 1155-117msayoke G Came a Cao ( mees-maoeiaequaoa gesmooi aac  uoe yaSscaSocieSees   7C79i  a gg ( geo a ckage geosscaasis WS  1(11 ISS19-31SacksWe W Mi a Wy (19 siga asisocomeemes SscaSciee    9-5Samo  a Guo (199ameic esmaooso sacoae suc uaoe AmecaSscaAssociao  1-119Sao a Guei ( Com oeeia a misc ecousi a yesiaaac  cica CESMA1SciAMa GeaAE( A yesiacogiooaacmuia u  ouaoGeoysicaseaAosesSmiA(1973 A geyesiaamo  uaoe yaSscaSocieSees (MeogicaSe  (19 Moi CSI S wse 9  1-Si M(1999  Ieooosa some eo kgiw Yo SieSu W  a k (199Assessme oyesiamuiaieooaacaimcses Eieics  95-5MeeAa k  (19 Muia gssioasisa cacaas e CaauaoSscs    -39Wackeage  (199 Muia Geosscs - AIcowiAcaoEo  SieagWes Ma iso  (1997  yesiacas a mic Moe; eo  SieWe  a uyou M(199e a imemeaooa seasomogioaiqua ocAia Was MageAssociao1WikC( A keesescaaacso-m-mic mo ocees oe 1sSsWosoSo-mMoi oEieaocesses (MEA 1-1WikCa i  ( Com ioaoacss sascas comeics   -91WikCa Cssie (1999 A meioceaac sce-me kaae omeika   5-9WikCa y (1999 Sce-me mo a mic sigoeieamo os uaoAgcuu ogicaa EieaSscs    9-5WikC Miica a i  ( So-mecayesiamoocaoceasuace wis uaoAmecaSscaAssociao 9  3-397YagmA(19  Coeoeo oSo a omo w YoSieagkSu Wa  ( sig a ieg comsios momuia gaussiauoes uaoeyaSscasocie   -791

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