Lecture 4 (D. Geman)

7/29/2019 Lecture 4 (D. Geman)

1/49

V]J]EV]EFJA ADJ^LELO EL FJLFD^NEBABOU0 ADF]T^D =

Mbljam Odijl! Iefkjda Bfks! Ajurdlt Ubulds@bkls Kbpcels Tlvdrsety

DLV)Fjfkjl

Gdnrujry :4! >8:6


2/49

ADF]T^D VD^EDV

Adfturd :0 Eltrbmuftebl +MO%

Adfturd >0 Fjlfdr Nebaboy +IB%

Adfturd 60 Fdaa Veoljaelo Elgdrdlfd +IB%

Adfturd =0 Odldtef Wjrejtebl +MO%

Adfturd 40 Ijssevd ]dstelo +AU%

Adfturd 70 Nebijrcdr Mesfbvdry +AU%

Adfturd ?0 Xkdlbtypd Xrdmeftebl +MO% Adfturd ;0 Dindmmelo Idfkjlesi +MO%

> " =5


3/49

BT]AELD

Odldtef Wjrejtebl

Kemmdl Ijrcbv Ibmdas Abss bg Kdtdrbzyobsety

Fbpy Luindr Wjrejtebl

6 " =5


4/49

ODLBID

= " =5


5/49

MLJ WJ^EJ]EBL

Dxtdlsevd! rjloelo grbi meggdrdlfds jt seload lufadbtemds tbdlterd fkbibsbids, Jiblo ibst stumedm0

Wdry abfja fkjlods jggdftelo j sijaa fblteoubus sdoidlt bg

MLJ! elfaumelo seload lufadbtemd pbayibrpkesis +VLXs%!wkefk rddft ljturja vjrejtebl el meggdrdlt jaadads wetkel

spdfeds, Elsdrtebls! mdadtebls! elvdrsebls jlm trjlsabfjtebls jt

vjrebus sfjads! sufk js wkbad odlds3 Fkjlods el tkd luindr bg dlterd fkrbibsbids +jldupabemy%,

4 " =5


6/49

MLJ WJ^EJ]EBL +FBL]%

Vbid es lbrija jlm sbid es aelcdm tb mesdjsd! dspdfejaay

fbpy luindr vjrejtebls +FLW%! sufk js mdadtebls jlm

mupaefjtebls! jlm abss bg kdtdrbzyobsety +ABK% elvbvaelo

ablo strdtfkds bg kbibzyobsety,

]kdsd jrd lbt rdojrmdm js iutjtebls! wkefk ijy ndsbijtef! bffurelo el sbijtef fdaas! sb tkd ldxt odldrjtebl es

lbt jggdftdm3 br odriaeld! el wkefk fjsd j kdrdmetjry

mespbsetebl tbwjrms fjlfdr ijy rdsuat,

Iutjtebls gbulm detkdr ny tjrodtdm sdqudlfelo gbr clbwl!

spdfef blds br wkbad odlbid sdqudlfelo gbr lbvda blds,

7 " =5


7/49

FBXU LTIND^ WJ^EJ]EBL

fkrbibsbid ;! fbltrba ijad odlbid

> IN rdoebl bg jppjrdlt trepabemy

Idjsurdm bl trjlsgbridm sfjad! wetk 8 idjlelo FL 9 >!dtf,

Bg ij`br eltdrdst el fjlfdr! jutesi! nepbajr mesbrmdr jlm

sfkezbpkrdlej,

? " =5


8/49

FBXU LTIND^ WJ^EJ]EBL +FBL]%

sburfd0 ^dmbl ^! dt ja Ljturd, >887 Lbv >63===+?::;%0===)4=, Oabnja vjrejtebl el fbpy luindr el tkd kuijl odlbid,

; " =5


9/49

FLW JLM ABK

Nbtk sddl el nbtk sbijtef jlm odriaeld fdaas! bgtdl ndleol,Nut odld)advda jipaefjtebls jlm mdadtebls js wdaa js ABK

ijy nd rdajtdm tb tuibreodldses! detkdr js j fjusd br dggdft,

]kd ijel sburfd bg mjtj gbr emdltegyelo FLW jlm ABK +jlm

rdajtdm vjrejtebl% es keok)mdlsety VLX jrrjys wkefk dljnad j

odlbid)wemd sdjrfk gbr fkrbibsbija vjrejtebls el j

sjipad3 el pjrtefuajr sufk jrrjys prbvemd nbtk odlbtypd jlm

fbpy luindr dsteijtdsgbr ibrd tkjl bld ieaaebl VLXs,

Gbr dxjipad! rdoebls bg ABK fjl nd gbulm el tuibr

sjipads ny fbipjrelo odlbtypds wetk ijtfkdm lbrijasjipads3 el jly rdoebl el wkefk bld jaadad es abst!

kdtdrbzyobus VLXs el lbrija jppdjr js kbibzyobus el

tkd tuibr,

5 " =5


10/49

V]J]EV]EFJA ID]KBMV

Tsdm tbmjy tb mdtdft wkdrd fkjlods bffur el jl elmevemuja

jlm mdtdrield jssbfjtebls ndtwddl vjrejtebl jlm mesdjsdel j pbpuajtebl,

]krdd njsef dsteijtebl prbnadis0 Mjtj Xrbfdsselo0 Fblvdrtelo tkd rjw eltdlsety mjtj +d,o,!

ubrdsfdlfd idjsurdidlts el Jggyidtrex VLX fkeps% gbr tkdVLX jrrjy tb dsteijtds bg FL jlm odlbtypd3 Vjipad Jllbtjtebl0 Mdtdftelo rdoeblsbg ABK jlm FLW

grbi odlbtypd jlm FL mjtj ny uteaezelo j prebre elgbrijtebl

jlm jssuiptebls jnbut VLX tb VLX mdpdlmdlfy!

pbpuajtebl stjtestefs jlm kemmdl trjlsetebl prbnjneaeteds3Adfturd= +tbmjy%,

Xbpuajtebl Vtumeds0 Fbipjrelo tkd mjtj grbi ijly

elmevemujas tb elgdr fbiibl rdoebls bg jnlbrijaety jlm tkder

jssbfejtebl wetk meggdrdlfds jiblo pkdlbtypds0 Adfturd7,

:8 " =5


11/49

BT]AELD

Odldtef Wjrejtebl



:: " =5


12/49

KEMMDL IJ^CBW IBMDAV

Mdvdabpdm ijelay gbr pjttdrl rdfboletebl +d,o,! spddfkrdfboletebl% el :5;8s,

]wb fbipbldlts0 Kemmdl stjtds! tkd bn`dftevd bg dsteijtebl! ibmdadm js j

Ijrcbv fkjel, Bnsdrvdm stjtds +seolja%! diettdm jt djfk elstjlt,

Ndfjid pbpuajr el :558s gbr jljayses bg nebaboefjasdqudlfds sufk js MLJ,

Dx0 Kemmdl stjtds jrd rdoebls bg ABK! FLW! FpO esajlms!

odlds! dtf, Bnsdrvdm stjtds jrd VLX fjaas,

Jasb pbpuajr gbr prbtdel sdqudlfd jaeolidlt jlm prdmeftelo

prbtdel strufturd,

:> " =5


13/49

KEMMDL X^BFDVV

J IF U:! U>! ,,,! U]! wkdrd Ut V! t 9 :! ,,,! ]! jlm V es j

letd sdt bg stjtds, ]jcd V 9 {:! ,,,! L}, Ijrcbv Xrbpdrty0 gbr jly t > jlm y:! ,,,! yt V0

X+Ut 9 yt|U: 9 y:! ,,,! Ut: 9 yt:% 9 X+Ut 9 yt|Ut: 9 yt:%,

Jssuid stjtebljry trjlsetebls0 X+Ut 9 c|Ut: 9 `% mbds lbtmdpdlm bl t! mdlbtdm ny j+`! c%,

j9 {j+`! c%}0 trjlsetebl ijtrex, +`% 9 X+[: 9 `%!` V0 stjrtelo mestrenutebl, ]kdl! gbr jly y 9 +y:! ,,,! y]% V]0

p+y% 9 X+U: 9 y:! ,,,! U] 9 yt% 9 +y:%]:t9:

j+yt! yt#:%,

:6 " =5


14/49

BNVD^WDM X^BFDVV

Diettdm seolja0 [:! ,,,! []! djfk [t ! j letd japkjndt bgsyinbas,

]wb njsef jssuiptebls0

]kd r,v,s [:! ,,,![] jrd fblmetebljaay elmdpdlmdlt oevdlU:! ,,,!U], ]kd mdpdlmdlfd bg [t bl U 9 y es abfja0

X+[t 9 |U 9 y% 9 X+[t 9 |Ut 9 yt%,

]kd diessebl prbnjneaetedsdt+|c% 9 X+[t 9 |Ut 9 c% jrd

pbssenay teid)mdpdlmdlt! btkdrwesd mdlbtdm seipay nyd+|c%! ! c V,

:= " =5


15/49

KII VXDFEGEFJ]EBL

]kd KII es mdtdrieldm ny vd qujlteteds0 V! ! j! ! d, ]kd pjrjidtdr es 9 +j! ! d%, ]kd `belt mestrenutebl p+x! y% 9 X+[ 9 x! U 9 y% bg +[! U% es

tkdl0

p+x! y% 9 p+x|y%p+y% 9 ]

t9:

dt+xt|yt%

+y:%

]:t9:

j+yt! yt#:%,

El bur jppaefjtebls! tkd kemmdl stjtds jrd ajndas gbr MLJ

abfjtebls sufk FL 9 6 br ABK! br elmefjtd idindrksepel j ajrodr strufturd! sufk js FpO esajlm br dxbl,

Bld sddcs tkd sdqudlfd bg ajndas wkefk es ibst aecday oevdl

tkd bnsdrvjtebls! jlm tkd pjrjidtdrs jrd adjrldm grbi mjtj

br nebaboy,

:4 " =5


16/49

]K^DD FAJVVEF X^BNADIV

Dvjaujtebl br Mjtj Aecdaekbbm0 Oevdl jl bnsdrvjteblsdqudlfd x ]! fbiputd p+x%! tkd prbnjneaety bg tkdbnsdrvdm stjtd,

Mdfbmelo br Xrdmeftebl0 Oevdl x! fbiputd tkd stjtd

sdqudlfd y V]

wkefk ijxeiezds p+x! y% +dquevjadltay!ijxeiezds p+y|x%%,

Adjrlelo br Ibmda Emdlfjtebl0 Oevdl sjipads bgsdqudlfds! adjrl tkd pjrjidtdrs tkjt ndst t tkdsd mjtj,]wb sunfjsds0

Fbipadtd mjtj0 Diessebl dxjipads tbodtkdr wetk tkd

fbrrdpblmelo stjtd sdqudlfds, Elfbipadtd bnsdrvjtebls0 Diessebl dxjipads blay,

:7 " =5


17/49

MJ]J AECDAEKBBM

Fbiputelo p+x|y% es strjeoktgbrwjrm0 p+x|y% 9

]t9: d+xt|yt%!wkefk blay elvbvads ] iuatepaefjtebls,

Veieajray! fbiputelo p+y% es jasb djsy! elvbavelo jasb blay ]iuatepaefjtebls,

Kbwdvdr! selfd

p+x% 9

yV]

p+x|y%p+y%!

fbiputelo p+x% etsdag grbi tkes gbriuaj es dxpbldlteja el ], J ij`br rdjsbl tkjt KIIs jrd usdgua es p+x% fjl nd

fbiputdm gjr ibrd dgfedltay uselo tkd gbrwjrm jaobretki,

:? " =5


18/49

GB^_J^M JAOB^E]KI

Gex x, Gbr djfk stdp t jlm stjtd c! mdldt+c% 9 X+[: 9 x:! ,,,! [t 9 xt! Ut 9 c%,

Oevdl{]+c%}0 p+x% 9L

c9: ]+c%,

Kbwdvdr! t+c% fjl nd fbiputdm ny elmuftebl bl t, :+c% 9 d+x:|c%+c% Gbr t 9 :!>! ,,,!] :! et fjl nd skbwl tkjt0

t#:+c% 9 d+xt#:|c%

`t+`%j+`! c%,

]kes jaobretki rdmufds tkd fbipadxety bg fbiputelo p+x%grbi >]L] tb L>],

:; " =5


19/49

X^DMEF]EBL

Bn`dftevd0 Mdtdrield tkd stjtd sdqudlfd y ibst aecday tbkjvd odldrjtdm tkd bnsdrvdm sdqudlfd x,

Vbautebl0 ]kd Wetdrne jaobretki! wkefk usds myljief

prborjiielo js el tkd gbrwjrm jaobretki! dxfdpt tkjt tkd

trjlsetebl prbnjneaeteds jrd ijxeiezdm rjtkdr tkjl suiidm

jt djfk stdp,

Mdld t+c% 9

ijxy:!,,,!yt:

X+[: 9 x:! ,,,! [t 9 xt! U: 9 y:! ,,,! Ut: 9 yt:! Ut 9 c%,

]kd Wetdrne jaobretki kjs twb stdps0 rdfursebl +gbrwjrm%

jlm njfctrjfcelo,

:5 " =5


20/49

WE]D^NE JAOB^E]KI

Gbrwjrm0 Gbr t 9 :! :+c% 9 +c%d+x:|c%, Gbr t 9 >! ,,,! ] jlm

jly c V0

t#:+c% 9 9 d+xt#:|c% ijx`

t+`%j+`! c%,

Adt t+c% V nd tkd stjtd `

jfkedvelo tkd ijxeiui, Njfcwjrm0 _d kjvd t+c% gbr dvdry t! c! el pjrtefuajr gbr

t 9 ], Adt 9 ijxc ]+c% jlm adt y

] 9 jro ijxc ]+c%, ]kdl es tkd ijxeiui bg p+x! y% bvdr jaa y! jlm y] es tkd

ajst dltry bg tkd ijxeiezelo stjtd sdqudlfd, ^dtredvd tkd btkdr ] : dadidlts bg tkd ijxeiezelo

sdqudlfd ny njfctrjfcelo0 yt 9 t#:+y

t#:% gbrt 9 ] :! ] >! ,,,! :,

]kd fbipadxety bg tkes jaobretki es jasb L>],

>8 " =5

B


21/49

BT]AELD

Odldtef Wjrejtebl



>: " =5

A K +ABK%


22/49

ABVV BG KD]D^BPUOBVE]U +ABK%

El fjlfdr! stumedm js j idfkjlesi gbr mesjnaelo tuibr

supprdssbr odlds murelo blfbodldses,

Faelefja mdletebl0 Abss bg bld jaadad el j kdtdrbzyobtef

mepabem brojlesi, Kdlfd j trjlsgbrijtebl grbi kbibzyobus

JJ el lbrija tb kbibzyobus J el fjlfdr es lbt ABK,

Xrbtbtypefja dxjipad0 el tkd kdtdrbzyobus stjtd! bld jaadades lbrija jlm tkd btkdr jaadad es j mdadtdrebus iutjlt +gbrdxjipad grbi jl elkdretdm iutjtebl% jlm kdlfd jardjmyeljftevjtdm, Ldw fdaa es detkdr0

Kdiezyobus0 bld mdadtdrebus jlm bld mdadtdm jaadad! br Mbunay iutjlt0 kbibzyobus gbr tkd iutjlt jaadad,

El nbtk fjsds lb gulfteblja jaadad rdijels! gbr dxjipad lb

gulfteblelo tuibr supprdssbr odld,

>> " =5

ABK + %


23/49

ABK +FBL]%

Ibrd odldrjaay el fbiputjteblja nebaboy +jlm el bur

jljayses wetk KIIs ndabw%0 seipay tkd abss bg bld jaadad, Gbr dxjipad! j fkjlod grbi kdtdrbzyobsety el tkd lbrija

odlbid tb kbibzyobsety el j pjerdm fjlfdr odlbid, _etk tkes mdltebl! tkd fkjlod grbi JJ el lbrija tb J el

fjlfdr esABK, Fbuam gbr dxjipad nd mud tb j fbipadtd abss bg bld jaadad

ny kdiezyobus mdadtebl! j fbpy abss dvdlt! br tb j

fbpy)ldutrja dvdlt sufk js fkrbibsbija mupaefjtebl, ABK fjl nd mdtdftdm el fjlfdrs ny lmelo kdtdrbzyobsety

jt j odldtef abfus el tkd odriaeld MLJ nut tkd jnsdlfd bg

kdtdrbzyobsety jt tkjt sjid abfus el fjlfdr fdaas, Tsujaay mbld wetk pbayibrpkef ijrcdrs! sufk js VLX

jrrjys,

>6 " =5

VLXV


24/49

VLXV

]kd ibst fbiibl gbri bg odldtef vjrejtebl,

_etk VLX jrrjys! tkdrd jrd spdfef prbnds tb idjsurd tkd

eltdlsety gbr tkd meggdrdlt lufadbtemds jt j pjrtefuajr abfus,

]kd prbfdss elvbavds dsteijtelo seoljas grbi lbesy eltdlsetymjtj jlm blay rdsuats el bld bg tkrdd pbsseneaeteds0 JJ0 Xrbfdsselo tkd rjw seoljas rdsuats el mdfajrelo blay typd

J +tkd fbiibl lufadbtemd br ij`br jaadad jt tkd abfus%

prdsdlt3 NN0 blay N es prdsdlt3 JN0 nbtk jrd +seolefjltay% prdsdlt,

>= " =5

AEIE]J]EBLV


25/49

AEIE]J]EBLV

Furrdlt tdfklbaboy! wkefk es njsdm bl MLJ grjoidlts!

mbds lbt mestelouesk ndtwddl fkrbibsbids el VLX fjaas! Elpjrtefuajr! bld mbds lbt clbw wkdtkdr bld br twb

fkrbibsbids fbltrenutdm tb tkd seolja,

Fblsdqudltay0 VLX fjaa JJ mbds lbt idjltkjt twb J

jaadads wdrd mdtdftdm3 jlm el VLX fjaa JN! et es lbt clbwlwkefk fkrbibsbid kjs tkd ielbr jaadad N,

Odlbtypd0 j fbineldm +ulbrmdrdm% mdsfreptebl bg tkd twb

jaadads3

Kjpabtypd0 tkd jaadads bl djfk fkrbibsbid! e,d,! ajndaelodjfk setd bl djfk pjrdltja fkrbibsbid js ij`br br ielbr,

]kd prbnadi bg jsseolelo kjpabtypds oevdl odlbtypds es

fjaadm pkjselo,

>4 " =5

VLX FJAAV


26/49

VLX FJAAV

= > 8 > =

=

>

8

>

= Fblfbrmjlt

JJJNNN

Mesfbrmjlt

fjaadm NN +JN%

Vdlsd

= > 8 > =

Jltesdlsd

e aa a a e ae e aa a e

e e a e e e ae e e e e e e a e

Geourd0 ^dpreltdm wetkbut pdriessebl grbi SY, KjpIjp odlbtypd fjaas

+tkd obam stjlmjrm% gbr j njm VLX +adgt% jlm j obbm VLX +reokt% gbr >75sjipads idjsurdm bl Jggyidtrex :88c VLX fkeps, ]kd KjpIjp

fblsdlsus odlbtypd fjaa es elmefjtdm ny fbabr0 JJ +idmeui ordy%! JN

+wketd%! jlm NN +mjrc ordy%, ]kd sdpjrjtebl ndtwddl odlbtypd

faustdrs es VLX)spdfef,

>7 " =5

JLB]KD^ AEIE]J]EBL


27/49

JLB]KD^ AEIE]J]EBL

Emdjaay! mdtdft ABK ny odlbtypyelo nbtktkd tuibr jlmtkdfbultdrpjrt lbrija odriaeld MLJ! jlm lbtd rdoebls wkdrd

kdtdrbzyobus jaadads el lbrija ndfbid kbibozybus el tkd

tuibr,

Kbwdvdr! pjerdm sjipads jrd lbt jawjys jvjeajnad +js wetkfdaa aelds! xdlborjgts! jrfkevja mjtj%! wkefk ibtevjtds tkd

idtkbmbaboy mdvdabpdm el SY,

Dvdl wetk blay tuibr sjipads! fjl lm ABK +elgdrrdmABK% nut iust jffbult gbr0

Vtjtestefja mdpdlmdlfy jiblo ldjrny VLXs mud tb tkd

kjpabtypd strufturd jlm aelcjod mdsdqueaenreui3 Wjrejtebl el kdtdrzyobsety rjtds bg VLX ijrcdrs,

>? " =5

ABK KII


28/49

ABK KII

t 9 :! ,,,! ]0 abfjtebls +abfe% bl j fkrbibsbid bg tkd ]VLXs jssjydm,

V 9 {ABVV! ^D]}! tkd kemmdl stjtds! rdprdsdltelo abss

jlm rdtdltebl bg kdtdrbzyobsety, ]kus! |V| 9 L 9 >, 9 {Kbi! Kdt}0 tkd bnsdrvdm odlbtypds! rdprdsdltelo

kbibzyobus +JJ! NN% jlm kdtdrbzyobus +JN% VLX fjaas,

Ut V0 ]kd ulbnsdrvdm ABK stjtd jt abfus t el tkd fjlfdr

fdaa, [t 0 ]kd bnsdrvdm odlbtypd jt abfus t el tkd fjlfdr fdaa,

>; " =5

XJ^JID]D^V


29/49

XJ^JID]D^V

Kdtdrbzyobus rjtds0 Jt djfk VLX t! adt rt nd tkd prbnjneaety

tkjt j pdrsbl fkbsdl jt rjlmbi grbi tkd rdgdrdlfd lbrija

pbpuajtebl kjs odlbtypd JN jt setd t,

VLX fjaas jrd sun`dft tb drrbr, Adt nd tkd ijppelo drrbrrjtd! jssuidm tb nd 8,8: gbr dvdry VLX,

rt! jrd mdrevdm diperefjaay,

El fbltrjst! t 9 +dt! ! jt%! t 9 :! ,,,! ] es ajroday mdtdrieldm

uselo nebaboefja jrouidlts,

>5 " =5

DIEVVEBL X^BNJNEAE]EDV


30/49

DIEVVEBL X^BNJNEAE]EDV

Eg Ut 9 ^D]! tkdl tkd prbnjneaety bg bnsdrvelo [t 9 Kdt es

seipay tkd bvdrjaa rjtd rt jt tkes abfus0 dt+Kdt|^D]% 9 rt, Eg Ut 9 ABVV! tkdl wd iust bnsdrvd [t 9 Kbiuladss

tkdrd es j ijppelo drrbr, Kdlfd dt+Kdt|ABVV% 9 ,

68 " =5

V]J^]ELO MEV]^ENT]EBL


31/49

V]J^]ELO MEV]^ENT]EBL

Idtkbm gbr mdtdrielo el SY0 jssuid dqueaenreui! e,d,! tkjt

tkd aecdaekbbm bg stjtd ^D] es tkd sjid jt dvdry abfus, MOrdgbriuajtebl0

Adt LKdt 9

t +[t 9 Kdt%! tkd luindr bg Kdt ijrcdrs eltkd sjipad,

DLKdt 9

tX+[t 9 Kdt%

9

t

X+[t 9 Kdt|Ut 9 ABVV%X+Ut 9 ABVV%

# X+[t 9 Kdt|Ut 9 ^D]%X+Ut 9 ^D]%9

t

X+Ut 9 ABVV% # rtX+Ut 9 ^D]%

t

rt+^D]%,

6: " =5

V]J^]ELO MEV]^ENT]EBL +FBL]%


32/49

V]J^]ELO MEV]^ENT]EBL +FBL]%

^dfjaa! DLKdt

t rt+^D]%,

Fblsdqudltay! :]

DLKdt 9 r+^D]% wkdrd r es tkd jvdrjodkdtdrbzyobus rjtd jt tkd abfe fblsemdrdm,

Lbw! gbr jly pjrtefuajr sjipad! rdpajfd tkd dxpdftdm

luindr ny LKdt etsdag! yedamelo0 +^D]% 9LKdt

r ],

6> " =5

]^JLVE]EBL X^BNJNEAE]EDV


33/49

]^JLVE]EBL X^BNJNEAE]EDV

]kd trjlsetebl

jt+`! c% 9 X+Ut#: 9 c|Ut 9 `%!`! c {ABVV! ^D]}! mdpdlmsbl tkd mestjlfd el tkd odlbid ndtwddl abfe t jlm t # :,

_kdl t! t # : jrd vdry gjr jpjrt tkd ABK stjtds jrd aecday tbnd +jaibst% elmdpdlmdlt wkdrdjs gbr twb ldjrny abfjtebls

tkdy jrd aecday tb nd tkd sjid,

Adt mt nd tkd odlbief mestjlfd ndtwddl t! t # : el ulets bg:88In jlm t 9 : dxp+>mt%,

Vdt jt+`! c% 9 +: t%+` 9 c% # t+c%!`! c {ABVV! ^D]},

Eltdrprdtjtebl0 Oevdl Ut 9 `! fkbbsd Ut#: 9 ` wetk prbnjneaety: t jlm fkbbsd Ut#: grbi wetk prbnjneaety t,

Dxjipad0 jt+ABVV! ABVV% 9 : t # t+ABVV%,

66 " =5

O^BTLM ]^T]K


34/49

O^BTLM ]^T]K

Orbulm ]rutk0 ]kd rdsuat bg j pjerdm lbrija)tuibr jljayses!mdlbtdm ny y,

Lbtd0 El j pjerdm jljayses! wd blay odt elgbrijtebl grbikdtdrbzyobus lbrija sjipads0

_kdl wd bnsdrvd JN el tkd lbrija sjipad! wd sdt

yt 9 ABVV eg wd sdd JJ br NN +e,d,! kbibzyobus% el tkdpjerdm tuibr sjipad! jlm yt 9 ^D] btkdrwesd +e,d,! sdd JNel nbtk tuibr jlm lbrija% br eg tkdrd es j lb fjaa el lbrija

nut JN el tuibr,

Bnsdrvelo JJ br NN es nbtk lbrija jlm tuibr eslblelgbrijtevd,

Vddelo JJ el lbrija jlm detkdr NN br JN el tuibr es j

fbleft jlm mesfjrmdm,

6= " =5

O^BTLM ]^T]K +FBL]%


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O^BTLM ]^T]K +FBL]%

Lddm tb jffbult gbr drrbrs ijmd jt abfe gbr wkefk tkd pjerdm

lbrija es kbibzyobus,

Fblteoubus sdftebls bg sufk kbibozybus VLXs ijy nd

gjasday fajssedm js ABVV el tkd jljayses bg tuibr sjipads

blay,

]b jmmrdss tkes trud ABK stjtds jrd jsseoldm ny

fblsemdrelo tkd fabsdst kdtdrbzyobus +kdlfd elgbrijtevd%

ijrcdrs! sjy s jlm u! bl djfk semd bg djfk kbibzyobus

ijrcdr t, Eg ys 9 yu 9 ABVV! wd sdt yt 9 ABVV3 btkdrwesdsdt yt 9 ^D],

64 " =5

XD^GB^IJLFD


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XD^GB^IJLFD

Oevdl tuibr fdaa odlbtypd mjtj x 9 +xt%! tkd IJX dsteijtbr

yijp V] gbr tkd ulbnsdrvdm ABK stjtds el tkd tuibr fdaaes tkd sdqudlfd wkefk ijxeiezds X+U 9 y|[ 9 x%! gbulmwetk tkd Wdtdrne jaobretki,

Dxpdreidlts wetk :88C VLX jrrjys gbr sjipads grbi aulo

jlm nrdjst fjlfdrs, Adt e elmdx j fbineljtebl bg sjipadjlm abfus,

VDLV 9&{e 0 ye 9 y

ijpe 9 ABVV}

&{e 0 ye 9 ABVV}9 ,55:

jlm

VXDF 9&{e 0 ye 9 y

ijpe 9 ^D]}

&{e 0 ye 9 ^D]}9 ,5=6,

67 " =5

BT]AELD


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BT]AELD

Odldtef Wjrejtebl



6? " =5

FLW


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FLW

FLWs0 ^doebls bg MLJ wkdrd j fdaa +el j mepabem brojlesi%

kjs ordjtdr br gdwdr tkjl tkd lbrija twb fbpeds,

Vdftebl adlotks rjlod grbi j seload abfus tb ieaaebls bg

njsds tb dlterd fkrbibsbids,

Tsuja fretdrebl0 j rdoebl bg jt adjst :cN tkjt es prdsdlt jt

vjrejnad fbpy luindr rdajtevd tb j rdgdrdlfd odlbid,

Vurpreseloay fbiibl el tkd kuijl odlbid,

El tkd KjpIjp Xrb`dft pbpuajtebl! :!==? mestelft FLWs

mesfbvdrdm! fbaadftevday fbvdrelo jpprbxeijtday 678

idojnjsds! br :>$ bg tkd kuijl odlbid,

El gjft! 7$):5$ bg jl elmevemujas fkrbibsbids dxkenet

FLWs! j refk sburfd bg odldtef mevdrsety,

6; " =5

JVVBFEJ]EBL _E]K MEVDJVD


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VVBF B V V

Jnbut kjag bg jaa FLWs jrd jssbfejtdm wetk prbtdel)fbmelo

rdoebls! dxtdlmelo grbi j seload odld tb j sdt bg+fblteoubus% odlds,

Ibst fbiibl FLWs jrd ndleol! nut sbid jrd faelfejaay

vdry eipbrtjlt ndfjusd j rdouajtbry dadidlt es mdadtdm br

ndfjusd sbid odlds jrd mbsjod)sdlsetevd, Vufk vjrejtebls jggdft pkdlbtypd vjrejtebls! mesdjsd resc

susfdpteneaety jlm rdsestjlfd, Dxjipads0 ]kd DOG^ odld bgtdl kjs jl dadvjtdm FL el LVFA fjlfdr,

Keok fbpy luindrs bg tkd D^NN> odld! rdsuatelo elbvdr)dxprdssebl! jrd emdltedm wetk nrdjst fjlfdr3 kdlfd

idjsurelo D^NN> dxprdssebl sdrvds js j mejolbsetf tbba, FLWs kjvd nddl aelcdm tb ldurbmdodldrjtevd mesdjsds sufk

js Xjrcelsbls jlm Jazkdeidrs,

65 " =5

IDJVT^ELO FLW


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J vjredty bg tdfklbaboeds dipabydm gbr mdtdftelo FLWs0 Iefrbsfbpds +djray ydjrs%3

Gaubrdsfdlt el setu kynremezjtebl3 Fbipjrjtevd odlbief kynremezjtebl3 VLX jrrjys +kdrd%3 Ldxt odldrjtebl sdqudlfelo,

=8 " =5

KEMMDL V]J]DV


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Ut0 ]kd kemmdl stjtd es tkd fbpy luindr,

Veipadst rdprdsdltjtebl0 V 9 {:! >! 6}! fbrrdspblmelo tb0 Kdiezyobus mdadtebl+FL 9 :%3 Lbrija br fbpy)ldutrja +FL 9 >%3 Jipaefjtebl+FL%,

=: " =5

VLX J^^JUV +^DWED_%


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+ %

]wb sburfds bg elgbrijtebl0 odlbtypds jlm sfjajr FL

dsteijtds! wetk tkd ajttdr usujaay mespajydm bl j abo> sfjad!

sb vjauds ldjr zdrb prbvemd dvemdlfd gbr mdadtebl! ldjr bldgbr lbrija jlm jnbvd bld gbr jipaefjtebl,

Vdd ldxt Geourd +grbi SFbrmdaajY% gbr jl eaaustrjtebl bg tkd

rjw butput idjsurdidlts grbi j VLX jrrjy,

=> " =5

FL


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`

Geourd0 +^dpreltdm wetkbut pdriessebl grbi Fbadaaj dt ja SY%

Fkrbibsbid)wemd mjtj, Abo ^ rjteb vjauds +tbp% jlm N jaadad

grdqudlfeds +nbttbi% pabttdm gbr djfk VLX grbi bld elmevemuja bl

fkrbibsbid 7, J mdadtebl bl tkd p)jri fjl nd emdltedm ny tkd skegt

el tkd abo ^ mbwlwjrms jlm tkd abss)bg)kdtdrbzyobsety elmefjtdm ny

tkd mesjppdjrjlfd bg kdtdrbzyobus stjtd +8,4% el tkd N jaadad

grdqudlfeds +js elmefjtdm ny tkd jrrbws%, =6 " =5

FLW KII FG, SVFKJ^XG D] JA,Y


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S Y

Gerst ibmda0 blay FL dsteijtds! e,d,! [t es tkd dsteijtd jt

abfus t gbr j pjrtefuajr VLX mdseol, Diessebl prbnjneaeteds0

dt+xt|yt 9 c% L+c! >%

> es dsteijtdm grbi mjtj,

]rjlsetebl ibmda0 sjid js gbr ABK0

jt+`! c% 9 +: t%+` 9 c% # t+c%

wkdrd `! c {:! >! 6}! jlm es jojel tkd prbnjneaety tkjt tkdkemmdl stjtds jt t jlm t # : jrd mdfbupadm ny j odlbiefdvdlt,

== " =5

EL]DO^J]ELO FL JLM ODLB]UXD


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FL dsteijtds jlm odlbtypds fjaas prbvemd fbipadidltjryelgbrijtebl jlm nd fbineldm tb skjrpdl tkd mdtdftebl bg

nbtk ABK jlm FLW,

Gbr dxjipad! grbi odlbtypd fjaas jabld bld fjllbt

mestelouesk ndtwddl fdrtjel typds bg ABK! sjy fjusdm nykdiezyobus mdadtebl jlm esbemsbiy +eTXM% wkdrd j sun`dft

elkdrets tkd sjid fbpy bg j pjrt bg tkd fkrbibsbid twefd

grbi bld pjrdlt,

Xrdvebus jljaysds fbineldm tkd lja rdsuats bg sdpjrjtday

mdtdftelo ABK jlm FLW +idtj)jljayses%,

Fblsemdr lbw j uledm jljayses wetk KIIs,

=4 " =5

TLEGEDM KII


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Ufl0 trud FL stjtd! jojel qujltezdm tb :!>!6,

Uabk0 trud ABK stjtd! jojel ABVV br ^D],

Kemmdl stjtds0

LB^IJA0 y

fl

9 >!

y

abk

9 ^D]! gbr dxjipad! JN +lbrija% tbJN +tuibr% br JJ tb JJ3 JIXAEGEFJ]EBL0 yfl 9 6! yabk 9 ^D]! d,o,! JJN tb JJN3 ABK0 yfl 9 >! yabk 9 ABVV3 d,o,! JN tb NN mud tb j

iutjtebl el tkd obbm fbpy! adjvelo twb mdadtdrebus iutjlt

jaadads, ]kes es tkd ibst faelefjaay rdadvjlt fjsd3 MDAD]EBL0 yfl 9 :! yabk 9 ABVV! d,o,! JJ tb J,

=7 " =5

]^JLVE]EBLV JLM DIEVVEBLV


47/49

]kd trjlsetebl ibmda es tkd sjid js ndgbrd! dxfdpt tkdrd

jrd lbw gbur stjtds jlm tkd eleteja mestrenutebl iust ndspdfedm,

Gbr diessebl prbnjneaeteds! bld fjl jssuid fblmeteblja

elmdpdlmdlfd ndtwddl [fl +d,o,! Ojussejl js jnbvd% jlm

[ot {Kdt! Kbi}0

d+xfl! xot|y% 9 d+xfl|y%d+xot|y%

9 d+xfl|yfl%d+xot|yabk%,

]kd rdsuats grbi jl dxpdreidlt el SY wetk rdja mjtj jrd

skbwl ndabw, ]kes elvbavds j KjpIjp sjipad wetk j

prdvebusay emdltedm +nut lbt dxpdreidltjaay fblridm%

TXM el fkrbibsbid >,

=? " =5

D[XD^EIDL]


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:88 :48 >88

:

>

6

=4

EFD

Wjl

MdadteblLbrija

ABKJipaegefjtebl

:58

:64 :=8 :=4 :48

:

>

6

=4

:=6

In

:=5 :=5,4 :48 :48,4 :4: :4:,4 :4>

EFD

Wjl

e 0 0 e e a, eaa e a e aa a e e e a

e e ! E e a a e e , a 0e e e a e , a e a e e e e

, aa e ! ae e e e ! e eaa

, e 0 e e eaa E e e ,e ! aa ! E a e e a

e e a,

Geourd0 +^dpreltdm wetkbut pdriessebl grbi Vfkjrpg dt ja SY% ]bp0 J

fblridm TXM ndtwddl :58 jlm >88 In es mdtdftdm el j KjpIjp

sjipad grbi tkd FDXK mjtjsdt, Nbttbi adgt0 j ijoledm vedw bg tkrdd

pbssenad ABK rdoebls +lbt fblridm%, ]kd fkrbibsbija sdoidlt

fbltjelelo tkd twb kdtdrbzyobus VLXs jt :=8 In es lbt j rdoebl bg

ABK! js prdmeftdm ny tkd vjleaaj KII, Nbttbi reokt0 ijolefjtebl bg

tkd prdmeftebls gbr tkd gdjturd jt :48 In, =; " =5

^DFJX BG EIXB^]JLFD EL FJLFD^


49/49

D^NN> Jipaefjtebl el >8$ bg Nrdjst Fjlfdrs3

]resbiy ; rdspblsenad gbr 5$ bg Jfutd Iydabem Aducdiej

jlm es tkd ibst fbiibl odldtef jndrrjtebl3

X]DL mdadtebl el up tb ?8$ bg Xrbstjtd Fjlfdrs3

^D] jipaefjtebl jssbfejtdm strbloay wetk joordssevd

gbris bg ]kyrbem Fjlfdr,

]kd DOG^ odld bgtdl kjs jl dadvjtdm FL el LVFA fjlfdr,

=5 " =5

Lecture 4 (D. Geman)

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Transcript of Lecture 4 (D. Geman)