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7/29/2019 Lecture1 (D. Geman)
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[WNWO[WOKNF FLNYCOCA OC KNCKLYIODFDA_: FLKW\YL >
Gdcnfg Alenc& Eokhnlf Dkhs& Fnurlct _duclsJdhcs Hdp`ocs \cvlrsoty
LC[%Knkhnc
Blirunry 1& 9=>;
7/29/2019 Lecture1 (D. Geman)
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D\WFOCL
[kdpl db thl [lrols
[ystles Iodfday td [ystles Elgokocl Lnrfy [ukklss [tdrols ncg Khnfflcals
Klctrnf Gdaen
Kncklr: Borst Edglf
9 $ 21
7/29/2019 Lecture1 (D. Geman)
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FLKW\YL [LYOL[
Flkturl >: Octrdguktodc (GA/
Flkturl 9: Kncklr Iodfday (ED/
Flkturl ;: Klff [oacnfoca Cltwdr`s (ED/
Flkturl 7: Alcltok Rnrontodc (GA/
Flkturl
7/29/2019 Lecture1 (D. Geman)
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OC[OGL WHL [LYOL[
{Kdctlct} {Kdeputntodcnf Edflkufnr Elgokocl}
Kdeputntodcnf: Whrll poffnrs: hypdthlsos tlstoca& stntostoknf flnrcoca ncg
stdkhnstok edglfoca ncg soeufntodc# [tntostoknf flnrcocans prdxy bdr nff thrll#
Edflkufnr: Ns oc edflkufnr iodfday& sd ocvdfvoca iodedflkufls oc klffs&
enocfy GCN& YCN ncg prdtlocs# Elgokocl:
Nssdkontoca alcltok vnrontodc woth goslnsl0 ]rlgoktoca phlcdtypls brde edflkufnr kdcklctrntodcs0 \cglrstncgoca goslnsl oc thl kdctlxt db edflkufnr cltwdr`s
db alcls ncg alcl prdgukts0
7 $ 21
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D\W[OGL WHL [LYOL[
Wlkhcdfday: (Nfedst/ cdthoca nidut ngvnckls oc alclrntoca deoks gntn# Oc pnrtokufnr& cdthoca nidut clxt%alc xyz& gntn nkquosotodc&
gntn prlprdklssoca#
Bdr us& gntn nrl n entrox db cueilrs# [dbtwnrl:
Kdeputntodcnf gdls cdt stncg bdrkdeputlr%inslg# Cdthoca dc pnk`nals bdr oepflelctoca splkok nfadrothes&
dc tddfs bdr thl kdeeucoty& dr dc Y dr ncy dthlr
prdarneeoca fncaunal#
Elgoknf Ocbdrentoks: Cdthoca nidut stdroca& rltrolvoca&drancozoca& shnroca gntn#
< $ 21
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RNYONIFL[
Edglrc knpturl glvokls lcnifl thl soeuftncldus ncgqunctotntovl nsslsselct db ency edflkufnr stntls:
YCN (eYCN& eoYCN& ltk#/ lxprlssodc# Eltnidfotl qunctokntodc# GCN pdfyedrphose elnsurlelcts (l#a#& [C]s/# ]rdtloc qunctokntodc (l#a#& von Enss[plk/# Elthfyntodc nrrnys#
GCN%prdtloc iocgoca (l#a#& KHO]%Khop/#
2 $ 21
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QH_ [WNWO[WOKNF FLNYCOCA4
Edflkufnr gntn nrl stdkhnstok# Qothoc socafl klffs& YCN ncg prdtloc lxprlssodc nrl
ochlrlctfy stdkhnstok# Enssovl vnroniofoty oc thl huenc alcdel brde plrsdc td
plrsdc# [oeofnrfy brde tossul td tossul ncg phlcdtypl td phlcdtypl#
Edflkufnr gntn nrl hoah%goelcsodcnf# Ncnfyzoca thle iy hncg dr iy ocsplktodc os oepdssoifl# Kdeputntodcnf elthdgs nrl clklssnry bdr ucionslg
goskdvlry& hypdthlsos alclrntodc ncg soeufntodc#
1 $ 21
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D\WFOCL
[kdpl db thl [lrols
[ystles Iodfday td [ystles Elgokocl
Lnrfy [ukklss [tdrols ncg Khnfflcals
Klctrnf Gdaen
Kncklr: Borst Edglf
8 $ 21
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FN[W KLCW\Y_: ALCL%KLCWYOK QDYFG
Krok`s klctrnf gdaen os n gorlktodcnffy dcl wny volw db thlalcltok kdgl ncg fovoca systles#
Whl alcdel os thl ifulproct ncg idd` db fobl#
Bucktodc ncg goslnsl nrosl brde splkok alcls (alcltok
gltlreocose/# Nc drancoses phlcdtypl ncg rlspdcsl td ncy
lcvordcelctnf stoeufus knc thldrltoknffyil gltlreoclg ob otsalcdel os kdepfltlfy khnrnktlrozlg#
N adfg rush bdr goslnsl alcls iy thl phnrenklutoknfocgustry#
Huenc Alcdel ]rdjlkt
? $ 21
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YLRO[ODC: [_[WLE[ IODFDA_
\cglrstncgoca goslnsl& glvlfdpelct ncg klff bucktodcocvdfvls n kdepflx& octlrwdvlc cltwdr` db pnrts#
HA] prdvogls dcfy n pnrts fost& ncg eokl ncg elc hnvl
nidut thl snel fost#
Alcls ncg thlor prdgukts gd cdt nkt ocglplcglctfy& iutocstlng nrl drancozoca octd bucktodcnf ucots#
Bucktodc ncg goslnsl nrl gltlreoclg iy cltwdr`
octlrnktodcs# [plkols gobblrlckls nrosl brde thl drkhlstrntodcdb alcl
lxprlssodc#
Whl dijlktovl os thlc td ncnfyzl rlfntodcshopsnedcaiodedflkufls oc thl kdctlxt db n cltwdr`#
>= $ 21
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[_[WLE[ IODFDA_ (KDCW/
Whlrlbdrl& nc octlarntovl& kdeputntodcnf npprdnkh tdiodfday glsoaclg td nkholvl n systles ucglrstncgoca#
Lcniflg iy thl gntn rlvdfutodc& o#l#& thl deoks
tlkhcdfdaols# [ystle prdplrotls nrl flnrclg brde gntn#
Octlarntovl elncs dvlr euftopfl iodfdaoknf sknfls ncgedflkufnr nalcts& hlckl gobblrlct brde thl trngotodcnf
rlguktodcost npprdnkh#
Nt thos flvlf db kdepflxoty& enthlentoknf edglfoca os
ocglsplcgsnifl bdr prlgoktoca systle prdplrtols# Oc pnrtokufnr& n gllp ucglrstncgoca rlquorls n stntostoknf
khnrnktlrozntodc: flnrcoca thl fo`lfy ncg ucfo`lfy edflkufnr
kdcklctrntodcs& cdt just ocgovogunffy iut kdfflktovlfy#
>> $ 21
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WDQNYG[ [_[WLE[ ELGOKOCL
Goslnsls knc il lxpfnoclg ns plrturintodcs db alcltok&
edflkufnr ncg klffufnr cltwdr`s#
Bdr lxnepfl& bdr grua glsoac ot os clklssnry td ucglrstncg
tnralt rlspdcsl wothoc thl kdctlxt db physodfdaoknf cltwdr`s#
Oc prockopfl& tdpdfdaoknf ncg stntostoknf soacnturls (l#a#&
fo`lfohddg rntods/ knc ocbdre kfocoknf glkosodcs#
Kdcslqulctfy& sdel tddfs nrl oc pfnkl td nppfy [I td
huenc goslnsls#
[ystles elgokocl: Whl nppfokntodc db systles iodfday
npprdnkhls td elgoknf rlslnrkh ncg prnktokl#
>9 $ 21
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IODENY@LY[
[delthoca elnsurnifl whokh knrrols ocbdrentodc nidut thl
dkkuftstntl db thl goslnsl# Hlckl n surrdantl bdr thlstntl db octlrlst#
Wypls: Gonacdstok: skrllcoca iodenr`lrs brde slrue& oenaoca&
snfovn dr urocl# [plkokoty gdeocntls# ]rdacdstok: inslg dc tuedr tossul (l#a#& lxprlssodc& KCR/#
[lcsotovoty gdeocntls# ]rlgoktovl db trlntelct dutkdel: inslg dc tuedr tossul#
>; $ 21
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[]LKOBOK DIJLKWORL[
Goskdvlr iodenr`lrs ncg iodenr`lr octlrnktodcs bdr goslnsl
prdarlssodc whokh nrl kfocoknffy uslbuf bdr lnrfy gonacdsos&
ros` nsslsselct& prdacdsos ncg plrsdcnfozlg trlntelct#
Lfukogntl thl pnthdphysodfdaoknf elkhncoses dbeuftobnktdronf$khrdcok goslnsls (l#a#&kncklr& goniltls&
dilsoty& eltnidfok gosdrglrs& naoca/#
Glvlfdp strntlaols bdr kdeiocntdronf grua thlrnpols ncg
skrllcocas& tlst lbblktovl trlntelct& ncg prlgokt gruaslbblkts ncg sogl%lbblkts#
>7 $ 21
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D\WFOCL
[kdpl db thl [lrols
[ystles Iodfday td [ystles Elgokocl
Lnrfy [ukklss [tdrols ncg Khnfflcals
Klctrnf Gdaen
Kncklr: Borst Edglf
>< $ 21
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KNCKLY GONACD[O[: ADF\I LW NF >???
Oc >?2=s& nkutl flu`leons wlrl govoglg octd nkutlfyephdifnstok flu`leon (NFF/ ncg nkutl eylfdog flu`leon
(NEF/#
[lpnrntodc wns inslg dc hostdkhleoknf tlstoca& ncg fntlr
dc nctoidgy%inslg tlstoca# Oc lothlr knsl& thlrl wns cd socafl lstnifoshlg tlst td en`l
thos gonacdsos#
Adfui lt nf uslg suplrvoslg enkhocl flnrcoca td flnrc n
prlgoktdr db NFF vs NEF inslg dc n soacnturl db alcllxprlssodc vnfuls#
Clw flu`leon knsls kdufg thlc il kfnssolg brde
eokrdnrrny gntn lxtrnktlg brde tossul#
>2 $ 21
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[\IW_]L GO[KDRLY_: NFOZNGLH LW NF 9===
Whl nuthdrs elnsurlg alcl lxprlssodc oc snepfls brdepntolcts gonacdslg woth gobbusl fnral I%klff fyephden& n
kncklr db I%fyephdkytls#
]rlvodusfy& sukh kncklrs wlrl govoglg octd fdw%&
octlrelgontl% ncg hoah%arngl kntladrols inslg dc ardwthpnttlrcs ncg oeeucdhostdkhleostry#
Nfoznglh nppfolg holrnrkhoknf kfustlroca td thlsl gntn&
rlvlnfoca n govosodc db I%klff fyephden snepfls octd nc
lqunf spfot db twd suitypls# Edrldvlr& pntolcts rltrdsplktovlfy gledcstrntlg soacoknct
gobblrlckls oc survovnf (@npfnc%Elolr ncnfysos/#
>1 $ 21
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WHLYN]L\WOK[: I\WWL LW NF 9===
Alclrntlg hypdthlsls nidut bucktodcnf rlfntodcshopsiltwllc pnors db alcls ncg phnrenklutoknfs#
Wwd gntninsls: Inslfocl eokrdnrrny elnsurlelcts db 21=> alcls oc n
stncgnrgozlg slt db 2= huenc kncklr klff focls# Grua susklptoiofoty elnsurlelcts bdr thl snel klff focls&
nkrdss clnrfy 8 $ 21
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HO[WD]NWHDFDA_: YNEN[QNE_ LW NF 9==>
Hostdpnthdfday: stugy db goslnslg tossul iy slktodcoca&
stnococa& ncg eufto%rlsdfutodc eokrdskdpy#
Kdeputntodcnf elthdgs knc gltlreocl whlthlr sukhsnepfls qunctotntovlfy rlsleifl n goslnsl#
\soca suppdrt vlktdr enkhocls& Ynenswney lt nf& 9==>&
prlgoktlg thl droaocnf sdurkl db n kncklr aovlc just n
eltnstntok snepfl#
>? $ 21
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D\WFOCL
[kdpl db thl [lrols
[ystles Iodfday td [ystles Elgokocl
Lnrfy [ukklss [tdrols ncg Khnfflcals
Klctrnf Gdaen
Kncklr: Borst Edglf
9= $ 21
I C _
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I\W CDW _LW
Iut glspotl thlsl prdeosoca ilaoccocas ncg pdst%HA]tlkhcdfdaoknf ngvnckls& ncg woth blw lxklptodcs& thlrlsufts td gntl brde kdeputntodcnf flnrcoca nrl cdt
subkolctfy nkkurntl dr rlprdgukoifl bdr kfocoknf usl#
Oc pnrtokufnr& thl lbblkt db deoks gntn dc grua goskdvlry ncgthl oglctokntodc db cdvlf& edrl lbblktovl thlrnpols hns illc
foeotlg#
Ncg ot rlenocs uckflnr hdw lxnktfy td lxtrnkt uslbuf elgoknf
`cdwflgal brde lxplroelctnf gntn& whlrl uslbuf elncsnkholvoca hoahlr prlkosodc ncg pntolct ilclt thnc knc il
kurrlctfy ditnoclg woth trngotodcnf kfockonf prnktokl#
9> $ 21
G
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GNWN
G : Hoah%goelcsodcnf& hoah%thrduahput alcdeok gntn#
Whl trngotodcnf npprdnkh lxplroelctnf ncg
edflkufl%iy%edflkufl os cdt blnsoifl bdr thos flvlf db
kdepflxoty# N prockopflg enthlentoknf npprdnkh hns ilkdel
ocgosplcsoifl bdr lxtrnktoca `cdwflgal brde G#
Bdr lxnepfl& dvlr thl fnst glkngl stntostoknf flnrcoca hns
lelralg ns n kdrl elthdgdfday bdr thl ncnfysos db G#
99 $ 21
I O W
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INYYOLY O: WLKHCDFDAOKNF
Kdfflktoca G usunffy rlquorls nc ocvnsovl prdklgurl#
G os dbtlc db fdw qunfoty& glarnglg iy fni ncg intkh lbblkts#
Whl cueilr db snepfls oc G os usunffy ocsubkolct tdrlprlslct thl pdpufntodcs ucglr stugy& ncg tdd senff td
alclrntl rlsufts whokh nrl stntostoknffy rdiust ncg
kdcsostlct nkrdss stugols ncg glvokls#
9; $ 21
I OO W [ D
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INYYOLY OO: WYNC[FNWODCNF
Qoth dbb%thl%shlfb stntostoknf flnrcoca tlkhcoquls& thl flnrclg
edglfs ncg glkosodc rufls usunffy ocvdfvl cdcfoclnr
bucktodcs db n arlnt ency vnronifls# Kdcslqulctfy& ot os gobkuft td fdd` ucglr thl hddg& ylt
thlrl os ngglg vnful oc trncspnrlcky bdr `cdwflgal
goskdvlry ncg trlntelct glsoac#
97 $ 21
INYYOLY OOO ENWHLENWOKNF
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INYYOLY OOO: ENWHLENWOKNF
Whl enthlentoknf khnfflcals nrl bdreognifl ilknusl c& thl
cueilr db snepfls& os vlry senff rlfntovl td g& thl cueilr
db edflkufnr splkols nssnylg#
Oglnffy& c g# Oc prnktokl& c g#
Hlckl& oc volw db trngl%dbbs iltwllc ions ncg vnronckl&
ockdrpdrntoca rokh n prodro`cdwflgal td kdcstrnoc thl
rlprlslctntodcs db G eny il ucnvdognifl#
9< $ 21
W_]OKNF KN[L[
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W_]OKNF KN[L[
Gltlkt goslnsl phlcdtypls brde eokrdnrrny gntn woth
g 5 >=& === trncskropts ncg c5 >== (dr blwlr/ pntolcts#
Elnsurl thl glarll db phlcdtypok%rlaufntodc oc pnthwnyswoth g 5 >== alcls bdr c5 >== snepfls#
Ocblr thl stntostoks (ncg pdssoify thl woroca gonarne/ db
soacnfoca ncg alcl rlaufntdry cltwdr`s woth g 5 >==vnronifls (alcls& prdtlocs/ ncg c5 >== snepfls#
92 $ 21
[ENFF C FNYAL G: DCL KDC[L^\LCKL
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[ENFF C& FNYAL G: DCL KDC[L^\LCKL
Gltlreococa soacoknckl db cgocas os prdiflentok# Eust kdeplcsntl bdr enssovl tlstoca#
Lxnepfl: \soca eokrdnrrnys ditnoclg bdr twd phlcdtypls
N& I& tlst thl hypdthlsos db cd gobblrlckl oc gostroiutodc bdr
lnkh db 7=&=== alcls (trncskropts/# Whos alclrntls n p%vnful bdr lnkh alcl0 tn`l =#=< ns thl
thrlshdfg#
Whlc lvlc ob N 5 I& dc nvlrnal ydu goskdvlr 9===
gobblrlctonffy lxprlsslg alcls# Edtovntls n gllplr stntostoknf ncnfysos& ockfugoca bnfsl
goskdvlry rntls#
91 $ 21
LXNE]FL: OE]YDRLG ]YLRLCWORL KNYL
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LXNE]FL: OE]YDRLG ]YLRLCWORL KNYL
[tncgnrg fni rlpdrt (l#a#& brde ifddg dr urocl/ usls
iodenr`lrs X>& X9& ###: Ob Xo 3 & khlk` dut goslnsls n& i
Elnsuroca octlrnktodcsnedca alcltok enr`lrs ncg
edflkufnr kdcklctrntodcs knc rlvlnf edrl ocbdrentodc: Oba(Xo& Xj& X / 3 & khlk` ###
Iut whnt os thl roaht slt {a} db bucktodcs& edglfs drkdeiocntdronf fdaok4
Qhnt woff senff c& fnral g nffdw4
98 $ 21
LXNE]FL: ]LY[DCNFOZLG KNCKLY
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LXNE]FL: ]LY[DCNFOZLG KNCKLY
WYLNWELCW
[tncgnrg trlntelct (prdacdsos& khdokl db gruas/ os inslg
dc pdpufntodc stntostoks# Iut& enssovl govlrsoty nedca tuedrs db thl snel alclrnf
kntladry gul td gobblroca eutntodcnf soacnturls#
Hdw rokh n sui%kntladrozntodc knc wl nbbdrg inslg dc thl
nvnofnifl gntn4
9? $ 21
LXNE]FL: EDFLK\FNY GONACD[O[ DB
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LXNE]FL: EDFLK\FNY GONACD[O[ DB
GO[LN[L
Goslnsls nrl dbtlc thl rlsuft db plrturilg iodedflkufnr
cltwdr`s& flngoca td gobblrlckls oc thl niucgnckls db
iodedflkufls (l#a#& eYCN& prdtlocs& eltnidfotls/#
Ncnfyzoca thlsl gobblrlckls lcnifls flnrcoca prlgoktdrs db
goslnsl prlslckl& stntus ncg rlspdcsl td trlntelct#
Oc pnrtokufnr& trncskroptdeoks prdvogls thl afdinf eYCN
lxprlssodc db pnrtokufnr tossul lxpdsoca trncskroptodcnf
gobblrlckls nedca goslnsls#
Qhnt enr`lr octlrnktodcs gd thlsl gntn rlvlnf4
;= $ 21
GNCALYD\[ FONO[DC[
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GNCALYD\[ FONO[DC[
Kdeputntodcnf iodfday& vosodc ncg spllkh: Hoah%goelcsodcnf gntn (fnral g/ N pnttlrc goskdvlry kdrl
Iut oepdrtoca elthdgdfday td iodfday os gncalrdus: Dur c os drglrs db enacotuglsenfflr0 Ifnk` idxls nrl dbtlc n foniofoty#
Knelrn bnkl gltlktdrs wlrl glvlfdplg woth edrl snepfls thlc thl
tdtnf cueilr db (puifokfy nvnofnifl/ huenc alcl khops (rduahfy
c5 7
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D\WFOCL
[kdpl db thl [lrols
[ystles Iodfday td [ystles Elgokocl
Lnrfy [ukklss [tdrols ncg Khnfflcals
Klctrnf Gdaen
Kncklr: Borst Edglf
;9 $ 21
GCN
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GCN
;; $ 21
]NK@NAOCA OC WHL C\KFL\[
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]NK@NAOCA OC WHL C\KFL\[
Whl huenc alcdel os nidut >#8 eltlrs fdca ncg thl
cukflus db n klff os 2 >=2
eltlrs oc goneltlr GCN os knrlbuffy pnk`nalg octd thl cukflus oc n rlaufntlg
wny0 pnk`naoca os kdrrlfntlg woth alcl lxprlssodc ncg
thlrlbdrl phlcdtypl#
;7 $ 21
YCN
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YCN
Yoidcukflok nkog
[ocafl%strncglg
suanr%phdsphntl ink`idcl
woth cukfldtogls# \rnkof(\/ ocstlng db
Whyeocl(W/#
Knc iocg td GCN dr YCN#
Ydfls: ocbdrentodc knrrolr&rlaufntdry& lczyentok#
;< $ 21
W_]L[ DB YCN
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W_]L[ DB YCN
eYCN: tn`ls ocbd brde GCN ncg lckdgls prdtlocs
rYCN: pfntbdre ncg lcvordcelct bdr prdtloc sycthlsos
tYCN: irocas neocd nkogs oc td bdre prdtlocs eoYCN: rlaufntdry ncg dthlr bucktodcs
soYCN: rlaufntdry ncg dthlr bucktodcs
roidzyels: hual nrrny db bucktodcs
;2 $ 21
KLCWYNF GDAEN
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KLCWYNF GDAEN
;1 $ 21
WYNC[KYO]WODC: GCN WD YCN
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WYNC[KYO]WODC: GCN WD YCN
Fdts db rlaufntodc rlquorlg#
GCN oc cukflus os vlry
kdepnkt#
YCN pdfyelrnsl cllg
nssdkontlg bnktdrs oc drglr td
iocg#
;8 $ 21
WYNC[FNWODC: YCN WD ]YDWLOC
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[ D D D
;? $ 21
ALCLWOK KDGL: EYCN [L^\LCKL WD
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]YDWLOC [L^\LCKL
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KHYDED[DEL[
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Wuedr [upprlssdr Alcls
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Flt (t// 5 (C=(t/& # # # & Cg(t//#
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5`
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N ENWFNI [OE\FNWODC
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LX]LKWLG QNOWOCA WOEL BDY KNCKLY
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t` 5 `(fda sug/9
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