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7/31/2019 Some Introductory Remarks on Bayesian Inference
1/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Pndg Keq}naw`qn}{ ]gdb}jp neMb{gpkbe Kehg}ge`g
Dkjkn L% M}bwe
Pgdkeb} ne Mb{g Qcgn}{, QW Mg}lke, PP?9
2 . = 1
http://find/http://goback/7/31/2019 Some Introductory Remarks on Bayesian Inference
2/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Nxg}xkgy
2
Keq}naw`qkneMb{g ]wlg
= @nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkne
Gsbdplg6 Ibwkbe }beand xb}kbmlg
Gspnegeqkbl Hbdklkg
0 _cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{
Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
= . = 1
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
3/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Mb{g ]wlg
Kei}gakgeq6
Dnagl D
Abqb A
_}kn} _#D+
@neakqknebl _}nmbmklkq{ _#A|D+
Mb{g ]wlg _#D|A+ 4_#A|D+_#D+
_#A+4
_#A|D+_#D+_#A|D+_#D+aD
0 . = 1
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
4/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Mb{g ]wlg
Kei}gakgeq6
Dnagl D
Abqb A
_}kn} _#D+
@neakqknebl _}nmbmklkq{ _#A|D+
Mb{g ]wlg _#D|A+ 4_#A|D+_#D+
_#A+4
_#A|D+_#D+_#A|D+_#D+aD
dwlqkplg abqb pnkeq m{ keagpgeage`g bwdpqkne6
_#A2, % % % ,Ae|D+ 4e
k42
_#Ak|D+%
0 . = 1
K a k
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
5/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Be gsbdplg
D zgxnlwqkne, keqgllkigeq agkie, qcg Dbq}kst%
A zhnkl, qcg mkmlg, agfob xwt
1 . = 1
K q a qk
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
6/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Be gsbdplg
D zgxnlwqkne, keqgllkigeq agkie, qcg Dbq}kst%
A zhnkl, qcg mkmlg, agfob xwt
Pn ycbq k _#gxnlwqkne|qcg mkmlg+>
1 . = 1
Keq}naw`qkne
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
7/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Be gsbdplg
D zgxnlwqkne, keqgllkigeq agkie, qcg Dbq}kst%
A zhnkl, qcg mkmlg, agfob xwt
Pn ycbq k _#gxnlwqkne|qcg mkmlg+>
N} _#keqgllkigeq agkie|hnkl+>
1 . = 1
Keq}naw`qkne
http://find/http://goback/7/31/2019 Some Introductory Remarks on Bayesian Inference
8/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Be gsbdplg
D zgxnlwqkne, keqgllkigeq agkie, qcg Dbq}kst%
A zhnkl, qcg mkmlg, agfob xwt
Pn ycbq k _#gxnlwqkne|qcg mkmlg+>
N} _#keqgllkigeq agkie|hnkl+>
N} _#qcg Dbq}ks|hnkl+ x% _#qcg Dbq}ks|dbe{ agfob xw+>
1 . = 1
Keq}naw`qkne
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
9/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Blqg}ebqkxgl{%%%
_#A|D+_#D+aD lnnj lkjg neg qgp ke b Db}jnx `cbke%
dnagl b}g ygkicqga b``n}akei qn qcgk} `neq}kmwqkne qn A
7 . = 1
Keq}naw`qkne
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
10/35
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nweaMb{g ]wlg
Yc{ `cnng akg}geq p}kn}>
Pcnwlaeq yg mg npge qn bll pnkmklkqkg>
Bea mg h}gg h}nd p}gfwak`g>
8 . = 1
Keq}naw`qkne
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
11/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Mb{g ]wlg
Yc{ `cnng akg}geq p}kn}>
Pcnwlaeq yg mg npge qn bll pnkmklkqkg>
Bea mg h}gg h}nd p}gfwak`g>
8 . = 1
Keq}naw`qkne Gsbdplg6 Mg}enwllk akq}kmwqkne
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
12/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
pGsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
@nefwib`{
Agpgeakei ne qcg p}nmbmklkqkg kexnlxga, `ndpwqkei Mb{g hn}dwlb}}grwk}g neg keqgi}bqkne yck`c db{ mg kehgbkmlg%
Cnygxg}, hn} dbe{ p}nmbmklkq{ akq}kmwqkne, kq k pnkmlg qn `cnngb p}kn} w`c qcbq
Mb{g }wlg `be mg bpplkga gsb`ql{,
qcg pnqg}kn} cb qcg bdg hwe`qknebl hn}d b qcg p}kn}%
Qck k `bllga `nefwib`{, bea qcg p}kn} k `bllga qcg `nefwibqg p}kn}%
9 . = 1
Keq}naw`qkne Gsbdplg6 Mg}enwllk akq}kmwqkne
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
13/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Mg}enwllk akq}kmwqkne
_#s 4 2|+ 4 _#s 4 ?|+ 4 2
_#s|+ 4 s#2 +2s
3 . = 1
Keq}naw`qkne@
Gsbdplg6 Mg}enwllk akq}kmwqkneI
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
14/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Iwgkei qcg p}kn}
_#D|A+ 4_A|D_#D+
_#A+ _#A|D+_#D+%
Bpp}nb`c6 Hn}igq qcg en}dblkvbqkne, lnnj hn} b _#D|+ w`c qcbq
_#A|D+_#D|+ _#D|+
Hn} gsbdplg6 b#2
+m6
s#2 +2sb#2 +m 4 s*b#2 +m*2s
; . = 1
Keq}naw`qkne@ f
Gsbdplg6 Mg}enwllk akq}kmwqkneG l I k a k ml
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
15/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Hkeakei qcg en}dblkvbqkne
Hn}qwebqgl{, qck cb bl}gba{ mgge `b}}kga nwq bea qcg `n}}g`q p}kn}akq}kmwqkne `be mg hnwea #ndgycg}g+%%%
Mgqb akq}kmwqkne6
Mgqb#|b, m+ 4#b * m+
#b+#m+b2#2 +m2%
Gspg`qbqkne6 b.b * m##e+ keqg}pnlbqg qcg hb`qn}kbl, #e+ 4 #e 2+"+%
2?.=1
Keq}naw`qkne@ f
Gsbdplg6 Mg}enwllk akq}kmwqkneG l I k a k ml
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
16/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Keqg}p}gqkei qcg p}kn}6 _gwan$`nweq
b, m b}g pgwan$`nweq6
s#2 +2sb2#2 +m2 4 b*s2#2 +m*#2s+2
Qcg}ghn}g6
b b * 2 ycge s 4 2
m m* 2 ycge s 4 ?
22.=1
Keq}naw`qkne@nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlg
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
17/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Qcg Mgqb$Akq}kmwqkne
2=.=1
Keq}naw`qkne@nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlg
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
18/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Qcg Mgqb$Akq}kmwqkne
2=.=1
Keq}naw`qkne@nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlg
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
19/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Qcg Mgqb$Akq}kmwqkne
2=.=1
Keq}naw`qkne@nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlg
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
20/35
@nefwib`{_cklnnpck`bl Mb`ji}nwea
Gsbdplg6 Ibwkbe }beand xb}kbmlgGspnegeqkbl Hbdklkg
Ke b kdklb} dbeeg}%%%
Mkendkbl akq}kmwqkne6e
j
j#b +ej 4 Mgqb#|b, m+%
Dwlqknekdbl akq}kmwqkne6
e
e2e= % % % eJ
Jj42
ejj
4 Ak}k`clgq akq}kmwqkne
Ak}#|+ 4#?+
#2+ % % % #J+
Jj42
2j
%
20.=1
Keq}naw`qkne@nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlg
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
21/35
f i {_cklnnpck`bl Mb`ji}nwea
pGspnegeqkbl Hbdklkg
Qcg Ibwkbe
Qcg Ibwkbe akq}kmwqkne6
p#s|, =+ g#s+=.==
Lgq w iwg qcg `n}}g`q p}kn} hn} 6 kq cnwla mg b rwba}bqk`hwe`qkne s6
p#|b, m+ gb#sm+=
%%% yck`c k mbk`bll{ bibke b Ibwkbe akq}kmwqkne%
_nqg}kn} hn} e abqb pnkeq6
e 4=
e=? * =? *
e=?e=? *
=DL
2
=e4
2
=?*
e
=%
21.=1
Keq}naw`qkne@nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlg
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
22/35
_cklnnpck`bl Mb`ji}nwea Gspnegeqkbl Hbdklkg
Qcg Ibwkbe
_}kn} hn} =6 ]gy}kqg 4 2.=, qcge
p#s|, + 2.=g#s+=.=%
Iwgkei qcg p}kn}6 mgm
Qck lgba qn qcg Ibddb$akq}kmwqkne6
#|b, m+ 42
#b+mbb2gm%
_nqg}kn} hn} e abqb pnkeq6
bE 4 b? *e
=
mE 4 m? *e
==DL%
27.=1
Keq}naw`qkne@nefwib`{
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlg
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
23/35
_cklnnpck`bl Mb`ji}nwea Gspnegeqkbl Hbdklkg
Gspnegeqkbl Hbdklkg
Ke igeg}bl, `nefwibqg p}kn} gskq hn} akq}kmwqkne h}nd qcggspnegeqkbl hbdkl{%
p#s|+ 4 c#s+g,s#+%
Iwgkei qcg p}kn}%%%
p#|b, m+ g,bm#+%
Mg`bwg6
g,s#+g,bm#+ 4 g,b*s#m*2+#+
28.=1
Keq}naw`qkne@nefwib`{
_ckl ck l M j a
Gsbdplg6 Mg}enwllk akq}kmwqkneGsbdplg6 Ibwkbe }beand xb}kbmlgG k l H klk
http://find/http://goback/7/31/2019 Some Introductory Remarks on Bayesian Inference
24/35
_cklnnpck`bl Mb`ji}nwea Gspnegeqkbl Hbdklkg
Gspnegeqkbl Hbdklkg #`neqa+
Lkjglkcnna _}kn}._nqg}kn}
Ibwkbe #dgbe+ Ibwkbe
Ibwkbe #xb}kbe`g+ Ibddb_nkne IbddbIbddb Ibddb
Mkendkbl MgqbEgibqkxg Mkendkbl Mgqb
Dwlqkendkbl Ak}k`clgq
29.=1
Keq}naw`qkne@nefwib`{
_ckl ck l M j a
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
25/35
_cklnnpck`bl Mb`ji}nwea{ r i
Mb{gkbekd x% H}grwgeqkd
H}grwgeqkpd6 Dbskdwd$lkjglkcnna, C{pnqcgk Qgqkei, WemkbgaGqkdbqg, Pwppn}q Xg`qn} Db`ckeg, gq`%
Mb{gpkbekpd6 Mb{gkbe gqkdbqkne, Ibwkbe _}n`gg, MglkghEgqyn}j, Hb`qn} I}bpc, gq`%
K}}g`ne`klbmlg Akg}ge`g n} Qyn Pkag nh qcg Pbdg @nke>
23.=1
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
26/35
_cklnnpck`bl Mb`ji}nwea{ r i
Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{
_$Qcgn ang enq p}nxkag be{ lkejbig qn qcg yn}la%
Kq mbk`bll{ fwq qck6
_#+ 4 ?, _#B+ 4 2 _#B+, _#
kBk+ 4
k
_#Bk+
G#S+, _#B M+ 4 _#B+_#M+ _#B|M+ 4 _#B M+._#M+
H}nd qck, gxg}{qckei glg k ag}kxga, ke`lwakei lby nh lb}igewdmg}, gq`%
2;.=1
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
27/35
_cklnnpck`bl Mb`ji}nwea
Mb{gkbekd x% H}grwgeqkd
Wg _$Qcgn qn%%%H}grwgeqkpd6 %%% dnagl keagpgeageq }gpgbqbmlg gspg}kdgeq
kh K wd wp dbe{ }gblkvbqkne, qcg{ ykll mg `lng qn qcggspg`qbqkne%
Mb{gpkbekpd6 %%% dnagl `ndpwqbqkne ne mglkgh akq}kmwqkne
kh K dnagl qcg abqb `n}}g`ql{, d{ mglkgh ykll mg wpabqgab``n}akeil{%
=?.=1
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
28/35
_cklnnpck`bl Mb`ji}nwea
Mb{gkbekd x% H}grwgeqkd
Wg _$Qcgn qn%%%
H}grwgeqkpd6 %%% dnagl keagpgeageq }gpgbqbmlg gspg}kdgeq
kh K wd wp dbe{ }gblkvbqkne, qcg{ ykll mg `lng qn qcggspg`qbqkne%
Mb{gpkbekpd6 %%% dnagl `ndpwqbqkne ne mglkgh akq}kmwqkne
kh K dnagl qcg abqb `n}}g`ql{, d{ mglkgh ykll mg wpabqgab``n}akeil{%
@ndpgqg nel{ ke qg}d nh }gbl$yn}la pg}hn}dbe`g, mwq enq nxg}ycbq k qcg `n}}g`q yb{ qn wg _$Qcgn%
=?.=1
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
29/35
_cklnnpck`bl Mb`ji}nwea
Mb{gkbekd x% H}grwgeqkd
Wg _$Qcgn qn%%%
H}grwgeqkpd6 %%% dnagl keagpgeageq }gpgbqbmlg gspg}kdgeq
kh K wd wp dbe{ }gblkvbqkne, qcg{ ykll mg `lng qn qcggspg`qbqkne%
Mb{gpkbekpd6 %%% dnagl `ndpwqbqkne ne mglkgh akq}kmwqkne
kh K dnagl qcg abqb `n}}g`ql{, d{ mglkgh ykll mg wpabqgab``n}akeil{%
@ndpgqg nel{ ke qg}d nh }gbl$yn}la pg}hn}dbe`g, mwq enq nxg}ycbq k qcg `n}}g`q yb{ qn wg _$Qcgn%
Gs`gpq hn}6 Mb{gkbe bpp}nb`cg }gwlq ke pnqg}kn} akq}kmwqkneycklg H}grwgeqkq dgqcna wwbll{ fwq }gqw}e b keilg nlwqkne%
=?.=1
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
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p i
M x Hke qg}d nh dnagllkei
Db`ckeg lgb}ekei dgqcna `be }nwicl{ mg ag`ndpnga ke qg}d nh
Dnagllkei #ycbq k kq K ybeq qn lgb}e+
]giwlb}kvbqkne #dbjg w}g yg aneq nxg}flq+
Kehg}ge`g #b`qwbll{ `ndpwqg qcg nlwqkne ikxge qcg abqb+
=2.=1
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
31/35
p i
M x Hke qg}d nh dnagllkei
Db`ckeg lgb}ekei dgqcna `be }nwicl{ mg ag`ndpnga ke qg}d nh
Dnagllkei #ycbq k kq K ybeq qn lgb}e+
]giwlb}kvbqkne #dbjg w}g yg aneq nxg}flq+
Kehg}ge`g #b`qwbll{ `ndpwqg qcg nlwqkne ikxge qcg abqb+
Bea qck cnla hn} mnqc6
Mb{gkbe H}grwgeqkq
dnagllkei _#A|D+ ln hwe`qkne}giwlb}kvbqkne _#D+ }giwlb}kvbqkne
kehg}ge`g Mb{g$}wlg npqkdkvbqkne
=2.=1
Keq}naw`qkne@nefwib`{
_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
32/35
M x Hakg}geq jkea nh we`g}qbkeq{
H}grwgeqkpd6 dnagllkei k jkea nh kegsb`q, mwq bq lgbq kehg}ge`gk gsb`q%
Mb{gpkbekpd6 dnagllkei k `lgb}, mwq kehg}ge`g k jkea nh kegsb`q%
==.=1
Keq}naw`qkne@nefwib`{_cklnnpck`bl Mb`ji}nwea
Ne Keqg}p}gqbqkne nh _}nmbmklkq{ Qcgn}{Mb{gkbekd x% H}grwgeqkd ke Qg}d nh Dnagllkei
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
33/35
M x Hk}}g`ne`klbmlg akg}ge`g>
Db{mg, ke`g qnnl b}g xg}{ akg}geq6
H}grwgeqkpq6 jeny yck`c `ndpwqbqkne ne bdplg`nexg}ig.`ne`geq}bqg, npqkdkvbqkne qcgn}{ #`nexgs npqkdkvbqkne,
i}bakgeq ag`geq, keqg}kn} pnkeq dgqcna%%%+, gq`%
Mb{gpkbep6 p}nmbmklkq{ akq}kmwqkne, yck`c p}kn} dbjg gekmlg`ndpwqbqkne, bdplkei dgqcna lkjg D@D@, bpp}nskdbqknedgqcna%
=0.=1
http://find/7/31/2019 Some Introductory Remarks on Bayesian Inference
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7/31/2019 Some Introductory Remarks on Bayesian Inference
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