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Computational and Inferential Difficulties with Mixture Posterior Distributions

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HAL Id: inria-00073049

https://hal.inria.fr/inria-00073049

Submitted on 24 May 2006

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Computational and Inferential Difficulties with Mixture Posterior Distributions

Gilles Celeux, Merrilee Hurn, Christian Robert

To cite this version:

Gilles Celeux, Merrilee Hurn, Christian Robert. Computational and Inferential Difficulties with Mix- ture Posterior Distributions. [Research Report] RR-3627, INRIA. 1999. �inria-00073049�

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a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Computational and inferential difficulties with mixture posterior distributions

Gilles Celeux, Merrilee Hurn, Christian Robert

No 3627

TH `EME 4

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(10)

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(11)

Tfh‹si^~n`ˆ "aƒ `Mr^~v`Luz`MqAmnkmnfpoCq3osš mv\^` ; fp–^–Uuunkw_ar^jh`2ksunuzot{fhkwmv` x • fpmv\ªk;unkw_ar^jh`osš

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(12)

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(13)

Tfh‹si^~n` 7 "5ƒ `r…~v`Luz`MqCm(kmnfpoCq—fhq3mn\^`

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p

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02468

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01234 02468

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Random walk sampling

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ot{M{i^~(u'–U`m•«`M`qmv\^`mn\^~n``5{oC_1r”osq…`qAmnuMœ

(14)

Tfh‹si^~n`„‰ "ƒ `r…~v`Luz`MqCm(kmnfpoCq!osš”mn\^` ¤ ks~v£Co¥{(\…kwfhq ¤ osqAmn`Ÿ¦'kw~njpo5unkw_ar^jh`„ksunuzot{flkmn` x • f©mn\k5uvks_ar^jp`

osš

,6,

uzfh_i^jlkmn` x rUoCfpqAm(uš›~voC_ k

{os_arUoCq^`qAm°q^oC~v_™kwjg_afp|Amni^~n`ksq x kŸ~(kwq x os_†•kwjh£ ¤ `mn~voCrUoCjpflu

´Ÿksuzmvfhq^‹Cu ksjp‹Cos~nf©mn\^_œ

Weight Variance

Mean

q…` x f©¨{i^j©my• fpmv\mv\…`~nksq x oC_+•kwjh£r^~nosr”oCunkwjlufhu„mv\…kwm„mv\^`Myks~v`*mvogo™~(kwq x oC_ ,„mno–”`kw–^jh`mvo

\…f©m5mn\^`™owmn\^`~5_ao

x

`Mu• f©mn\ uvit¨{fh`qAm~n`‹Ci^jhks~vfpmysœ

¸

_aos~n`™k

x

ksrtmvfh¥s`™kwjpmv`M~vqUkmvfh¥s`1flumv\^`{jhkCuvuosš

³kwq^‹C`¥gfhq

x

fp¶”i…uvfhosq

¤

`mv~nosr”osjhflu t´¹ksuzmvfhq^‹AuFkwjh‹soC~vfpmv\…_auFr^~nosr”oCuv`

x

–gyƒ oC–U`M~zm(uksq

x

[•'``

x

fp`

'4:4:7:

• \…fh{(\kw~n`–…ksuv`

x

osqk1~nksq

x

os_+•'ksjp£

x

~vfpšãm„r^~nosr”oCunkwj

.

&

`

.

ˆ

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