Model-based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

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Eprints ID : 18353

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_{: DOI:10.1111/micc.12343}

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https://doi.org/10.1111/micc.12343

To cite this version

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Rasmussen, Peter M. and Smith, Amy and Sakadži , Sava and Boas,

David A. and Pries, Axel R. and Secomb, Timothy W. and

Østergaard, Leif Model-based inference from microvascular

measurements: Combining experimental measurements and model

predictions using a Bayesian probabilistic approach. (2017)

Microcirculation, vol. 24 (n° 4). pp. e12343. ISSN 1073-9688

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Model- based inference from microvascular measurements:

ol0bmbm];Šr;ubl;m|-Ѵl;-v†u;l;m|v-m7lo7;Ѵru;7b1ঞomv

†vbm]--‹;vb-mruo0-0bѴbvঞ1-rruo-1_

Peter M. Rasmussen

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00u;ˆb-ঞomvĹu|ķ-u|;uboѴ-uĸ-rķ1-rbѴѴ-u‹ĸ buķ7bu;1ঞomĸ"ķ;m7o|_;Ѵb-Ѵv†u=-1;Ѵ-‹;uĸķ-uhoˆ1_-bmom|;-uѴoĸ$ķorঞ1-Ѵ1o_;u;m1;|olo]u-r_‹ĸ!ķu;70Ѵoo71;ѴѴĸ$ķ |‰oŊr_o|omlb1uov1or‹ĸ(;mķˆ;m†Ѵ-uĺ 1 _{;r-u|l;m|o=Ѵbmb1-Ѵ;7b1bm;ķ;m|;uo=} †m1ঞom-ѴѴ‹m|;]u-ঞˆ;;†uov1b;m1;-m7  -0ķ-u_†v&mbˆ;uvb|‹ovrb|-Ѵķ-u_†vķ ;ml-uh 2_{mvঞ|†|7;࣐1-mbt†;7;v Ѵ†b7;v} 7;$o†Ѵo†v;Ő $őŊ&mbˆ;uvb|࣐7; $o†Ѵo†v;ķ!"Ŋ$Ŋ&"ķ$o†Ѵo†v;ķ u-m1; ƒ_{|_bmo†Ѵ-ĺ-uঞmov;m|;u=ou} bol;7b1-Ѵl-]bm]ķ ;r-u|l;m|o= !-7boѴo]‹ķ-vv-1_†v;‚v;m;u-Ѵ ovrb|-Ѵķ-uˆ-u7;7b1-Ѵ"1_ooѴķ _-uѴ;v|o‰mķķ&" Ɠ_{-uˆ-u7Ŋ$ bˆbvbomo=;-Ѵ|_"1b;m1;v-m7} $;1_moѴo]‹ķ-l0ub7];ķķ&" 5 _{;r-u|l;m|o=_‹vboѴo]‹ķ_-ub|࣐Ŋ} &mbˆ;uvb|࢜|vl;7bŒbm;uѴbmķ;uѴbmķ;ul-m‹ 6 _{;r-u|l;m|o=_‹vboѴo]‹ķ&mbˆ;uvb|‹o=} ubŒom-ķ$†1vomķ,ķ&" 7 _{;r-u|l;m|o=;†uou-7boѴo]‹ķ-u_†v} &mbˆ;uvb|‹ovrb|-Ѵķ-u_†vķ ;ml-uh Correspondence ;|;uĺ!-vl†vv;mķ;m|;uo= †m1ঞom-ѴѴ‹ m|;]u-ঞˆ;;†uov1b;m1;-m7 -0ķ -u_†vķ ;ml-uhĺ l-bѴĹrluŠ1Cmĺ-†ĺ7h †m7bm]bm=oul-ঞom $_bvv|†7‹‰-vv†rrou|;70‹|_; -mbv_ bmbv|u‹o="1b;m1;ķmmoˆ-ঞomķ-m7 7†1-ঞomŐ -0ĸķ!őķ|_;(&* o†m7-ঞomŐ! ĸķ!őķ]u-m|v ƏƒƓƔƔƔ-m7ƏƕƏѵƔƕŐ$)"őķ-m7! u-bmb1uo Ѵo‰ѵƐƔƐƏƑŐ "őĺ

0v|u-1|

0f;1ঞˆ;Ĺ m ˆbˆo bl-]bm] o= |_; lb1uo1bu1†Ѵ-ঞom -m7 m;|‰ouhŊoub;m|;7 lo7;Ѵbm]

_-ˆ;;l;u];7-vro‰;u=†Ѵl;-mvo=v|†7‹bm]lb1uoˆ-v1†Ѵ-u=†m1ঞom-m7†m7;uv|-m7Ŋ

bm]b|vr_‹vboѴo]b1-Ѵvb]mbC1-m1;ĺ;|‰ouhŊoub;m|;7lo7;Ѵbm]l-‹ruoˆb7;|_;l;-mv

o= v†ll-ubŒbm] ˆ-v| -lo†m|v o= 7-|- ruo7†1;7 0‹ _b]_Ŋ|_uo†]_r†| bl-]bm] |;1_Ŋ

mbt†;vbm|;ulvo=h;‹ķr_‹vboѴo]b1-Ѵbm7b1;vĺ$o;vঞl-|;v†1_bm7b1;v‰b|_v†L1b;m|

1;u|-bm|‹ķ_o‰;ˆ;uķm;|‰ouhŊoub;m|;7-m-Ѵ‹vbvl†v|0;uo0†v||o|_;bm;ˆb|-0Ѵ;ru;vŊ

;m1;o=†m1;u|-bm|‹7†;|ol;-v†u;l;m|;uuouv-v‰;ѴѴ-vlo7;Ѵ;uuouvĺ

;|_o7vĹ);ruorov;|_;-‹;vb-mruo0-0bѴbvঞ17-|--m-Ѵ‹vbv=u-l;‰ouh-v-l;-mv

o=bm|;]u-ঞm];Šr;ubl;m|-Ѵl;-v†u;l;m|v-m7m;|‰ouhlo7;Ѵvbl†Ѵ-ঞomvbm|o-1olŊ

0bm;7-m7v|-ঞvঞ1-ѴѴ‹1o_;u;m|-m-Ѵ‹vbvĺ$_;=u-l;‰ouhm-|†u-ѴѴ‹_-m7Ѵ;vmobv‹l;-vŊ

†u;l;m|v -m7 ruoˆb7;v rov|;ubou 7bv|ub0†ঞomv o= lo7;Ѵ r-u-l;|;uv -v ‰;ѴѴ -v

r_‹vboѴo]b1-Ѵbm7b1;v-vvo1b-|;7‰b|_†m1;u|-bm|‹ĺ

Results:

);-rrѴb;7|_;-m-Ѵ‹vbv=u-l;‰ouh|o;Šr;ubl;m|-Ѵ7-|-=uol|_u;;u-|l;vŊ

;m|;u‹m;|‰ouhv-m7om;lo†v;0u-bm1ou|;Šm;|‰ouhĺ);bm=;uu;77bv|ub0†ঞomv=ou

lou;|_-mƔƏƏ†mhmo‰mru;vv†u;-m7_;l-|o1ub|0o†m7-u‹1om7bঞomvĺo7;Ѵru;7b1Ŋ

ঞomv‰;u;1omvbv|;m|‰b|_ru;ˆbo†v-m-Ѵ‹v;vķ-m7u;l-bm;7uo0†v|‰_;ml;-v†u;Ŋ

l;m|v‰;u;olb‚;7=uollo7;Ѵ1-Ѵb0u-ঞomĺ

Conclusion:

†u-‹;vb-mruo0-0bѴbvঞ1-rruo-1_l-‹0;v†b|-0Ѵ;=ouorঞlbŒbm]7-|-

-1t†bvbঞom-m7=ou-m-Ѵ‹Œbm]-m7u;rouঞm]Ѵ-u];7-|-v;|v-1t†bu;7-vr-u|o=lb1uoŊ

ˆ-v1†Ѵ-ubl-]bm]v|†7b;vĺ

  + )  ! " -‹;vb-m-m-Ѵ‹vbvķYo‰vbl†Ѵ-ঞomķlb1uo1bu1†Ѵ-|ou‹l;-v†u;l;m|vķm;|‰ouhŊoub;m|;7-m-Ѵ‹vbv

ƐՊ|Պ$! &$

$_;v|†7‹o=_;lo7‹m-lb1v-m7voѴ†|;|u-mvrou|‰b|_bmlb1uoˆ-v1†Ѵ-u m;|‰ouhvbv|‹rb1-ѴѴ‹0-v;7om;Šr;ubl;m|-Ѵo0v;uˆ-ঞomv‰_b1_-u; |_;mv†0f;1|;7|o|_;ou;ঞ1-Ѵlo7;Ѵbm]ĺ$_bvv;t†;mঞ-Ѵ-rruo-1__-v 0;;m1u†1b-Ѵ=ouo†u1†uu;m|†m7;uv|-m7bm]o=|_;0bor_‹vb1-Ѵruor;uŊ ঞ;vo=|_;lb1uo1bu1†Ѵ-ঞom-m7u;ˆ;-Ѵ;7r_;mol;m-‰_b1_1o†Ѵ7mo| 0;]Ѵ;-m;7=uolbmˆbˆol;-v†u;l;m|v-Ѵom;ĺ1

$;1_moѴo]b1-Ѵ-7ˆ-m1;vmo‰r;ulb|_b]_Ŋ|_uo†]_r†|bmˆbˆol;-Ŋ v†u;l;m| o= v|u†1|†u-Ѵ -m7 =†m1ঞom-Ѵ m;|‰ouh ruor;uঞ;vĺ $_;v; bm1Ѵ†7; _b]_Ŋu;voѴ†ঞomķ |_u;;Ŋ7bl;mvbom-Ѵ bl-]bm] o= lb1uoˆ-v1†Ѵ-u m;|‰ouhvķ l;-v†u;l;m|v o= 0Ѵoo7 Yo‰ķ !ˆ;Ѵo1b|‹ -m7 Y†Š‰b|_ _b]_vr-ঞo|;lrou-Ѵu;voѴ†ঞomķ-m7l;-v†u;l;m|vo=oŠ‹];mr-uঞ-Ѵ ru;vv†u;bm0Ѵoo7-m7ঞvv†;ĺ2–6_{)b|_|_bvѴ;-rbmvr-ঞo|;lrou-Ѵu;vŊ} oѴ†ঞom1ol;v-m;;7|ov†ll-ubŒ;ˆ-v|7-|-t†-mঞঞ;vbml;-mbm]Ŋ =†Ѵ‰-‹vĺ†uu;m|Ѵ‹ķ7-|--u;|‹rb1-ѴѴ‹u;rou|;7-vv†ll-u‹v|-ঞvঞ1v -1uovv|‹rb1-Ѵˆ;vv;Ѵ|‹r;vķ;]ķ-ˆ;u-];1_-m];vbm1-rbѴѴ-u‹!Y†Š ou1-rbѴѴ-u‹7b-l;|;u;ˆoh;70‹=†m1ঞom-Ѵ-1ঞˆ-ঞomķ0†|v;;ĺ7_{)_bѴ;}

v†1_ -m-Ѵ‹vbv ruoˆb7;v blrou|-m| bm=oul-ঞom -0o†| |_; =†m1ঞom o= bm7bˆb7†-Ѵˆ;vv;Ѵvķb|=-ѴѴvv_ou|o=-77u;vvbm]|_;m;|ķ0bor_‹vb1-Ѵ;@;1| o=|_;v;1_-m];vķ8–10_{=ou;Š-lrѴ;bm|;ulvo=|_;1_-m];bmm†|ub;m|}

-ˆ-bѴ-0bѴb|‹=ou|_;ঞvv†;v†rrѴb;70‹|_;lb1uoˆ-v1†Ѵ-|†u;ĺ

$_;1olrѴ;Š|oroѴo]‹-m7lour_oѴo]‹o=lb1uoˆ-v1†Ѵ-um;|‰ouhv ]bˆ;ubv;|o1omvb7;u-0Ѵ;_;|;uo];m;b|‹ķ=ou;Š-lrѴ;bm|;ulvo=|_; 7bv|ub0†ঞom o= 0Ѵoo7ķѶķƐƐ_{ -m7 bm=;u;m1; u;]-u7bm] voѴ†|; |u-mvrou|}

‰b|_bm |_;v; m;|‰ouhv l†v| |_;u;=ou; -11o†m| =ou |_bv _;|;uo];m;Ŋ b|‹ĺ11_{11ou7bm]Ѵ‹ķ m;|‰ouhŊoub;m|;7 -m-Ѵ‹vbv v;;lbm]Ѵ‹ u;voѴˆ;v |_;}

7bv1u;r-m1b;v;m1o†m|;u;7‰_;m|u-1;u†r|-h;7-|--u;C‚;7|o1olŊ r-u|l;m|-Ѵlo7;Ѵv‰_b1_-vv†l;b7;mঞ1-Ѵ1-rbѴѴ-u‹;Š|u-1ঞomruor;uŊ ঞ;v-1uovv-ѴѴ1-rbѴѴ-ub;vĺѶķƐƑ_{;|‰ouhŊoub;m|;77-|--m-Ѵ‹vbv1ol0bm;v}

lb1uoˆ-v1†Ѵ-ul;-v†u;l;m|v-m7lo7;Ѵvbl†Ѵ-ঞomv|oru;7b1|0Ѵoo7 Yo‰ -m7 voѴ†|; ;Š|u-1ঞom -| |_; v1-Ѵ; o= |_; ;Šr;ubl;m|-Ѵ 7-|- -| _-m7ķ-m7_-v0;;m†v;7|o;vঞl-|;bm|ubmvb1m;|‰ouht†-mঞঞ;vou r-u-l;|;uv‰_b1_1-mmo|0;bm=;uu;77bu;1|Ѵ‹=uol|_;;Šr;ubl;m|-Ѵ l;-v†u;l;m|vĺѶķƖķƐƐ

$o vbl†Ѵ-|; 0Ѵoo7 Yo‰ |_uo†]_ lb1uoˆ-v1†Ѵ-u m;|‰ouhvķ lb1uov1or‹Ŋ0-v;7|oroѴo]b1-Ѵ-m7lour_oѴo]b1-Ѵbm=oul-ঞomŐbm|_; =oulo=ˆ-v1†Ѵ-u]u-r_vőbv|‹rb1-ѴѴ‹1ol0bm;7‰b|_r_‹vb1-ѴѴ-‰v]oˆŊ ;umbm]0Ѵoo7Yo‰ķ-m7;lrbub1-Ѵ7;v1ubrঞomvo=u_;oѴo]b1-Ѵ;@;1|vĺƖ

$_;bm|;u1omm;1|;7m-|†u;o=lb1uoˆ-v1†Ѵ-um;|‰ouhvķ_o‰;ˆ;uķru;vŊ ;m|v - 1_-ѴѴ;m];ĺƖķƐƒķƐƓ_{ $‹rb1-Ѵ ˆ-v1†Ѵ-u ]u-r_v _-ˆ; - 1omvb7;u-0Ѵ;}

m†l0;uo=or;m;m7vou0o†m7-u‹mo7;vĺ$_;1_ob1;o=ru;vv†u;ou Yo‰-m7_;l-|o1ub|ˆ-Ѵ†;v=ou|_;v;0o†m7-u‹mo7;vbv1ubঞ1-Ѵķbm|_-| vbl†Ѵ-|;7 Yo‰ r-‚;umv -u;ˆ;u‹ v;mvbঞˆ; |o v†1_ 0o†m7-u‹ 1om7bŊ ঞomvĺƖķƐƓ_{ub;v-m71oŊ‰ouh;uv1olr-u;7;Šr;ubl;m|-Ѵl;-v†u;l;m|v}

o=0Ѵoo7Yo‰ˆ;Ѵo1b|‹-m7_;l-|o1ub|‰b|_lo7;Ѵvbl†Ѵ-ঞomv-m7=o†m7 |_-|0o†m7-u‹1om7bঞomvu;t†bu;7l-m†-Ѵ-7f†v|l;m|v|o-1_b;ˆ;v-|Ŋ bv=-1|ou‹1ouu;vrom7;m1;ĺƖķƐƔ_{!;1;m|-rruo-1_;v7;|;ulbm;ru;vv†u;}

0o†m7-u‹1om7bঞomv0‹lbmblbŒbm]|_;7b@;u;m1;0;|‰;;mo0v;uˆ;7 -m7 lo7;Ѵ;7 Yo‰ 7bu;1ঞomv ou ˆ;Ѵo1b|‹ķ ou 0;|‰;;m Ѵb|;u-|†u; -m7 lo7;Ѵ;7ru;vv†u;v-m7ˆ;vv;Ѵ‰-ѴѴv_;-uv|u;vv;vĺƐƒķƐѵķƐƕ

$_; bm=oul-ঞom ‰_b1_ 1-m 0; o0|-bm;7 0‹ 1ol0bmbm] lo7;Ѵ vbl†Ѵ-ঞomv‰b|_ ;Šr;ubl;m|-Ѵ l;-v†u;l;m|v bm - m;|‰ouhŊoub;m|;7 -m-Ѵ‹vbv bv Ѵblb|;7 0‹ |_; †m1;u|-bmঞ;v ‰_b1_ bm;ˆb|-0Ѵ‹ -ubv; =uol l;-v†u;l;m| ;uuouv -m7 †m1;u|-bmঞ;v u;]-u7bm] ˆ-v1†Ѵ-u |oroѴo]‹ķ lour_oѴo]‹ķ -m7 lo7;Ѵ v|u†1|†u-Ѵ -m7 r-u-l;|;u †m1;u|-bm|‹ĺ m |_bv v|†7‹ķ‰; ru;v;m| - -‹;vb-m ruo0-0bѴbvঞ1 -rruo-1_ |o -77u;vv |_bv 1_-ѴѴ;m];ĺ -‹;vb-m ruo0-0bѴbvঞ1 -m-Ѵ‹vbv ruoˆb7;v - ub]ouo†v =u-l;‰ouh bm ‰_b1_ vo†u1;v o= †m1;u|-bm|‹ 1-m 0; bm1ourou-|;7 0‹ |_;bu u;vr;1ঞˆ; ruo0-0bѴb|‹ 7bv|ub0†ঞomvĺ 11ou7bm]Ѵ‹ķ o†u -bl ‰-v |o 7;lomv|u-|; |_-| |_bv =u-l;‰ouh Őbő 1ol0bm;v lb1uo1bu1†Ѵ-|ou‹

;Šr;ubl;m|-Ѵl;-v†u;l;m|ķѴb|;u-|†u;7-|-ķ-m7lo7;Ѵru;7b1ঞomvbm -v|-ঞvঞ1-ѴѴ‹1o_;u;m|‰-‹ķŐbbő_-m7Ѵ;vmobv‹l;-v†u;l;m|vķŐbbbő1-m 0;†v;7|obm=;u7bv|ub0†ঞomv=ou†m1;u|-bmlo7;Ѵt†-mঞঞ;vՉ;=o1†v om0o†m7-u‹1om7bঞomvbm|_bvu;rou|őķ-m7Őbˆő-vvb]mv†m1;u|-bmঞ;v|o lo7;Ѵru;7b1ঞomvĺ $_;ru;v;m|‰ouhbv|o|_;0;v|o=o†uhmo‰Ѵ;7];|_;Cuv||obm|;Ŋ ]u-|; ;Šr;ubl;m|-Ѵ l;-v†u;l;m|v -m7 m;|‰ouh lo7;Ѵ vbl†Ѵ-ঞomv bm|o--‹;vb-m-m-Ѵ‹vbvĺ);†v;;Šr;ubl;m|-Ѵ7-|-=uolu-|l;v;m|;u‹ -m7lo†v;1;u;0u-Ѵ1ou|;Š|obѴѴ†v|u-|;|_;r;u=oul-m1;o=|_;-m-Ѵ‹vbv -m7v_o‰|_-||_;-m-Ѵ‹vbv-rruo-1_Őbő]bˆ;vu;v†Ѵ|v1omvbv|;m|‰b|_ ru;ˆbo†v-m-Ѵ‹v;vo=-1olru;_;mvbˆ;7-|-v;|‰b|_l;-v†u;l;m|vo= 0Ѵoo7Yo‰ˆ;Ѵo1b|‹-m7_;l-|o1ub|-ˆ-bѴ-0Ѵ;bm-ѴѴˆ;vv;Ѵv;]l;m|vķ†r |oƔƓѵv;]l;m|v-m7ƓƏ0o†m7-u‹mo7;vķ-m7Őbbőbvuo0†v||o|_;olbvŊ vbomo=l;-v†u;l;m|v-ˆ-bѴ-0Ѵ;=oulo7;Ѵ1-Ѵb0u-ঞomĺ$_;†ঞѴb|‹o=|_; =u-l;‰ouhbv|_;m7;lomv|u-|;7bm|_;0u-bm1ou|;Š7-|-Ō-Ѵ-u];m;|Ŋ ‰ouh‰b|_ƐѶƕѶv;]l;m|v-m7ƑƖƔ0o†m7-u‹mo7;v-m7omѴ‹-Ѵblb|;7 m†l0;uo=ˆ;Ѵo1b|‹l;-v†u;l;m|vĺ bm-ѴѴ‹ķ‰;7bv1†vvo†uu;v†Ѵ|v-m7 o†|Ѵbm;_o‰|_;=u-l;‰ouhlb]_|]†b7;|_;-1t†bvbঞom-m7bm|;uru;Ŋ |-ঞomo=;Šr;ubl;m|-Ѵlb1uo1bu1†Ѵ-ঞom7-|-ĺ

ƑՊ|Պ$!" $ "

ƑĺƐՊ|Պ"bl†Ѵ-ঞomlo7;Ѵ

);†v;-vbl†Ѵ-ঞomlo7;Ѵ‰_b1_‰-voub]bm-ѴѴ‹7;ˆ;Ѵor;7|o7;v1ub0; 0Ѵoo7Yo‰bmu-|l;v;m|;u‹m;|‰ouhvƖķƐƔķƐѶ_{-m7Ѵ-|;u-Ѵvoruoˆ;m|o}

-rrѴ‹ |o o|_;u ঞvv†; |‹r;vķ bm1Ѵ†7bm] |_; 0u-bmĺƐƓķƐƖ_{ $_; vbl†Ѵ-ঞom}

lo7;Ѵbvr-u|Ѵ‹0-v;7omr_‹vb1-Ѵrubm1brѴ;vu;]-u7bm]Yo‰Ŋru;vv†u; u;Ѵ-ঞomv_brv -m7 l-vv 1omv;uˆ-ঞom -| 0b=†u1-ঞomvķ -m7 r-u|Ѵ‹ om ;lrbub1-Ѵ7;v1ubrঞomvo=u_;oѴo]b1-Ѵ;@;1|vĺ11ou7bm]Ѵ‹ķYo‰u;vbv|Ŋ -m1;bvlo7;Ѵ;7‰b|_obv;†bѴѴ;ĽvѴ-‰ķ‰_b1_7;v1ub0;vYo‰u;vbv|-m1; bm|;ulvo=ˆ;vv;ѴѴ;m]|_ķˆ;vv;Ѵ7b-l;|;uķ-m7Y†b7ˆbv1ovb|‹ĺ$_;momŊ ;‰|omb-mm-|†u;o=0Ѵoo7bvbm1ourou-|;70‹1omvb7;ubm]-m-rr-u;m| ˆbv1ovb|‹ĺƐƔķƐѶķƑƏķƑƐ_{rr-u;m|ˆbv1ovb|‹ķbm|†umķbvlo7;Ѵ;7-11ou7bm]|o} -m;lrbub1-Ѵu;Ѵ-ঞomv_br-v-=†m1ঞomhFLŐdķhctDĸθőo=ˆ;vv;Ѵ7b-l;|;u d-m7ˆ;vv;Ѵ7bv1_-u];_;l-|o1ub|hct_DŐθ7;mo|;vr-u-l;|;uvo=|_;

;lrbub1-Ѵ =†m1ঞomőĺ rr-u;m| ˆbv1ovb|‹ 7;1u;-v;v ‰b|_ ˆ;vv;Ѵ 7b-lŊ ;|;u7o‰m|oŜƔμl0†||_;mbm1u;-v;v=ouѴo‰;u7b-l;|;uvŐ ࢟_u/†vŊ bm7tˆbv| ;@;1|őĺ $_; u;7†1ঞom bm |†0; _;l-|o1ub| u;Ѵ-ঞˆ; |o 7bvŊ 1_-u];_;l-|o1ub|bvlo7;Ѵ;70‹-m;lrbub1-Ѵu;Ѵ-ঞomv_brh_FŐdķhct_Dĸ θő-v-=†m1ঞomo=ˆ;vv;Ѵ7b-l;|;u-m77bv1_-u];_;l-|o1ub|Ő ࢟_u/†v ;@;1|őĺƖķƑƏ_{ ! 1om1;m|u-ঞomv -| 0b=†u1-ঞom o†Ѵo‰ 0u-m1_;v -u;}

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v;]l;m|0Ѵoo7Yo‰-m7v†0v1ubr|vmķαķ-m7β7;mo|;lo|_;uˆ;vv;Ѵ -m77-†]_|;uˆ;vv;Ѵvķu;vr;1ঞˆ;Ѵ‹ĺƐѶķƑƑ_{m-77bঞom|oˆ;vv;Ѵlour_oѴŊ}

o]‹ķ |oroѴo]‹ķ -m7 |_; ;lrbub1-Ѵ 7;v1ubrঞomv o= u_;oѴo]b1-Ѵ ;@;1|ķ |_;lo7;Ѵ7;r;m7vom-v;ub;vo=0o†m7-u‹1om7bঞomvķζĺ"r;1bC1-ѴѴ‹ķ ru;vv†u;vķou;t†bˆ-Ѵ;m|Ѵ‹0Ѵoo7Yo‰u-|;vķl†v|0;vr;1bC;7=ou-ѴѴ 0o†m7-u‹mo7;v;Š1;r|om;ķ-m77bv1_-u];_;l-|o1ub|l†v|0;vr;1bŊ C;7=ou-ѴѴbmYo‰mo7;vĺmb|;u-ঞˆ;ruo1;7†u;=ouYo‰vbl†Ѵ-ঞombv u;t†bu;7ķvbm1;|_;u_;oѴo]b1-Ѵ7;v1ubrঞomvblrov;bm|;u7;r;m7;m1;

0;|‰;;m0Ѵoo7Yo‰-m7Yo‰u;vbv|-m1;ĺ$_;vbl†Ѵ-ঞomlo7;Ѵru;Ŋ 7b1|v ru;vv†u;ķ 0Ѵoo7 Yo‰ u-|;ķ _;l-|o1ub|ķ -m7 Yo‰ u;vbv|-m1; =ou -ѴѴ ˆ;vv;Ѵ v;]l;m|vķ -m7 - v;ub;v o= v†0v;t†;m| r-u-l;|;uv 1-m 0; 7;ubˆ;7=uol|_;v;ĺ11_{$_;vbl†Ѵ-ঞomlo7;Ѵbv=†ѴѴ‹vr;1bC;70‹ˆ;vv;Ѵ}

|oroѴo]‹ķlour_oѴo]‹ϕƷŐdķlőķr-u-l;|;uvo=|_;;lrbub1-Ѵ=†m1ঞomv θķ -m7 0o†m7-u‹ 1om7bঞomv ζĺ )_bѴ; |oroѴo]‹ -m7 lour_oѴo]‹ -u; u;-7bѴ‹ -ˆ-bѴ-0Ѵ; =uol |_; ˆ-v1†Ѵ-u ]u-r_ Ő-Ѵ|_o†]_ ro|;mঞ-ѴѴ‹ 1omŊ =o†m7;70‹†m1;u|-bmঞ;v-m7l;-v†u;l;m|;uuouvőķ|_;ru;v1ubrঞom o= -rruorub-|; ru;vv†u; -m7 _;l-|o1ub| 0o†m7-u‹ 1om7bঞomv bv Ѵ;vv v|u-b]_ou‰-u7ĺm|_;=oѴѴo‰bm]ķ‰;-77u;vv_o‰|_bv1_-ѴѴ;m];1-m 0;1om=uom|;70‹-7orঞm]--‹;vb-mruo0-0bѴbvঞ1-m-Ѵ‹vbvv|u-|;]‹ĺ

ƑĺƑՊ|Պ-‹;vb-mruo0-0bѴbvঞ1-m-Ѵ‹vbv

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$_;u;=ou;ķ - 1ol0bm;7 -m-Ѵ‹vbv o= ;Šr;ubl;m|-Ѵ l;-v†u;l;m|v -m7 lo7;Ѵvbl†Ѵ-ঞomvu;t†bu;v-7f†v|l;m|o=|_;lo7;ѴĽvr-u-l;|;uv|o ;v|-0Ѵbv_ 1ouu;vrom7;m1; 0;|‰;;m |_; lo7;ѴĽv ru;7b1ঞomv -m7 |_; l;-v†u;l;m|vķ|-hbm]bm|o-11o†m||_;ru;v;m1;o=;uuouvĺ ;|y0;-ˆ;1|ouo=mo0v;uˆ-ঞomvo=vol;lb1uoˆ-v1†Ѵ-ut†-mŊ ঞঞ;vo=bm|;u;v|ķ;]ķ0Ѵoo7Yo‰ˆ;Ѵo1b|‹ķ_;l-|o1ub|ķ-m70Ѵoo7Yo‰ 7bu;1ঞomķ-m7Ѵ;|fŐxő7;mo|;-ˆ;1|ouo=|_;vbl†Ѵ-ঞomlo7;ѴĽvru;Ŋ 7b1ঞomvo=|_;1ouu;vrom7bm]t†-mঞঞ;vķ‰_;u;xvb]mbC;v|_;7;r;mŊ 7;m1;om-v;ub;vo=Նmhmo‰mőr-u-l;|;uvķ;]ķ0o†m7-u‹1om7bঞomvĺ $_; ˆ;1|ou o= ;uuouv ou u;vb7†-Ѵv ε = y−f(x) l;-v†u;v |_; lbvl-|1_ 0;|‰;;m |_; o0v;uˆ-ঞomv -m7 |_; lo7;ѴĽv ru;7b1ঞomv -m7 Ѵ†lrv |o];|_;u-ѴѴvo†u1;vo=;uuouvĺ1ollomv|u-|;]‹|o-1_b;ˆ;1ouu;Ŋ vrom7;m1; 0;|‰;;m lo7;Ѵ -m7 o0v;uˆ-ঞomvķ =uol -m orঞlbŒ-ঞom r;uvr;1ঞˆ;ķ bv |o o0|-bm -m ;vঞl-|; o= |_; †mhmo‰m r-u-l;|;uv x vo|_-||_;v†lo=vt†-u;7u;vb7†-ѴvbvlbmblbŒ;7ŐѴ;-v|Ŋvt†-u;vvoѴ†Ŋ ঞomőķoulou;];m;u-ѴѴ‹ķ|o†v;‰;b]_|;7Ѵ;-v|Ŋvt†-u;vou];m;u-ѴbŒ;7 Ѵ;-v|Ŋvt†-u;v|o-ѴѴo‰=ou7b@;u;m|‰;b]_ঞm]o=bm7bˆb7†-Ѵl;-v†u;Ŋ l;m|vĺ uol-v|-ঞvঞ1-Ѵr;uvr;1ঞˆ;ķv†1_Ѵ;-v|Ŋvt†-u;vvoѴ†ঞomv1ouŊ u;vrom7|ol-Šbl†lѴbh;Ѵb_oo7voѴ†ঞomv†m7;u-†vvb-m;uuoulo7Ŋ ;ѴvĺƑƒ_{ ;-v|Ŋvt†-u;v ;vঞl-ঞom _-v bm7;;7 ruoˆ;m †v;=†Ѵ bm - v;ub;v}

o=v|†7b;v=o1†v;7om1ol0bmbm]lb1uo1bu1†Ѵ-|ou‹l;-v†u;l;m|v-m7 Ѵb|;u-|†u;hmo‰Ѵ;7];‰b|_lo7;Ѵvbl†Ѵ-ঞomvĺƖķƐƒķƐƕķƑƓ_{o‰;ˆ;uķbm|_;}

ru;v;m1; o= bm1olrѴ;|; -m7 blr;u=;1| ;Šr;ubl;m|-Ѵ 7-|-ķ |_bv orঞŊ lbŒ-ঞomruo0Ѵ;ll-‹0;1ol;†m7;u7;|;ulbm;7-m7=†u|_;uŐv|uom]ő -vv†lrঞomv-u;u;t†bu;7ķ;]ķ|ov;-u1_=ou-voѴ†ঞom|_-|lbmblbŒ;v |_;†1Ѵb7;-mmoulo=|_;u;vb7†-Ѵv17_{ou|oblrov;;Š-1|Ѵb|;u-|†u;}

0o†m7-u‹ 1om7bঞomvĺƑƓ_{ †u|_;ulou;ķ orঞlbŒ-ঞom Ѵ;-7v |o - vbm]Ѵ;}

;vঞl-|;o=|_;0;v|r-u-l;|;uˆ-Ѵ†;vķ-m7|_;†m1;u|-bmঞ;vo=|_; lo7;ѴĽvru;7b1ঞomv-u;|_;u;=ou;mo|7bu;1|Ѵ‹-ˆ-bѴ-0Ѵ;ĺ

m -Ѵ|;um-ঞˆ; |o r-u-l;|;u b7;mঞC1-ঞom 0‹ orঞlbŒ-ঞom bv |o -7or|--‹;vb-m-m-Ѵ‹vbvv|u-|;]‹ĺ-‹;vb-m-m-Ѵ‹vbvruoˆb7;v-ub]Ŋ ouo†v=u-l;‰ouh=oubm1ourou-ঞm]Ѵb|;u-|†u;ourubouhmo‰Ѵ;7];Ő-m7 |_;bu-vvo1b-|;7†m1;u|-bmঞ;vő-m7o0v;uˆ-ঞomvbm|o-1ol0bm;7-m-ѴŊ ‹vbvķb|‹b;Ѵ7v-m;vঞl-|;o=|_;ruo0-0bѴb|‹7;mvb|‹=†m1ঞomo=xu-|_;u |_-m-vbm]Ѵ;robm|;vঞl-|;̂xķ-m7Cm-ѴѴ‹ķb|ruoˆb7;v;vঞl-|;vo=|_; †m1;u|-bmঞ;vbm|_;vbl†Ѵ-ঞomlo7;ѴĽvru;7b1ঞomvĺ-‹;vb-m-m-Ѵ‹vbv |‹rb1-ѴѴ‹bmˆoѴˆ;vŐbőbm=;u;m1;vom-v;|o=†m1;u|-bmr-u-l;|;uvķŐbbő ru;7b1ঞomv0-v;7ombmŊv-lrѴ;-m7o†|Ŋo=Ŋv-lrѴ;7-|-ķ-m7Őbbbőlo7;Ѵ 1olr-ubvomķv;Ѵ;1ঞomķ-m7-ˆ;u-]bm]ĺƑƔķƑѵ

0v;uˆ-ঞomvķ lo7;Ѵ ru;7b1ঞomvķ -m7 lo7;Ѵ r-u-l;|;uv -u; |u;-|;7 -v u-m7ol ˆ-ub-0Ѵ;v ]oˆ;um;7 0‹ ruo0-0bѴb|‹ 7bv|ub0†ঞomvĺ $_;v;7bv|ub0†ঞomv-u;1ol0bm;70‹†v;o=ruo0-0bѴb|‹u†Ѵ;v|o‹b;Ѵ7 bm=oul-ঞomom-m‹t†-mঞ|‹o=bm|;u;v|ĺ$_;-‹;vĽ|_;ou;l‹b;Ѵ7v|_; rov|;ubou7bv|ub0†ঞomo=lo7;Ѵr-u-l;|;uv]bˆ;m|_;o0v;uˆ-ঞomv-v -1ol0bm-ঞomo=|_;rubou0;Ѵb;=vu;]-u7bm]lo7;Ѵr-u-l;|;uv-m7|_; ruo0-0bѴb|‹7;mvb|‹o=|_;o0v;uˆ-ঞomv]bˆ;mr-u-l;|;uˆ-Ѵ†;v ‰_;u;pŐx|yķmőbv|_;rov|;ubou7bv|ub0†ঞomo=xķpŐx|mőbv|_;rubou7bv|ubŊ 0†ঞomo=xķLŐx|yķmőƷpŐy|xķmőbv|_;Ѵbh;Ѵb_oo7=†m1ঞomo=xķ-m7pŐy|mő bv-‹;vb-m;ˆb7;m1;=oulo7;Ѵm-1ঞm]-v-moul-ѴbŒ-ঞom1omv|-m|ĺ ;u;ķmvb]mbC;v-vv†lrঞomvu;]-u7bm]|_;v|u†1|†u;o=|_;vbl†Ѵ-ঞom lo7;Ѵ-v‰;ѴѴ-v|_;v|u†1|†u;o=|_;ruo0-0bѴbvঞ1lo7;Ѵvĺ$_;-‹;vb-m ;ˆb7;m1;bvo=r-uঞ1†Ѵ-ubm|;u;v|bm|_;1om|;Š|o=lo7;Ѵ1olr-ubvomķ v;Ѵ;1ঞomķ-m7-ˆ;u-]bm]ķ0†|bvmo|m;1;vv-ubѴ‹u;t†bu;7=ourov|;ubou bm=;u;m1;ĺ$_;ru;7b1ঞˆ;7bv|ub0†ঞom]oˆ;umbm]|_;lo7;Ѵru;7b1ঞomv 1-m0;=o†m70‹bm|;]u-ঞm]oˆ;u|_;†m1;u|-bmlo7;Ѵr-u-l;|;uv

$_; ruo0-0bѴbvঞ1 7;v1ubrঞom o= |_; o0v;uˆ;7 7-|- -m7 rubou hmo‰Ѵ;7];-ѴѴo‰v|_;lo7;Ѵ;u|obm1ourou-|;-vv†lrঞomvu;]-u7bm] ;uuouvˆb-|_;Ѵbh;Ѵb_oo7=†m1ঞom-m7-vv†lrঞomvu;]-u7bm]†mhmo‰m lo7;Ѵr-u-l;|;uv-m7|_;bu†m1;u|-bmঞ;vˆb-|_;rubou7bv|ub0†ঞom-m7 1ol0bm;|_;v;bm-v|-ঞvঞ1-ѴѴ‹1o_;u;m|‰-‹0‹-‹;vĽ|_;ou;lĺ$_; lo7;Ѵ;u=-1;vru-1ঞ1-Ѵ1_-ѴѴ;m];v‰_;m-rrѴ‹bm]-‹;vb-m-m-Ѵ‹vbvķ m-l;Ѵ‹ Őbő |_; vr;1bC1-ঞom o= |_; Ѵbh;Ѵb_oo7 =†m1ঞom -m7 |_; rubou 7bv|ub0†ঞom -m7 Őbbő bm=;u;m1; o= |_; rov|;ubou 7bv|ub0†ঞom o= lo7;Ѵ r-u-l;|;uvĺ$_;v;|orb1v‰bѴѴ0;-77u;vv;7bm|_;=oѴѴo‰bm]ĺ

ƑĺƒՊ|Պbh;Ѵb_oo7=†m1ঞomv

$o=oul†Ѵ-|;|_;Ѵbh;Ѵb_oo7=†m1ঞomķ‰;r-uঞঞomo0v;uˆ-ঞomvbm|o |_u;;o0v;uˆ-ঞom|‹r;vĹy_ˆ;ѴŐ0Ѵoo7Yo‰ˆ;Ѵo1b|‹őķy_{_1|}Ő7bv1_-u];_;lŊ -|o1ub|őķ-m7y7buŐ0Ѵoo7Yo‰7bu;1ঞomőķ-m7r-uঞঞomlo7;Ѵru;7b1ঞomv

1ouu;vrom7bm]Ѵ‹ķ‰b|_7bl;mvbomvm_ˆ;Ѵķm_{_1|}ķ-m7m_7buķu;vr;1ঞˆ;Ѵ‹ĺ); -vv†l;|_-||_;Ѵbh;Ѵb_oo7=†m1ঞom7;1olrov;v-vLŐx|yķmőƷLˆ;ѴŐx|yˆ;Ѵķ

mőƵL_{_1|}Őx|y_{_1|}ķmőƵL_7buŐx|y_7buķmőĺѴoo7Yo‰ˆ;Ѵo1b|‹;uuouv-m7_;l-|oŊ

1ub|;uuouvŐεvel-m7εhctő-u;-vv†l;7|o0;-†vvb-m7bv|ub0†|;7ķ†m1ouŊ

u;Ѵ-|;7ķ -m7 ‰b|_ b7;mঞ1-Ѵ ;uuou ˆ-ub-m1;v ‰b|_bm ;-1_ o0v;uˆ-ঞom |‹r;Őb;ķ_olov1;7-vঞ1b|‹‰b|_bmo0v;uˆ-ঞom|‹r;ő

ŐƐő

p(x|y, m) =p(y|x, m)p(x|m)_p(y|m) ∝ L(x|y, m)p(x|m),

ŐƑő

$olo7;Ѵ|_;Ѵbh;Ѵb_oo7-vvo1b-|;7‰b|_0Ѵoo7Yo‰7bu;1ঞomķ‰;7;Cm; -ľv†11;vvĿ|o0;|_;;ˆ;m|o=1ouu;vrom7;m1;0;|‰;;mo0v;uˆ;7-m7 ru;7b1|;7 Yo‰ 7bu;1ঞomķ -m7 lo7;Ѵ |_; Ѵbh;Ѵb_oo7 -vvo1b-|;7 ‰b|_ Yo‰7bu;1ঞom-v-v;t†;m1;o=m7bubm7;r;m7;m|;umo†ѴѴb|u-bѴvķ;-1_

‰b|_ruo0-0bѴb|‹o=v†11;vvγ ‰_;u;IŐŏőbv|_;bm7b1-|ou=†m1ঞom|_-|u;|†umvom;b=|_;-u]†l;m|bv |u†;-m7Œ;uo;Ѵv;‰_;u;ĺ

ƑĺƓՊ|Պubouv]oˆ;umbm]vbl†Ѵ-ঞomlo7;ѴŐ0o†m7-u‹

1om7bঞomvő

);lo7;Ѵ|_;ru;vv†u;0o†m7-u‹1om7bঞomv-m7_;l-|o1ub|0o†m7Ŋ -u‹1om7bঞomv0‹v1-Ѵ;7v_b[;70;|-7bv|ub0†ঞomv

‰_;u; α -m7 β -u; v_-r; _‹r;uŊr-u-l;|;uvķ a -m7 b -u; _‹r;uŊ r-u-l;|;uv7;Cmbm]|_;0o†m7vo==;-vb0Ѵ;r-u-l;|;uvr-1;vķ-m7mx bv|_;7bl;mvbomo=xĺ$_;†v;o=0;|-7bv|ub0†ঞomv-ѴѴo‰v|_;r-u-l;Ŋ |;uv|o0;1omv|u-bm;7|or_‹vboѴo]b1-ѴѴ‹1om1;bˆ-0Ѵ;u-m];v‰_bѴ;-Ѵvo -ѴѴo‰bm]|_;r-u-l;|;u7bv|ub0†ঞom|o_-ˆ;u;Ѵ-ঞˆ;Ѵ‹Y;Šb0Ѵ;v_-r;v 7;r;m7bm]om|_;r-uঞ1†Ѵ-u1_ob1;o=v1-Ѵ;_‹r;uŊr-u-l;|;uvĺ

ƑĺƔՊ|Պubouv]oˆ;umbm]Ѵbh;Ѵb_oo7=†m1ঞomv

$_;†v;o=-†vvb-m7bv|ub0†ঞomv=ou0Ѵoo7Yo‰ˆ;Ѵo1b|‹;uuouv-m7 _;l-|o1ub| ;uuouv bm|uo7†1;v -vvo1b-|;7 mobv; 1olrom;m|v σ_i bm|o |_; Ѵbh;Ѵb_oo7 =†m1ঞomv t†-ঞomƒ -m7 _;m1; -Ѵvo bm|o |_; -‹;vĽ |_;ou;lt†-ঞomƐĺo‰;ˆ;uķ|_;mobv;ˆ-ub-m1;v-u;†mhmo‰m-m7 |_;u;=ou;lo7;Ѵ;7-v†m1;u|-bmr-u-l;|;uvĺubou7bv|ub0†ঞomv]oˆŊ ;umbm]0Ѵoo7Yo‰ˆ;Ѵo1b|‹;uuouv-m77bv1_-u];_;l-|o1ub|;uuouv-u; lo7;Ѵ;70‹v1-Ѵ;7bmˆ;uv;1_bŊvt†-u;7bv|ub0†ঞomv

‰b|_ m0 -m7 s0 0;bm] _‹r;uŊr-u-l;|;uvĺ ol0bm-ঞom o= -†vvb-m

;uuou lo7;Ѵv ‰b|_ v1-Ѵ;7 bmˆ;uv; 1_bŊvt†-u; 7bv|ub0†ঞomv =ou mobv; ˆ-ub-m1;bv1omˆ;mb;m|ķvbm1;|_bvmo|omѴ‹Ѵ;-7v|o-m-m-Ѵ‹ঞ1-ѴvoѴ†Ŋ ঞom|o|_;rov|;ubouo=|_;mobv;ˆ-ub-m1;ķ0†|-Ѵvo-ѴѴo‰v=oubm|;]u-|Ŋ bm]|_;mobv;ˆ-ub-m1;vo†|o=|_;bm=;u;m1;;t†-ঞomv0‹-m-Ѵ‹ঞ1-Ѵ l;-mvĺƑƔķƑƕ

$_; rubou 7bv|ub0†ঞom o= |_; ruo0-0bѴb|‹ o= 1ouu;1|Ѵ‹ ru;7b1ঞm] 0Ѵoo7Yo‰7bu;1ঞombvlo7;Ѵ;7-v-0;|-7bv|ub0†ঞom ‰b|_α-m7β0;bm]_‹r;uŊr-u-l;|;uvĺ$_bv1_ob1;r;ulb|v-m-m-Ŋ Ѵ‹ঞ1-ѴvoѴ†ঞom|o|_;rov|;ubouo=|_;ruo0-0bѴb|‹o=ru;7b1ঞm]1ouu;1| Yo‰7bu;1ঞomĺ

ƑĺѵՊ|Պo7;Ѵbm=;u;m1;

$_;o0f;1ঞˆ;o=lo7;Ѵbm=;u;m1;bv|obm=;u|_;rov|;ubou7bv|ub0†ঞom o= lo7;Ѵ r-u-l;|;uv pŐx|y,mőķ Őt†-ঞomƐőĺ 11ou7bm] |o |_; -‹;vĽ |_;ou;lt†-ঞomƐķ|_bvrov|;ubou7bv|ub0†ঞombvruorouঞom-Ѵ|o|_; ruo7†1|o=|_;Ѵbh;Ѵb_oo7-m7|_;rubou7bv|ub0†ঞomķ-m7b|bvv|u-b]_|Ŋ =ou‰-u7|o1ol0bm;|_;Ѵbh;Ѵb_oo7-m7rubou|o=oul-l-|_;l-ঞ1-Ѵ ;Šru;vvbom=ou|_;rov|;ubou7bv|ub0†ঞomĺ"blbѴ-uѴ‹ķ;ˆ-Ѵ†-ঞm]|_;Ѵbh;Ŋ Ѵb_oo7=†m1ঞom-m7|_;rubou7bv|ub0†ঞom=ou-]bˆ;mr-u-l;|;uˆ-Ѵ†; ̃ xbv-Ѵvov|u-b]_ou‰-u7Ő-Ѵ|_o†]_ro|;mঞ-ѴѴ‹m†l;ub1-ѴѴ‹;Šr;mvbˆ;őĺ o‰;ˆ;uķ-m-m-Ѵ‹ঞ1-Ѵ;Šru;vvbom=oupŐx|y,mő1-mmo|0;7;ubˆ;7ķr-u|Ѵ‹ 0;1-†v; o= |_; l-|_;l-ঞ1-Ѵ =oulv o= |_; Ѵbh;Ѵb_oo7 -m7 |_; rubouķ -m7r-u|Ѵ‹0;1-†v;x;m|;uv|_;Ѵbh;Ѵb_oo7=†m1ঞomˆb-|_;momѴbm;-u vbl†Ѵ-ঞom lo7;Ѵ fŐxőĺ mv|;-7ķ ‰; †v;  vbl†Ѵ-ঞomĺ26_{ }

];m;u-|;v - v;t†;m1; o= v-lrѴ;v ‰_bѴ; ;ŠrѴoubm] |_; r-u-l;|;u vr-1;ĺ"-lrѴ;v-u;7u-‰mv†1_|_-||_;‹lblb1v-lrѴ;v=uolpŐx|y,mőķ -m71-m0;†v;7|ou;ru;v;m||_;rov|;ubou7bv|ub0†ঞomķ|o1-Ѵ1†Ѵ-|; lol;m|v‰b|_u;vr;1||ob|Ő;]ķl;-m-m7l;7b-mőķ-m7|o-rruoŠbl-|; bm|u-1|-0Ѵ;bm|;]u-Ѵv0‹;lrbub1-Ѵ-ˆ;u-];vbm|_;1om|;Š|o=ru;7b1ঞom Őt†-ঞomƑőĺv-lrѴbm]b|;u-ঞomruo1;;7v-v=oѴѴo‰vĹ;|x_tŊƐ 7;mo|;|_;1†uu;m|v|-|;o=-1_-bmĺ|ub-Ѵloˆ;|o-ruorov-Ѵv|-|; x_pbv];m;u-|;7ĺ$_;Yo‰vbl†Ѵ-ঞomlo7;Ѵbvu†m‰b|_|_;ruorov;7 r-u-l;|;uv-m7|_;†mŊmoul-ѴbŒ;7rov|;ubou7;mvb|‹LŐx|yķmőpŐx|mőbv ;ˆ-Ѵ†-|;7ķb;ķ|_;vbl†Ѵ-ঞomlo7;ѴĽvru;7b1ঞomv-u;1olr-u;7|o|_; o0v;uˆ-ঞomvˆb-|_;Ѵbh;Ѵb_oo7=†m1ঞom-m7|_;ruorov;7r-u-l;|;uv -u; 1olr-u;7 |o |_; rubou 7bv|ub0†ঞomĺ $_; ruorov;7 v|-|; bv |_;m ;b|_;u-11;r|;7ouu;f;1|;7-11ou7bm]|o|_;;|uoroѴbvu†Ѵ;

u-m7olˆ-Ѵ†;ubvv-lrѴ;7†mb=oulѴ‹om|_;bm|;uˆ-ѴŒƏķƐœĺ=u<u1ķ

|_; ruorov;7 v-lrѴ; bv -11;r|;7 Őxt=xpőķ o|_;u‰bv; |_; v-lrѴ; bv

u;f;1|;7 Őxt=xtŊƐőĺ $_bv b|;u-ঞˆ; ruo1;7†u; o= ];m;u-ঞm]ķ -m7 |_;m

-11;rঞm]ouu;f;1ঞm]|_;ruorov;7v-lrѴ;vķbvu;r;-|;7†mঞѴ;b|_;u -7;vbu;7m†l0;uo=;ˆoѴ†ঞomv|;rvbv-1_b;ˆ;7ou|_;b|;u-ঞomv-u; v|orr;7-11ou7bm]|o-rruorub-|;1omˆ;u];m1;7b-]movঞ1vĺ );†v;|_; !Ő,"ő-Ѵ]oub|_lƑѶŋƒƏ|o];m;u-|;ruorov-Ѵv-lŊ rѴ;vĺ !_Ő,"ő bv - l†ѴঞrѴ;Ŋ1_-bm l;|_o7 |_-| †v;v 7b@;u;mঞ-Ѵ ;ˆoѴ†ঞom-7-rঞˆ;;|uoroѴbv‰b|_v-lrѴbm]=uol-m-u1_bˆ;o=r-v| v|-|;v=ourov|;ubou;ŠrѴou-ঞomĺ$_u;;1_-bmv-u;b|;u-|;7bmr-u-ѴѴ;Ѵķ -m7ruorov-Ѵrobm|v-u;];m;u-|;7=uol-fobm|-u1_bˆ;o=r-v|v|-|;v |_-| bv r;ubo7b1-ѴѴ‹ †r7-|;7 =ou ;-1_ ƐƏƏ|_ b|;u-ঞom -v |_; 1_-bmv ;ŠrѴou; r-u-l;|;u vr-1;ĺ !Ő,"ő -†|ol-ঞ1-ѴѴ‹ -7-r|v |_; v1-Ѵ;

-m7oub;m|-ঞomo=|_;ruorov-Ѵ7bv|ub0†ঞomķ-m71omv|-m|Ѵ‹bm|uo7†1;v m;‰v-lrѴbm]7bu;1ঞomvbmr-u-l;|;uvr-1;0‹v;Ѵ=Ŋ-7-rঞˆ;u-m7olŊ bŒ;7v†0vr-1;v-lrѴbm]ĺƑѶŋƒƏ

omˆ;u];m1; o= |_;  1_-bmv |o |_; rov|;ubou 7bv|ub0†ঞom bvf†7];70‹1olr†ঞm]|_;;Ѵl-mŊ!†0bm ̂R1omˆ;u];m1;7b-]movঞ1 =uol|_;l†ѴঞrѴ;1_-bmvb|;u-|;7bmr-u-ѴѴ;ѴĺƒƏķƒƐ Őƒő L_i(x,σ_i|yi ) ∝ ni ∏ j=1 1 σ_iexp [ − 1 2σ_i2 ( y_i,j−f_i,j(x))2 ] , i ∈ {vel,hct} , ŐƓő Ldir ( x,γ|ydir ) = ndir ∏ j=1

γI(ydir,j=fdir,j(x))_{(1 − γ)}I(ydir,j≠fdir,j(x))_,

ŐƔő p(x|α,β,a,b) ∝ nx ∏ j=1 ( xj− aj )𝛼_j−1( bj− xj )βj−1 Őѵő p(σ2_i ) ∝ 1 σn0,i+2 i exp ⎛ ⎜ ⎜ ⎝ − n_0,is2 0,i 2σ2 i ⎞ ⎟ ⎟ ⎠ , i ∈ {vel,hct} , Őƕő p(γ|α,β) ∝ γα−1(_{1 − γ})β−1 ŐѶő u1= min { L(xp|y, m)p(xp|m) L(x_t−1|y, m)p(xt−1|m) ,1 } .

);†v;|_;v-lrѴ;v|ot†-mঞ=‹|‰o|‹r;vo=†m1;u|-bmঞ;vŌru;Ŋ 7b1ঞom †m1;u|-bm|‹ 7†; |o lo7;Ѵ r-u-l;|;u †m1;u|-bm|‹ķ -m7 |o|-Ѵ ru;7b1ঞˆ; †m1;u|-bm|‹ĺ u;7b1ঞom †m1;u|-bm|‹ 7†; |o lo7;Ѵ r-u-lŊ ;|;u †m1;u|-bm|‹ bv 1olr†|;7 0‹ ruor-]-ঞm] |_; bm7bˆb7†-Ѵ v-lrѴ;v |_uo†]_|_;Yo‰vbl†Ѵ-ঞomlo7;Ѵķ|_;u;0‹ruoˆb7bm]-7bv|ub0†ঞom oˆ;u|_;vbl†Ѵ-ঞomlo7;ѴĽvru;7b1ঞomvĺ$o|-Ѵru;7b1ঞˆ;†m1;u|-bm|‹ bv1-Ѵ1†Ѵ-|;70‹-77bm]ķ|o|_;vbl†Ѵ-ঞomlo7;ѴĽvru;7b1ঞomvķmobv; 1om|ub0†ঞomv v-lrѴ;7 =uol -†vvb-m 7bv|ub0†ঞomv‰b|_ Œ;uo l;-mv -m7 ˆ-ub-m1;v v-lrѴ;7 =oul |_; rov|;ubou 7bv|ub0†ঞomv o= mobv; ˆ-ub-m1;vĺ26

ƑĺƕՊ|Պ-v;v|†7‹7-|-v;|v

ƑĺƕĺƐՊ|Պ;v;m|;u‹7-|-$_;l;v;m|;u‹7-|-oub]bm-|;=uol;Šr;ubl;m|-Ѵo0v;uˆ-ঞomvo=|_; l;v;m|;ub1 lb1uoˆ-v1†Ѵ-|†u; bm u-|vĺƖķƐƔ_{ m |_;v; ;Šr;ubl;m|vķ |_;}

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lour_oѴo]‹-m7r_‹vboѴo]‹-u;-ˆ-bѴ-0Ѵ;bm$-0Ѵ;Ɛĺ

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ƑĺƕĺƑՊ|Պu-bm1ou|;Š7-|-$_; 0u-bm 1ou|;Š 7-|- oub]bm-|; =uol ;Šr;ubl;m|-Ѵ o0v;uˆ-ঞomv o= |_; 1ouঞ1-Ѵ lb1uoˆ-v1†Ѵ-|†u; bm lb1; -m7 v|;lv =uol |‰o v;r-u-|; ;Šr;ubl;m|vŐ0†|‰b|_b7;mঞ1-Ѵlo†v;v|u-bm-m7-m;v|_;ঞ1u;]bl;őĹ Cuv|ķ l;-v†u;l;m|v o= m;|‰ouh lour_oѴo]‹ -m7 |oroѴo]‹ 0-v;7 om -m -m]bo]u-l =uol $ bl-]bm] Ő b]†u;Ɛő -m7 -11olr-m‹bm] l;-v†u;l;m|vo=0Ѵoo7Yo‰ˆ;Ѵo1b|‹bmˆ;m†Ѵ;v0-v;7om$bl-]Ŋ bm]ķƕķƑƓ_{-m7v;1om7ķl;-v†u;l;m|vo=-u|;uboѴ-u-m7ˆ;m†Ѵ-u1;m|;uŊ}

Ѵbm;!vr;;70-v;7om$bl-]bm]ĺƒƒ_{m|_;v;7-|-ķ|_;7b-l;|;u}

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l-m†-ѴѴ‹ 1Ѵ-vvbC;7 bm|o -u|;uboѴ;vķ 1-rbѴѴ-ub;vķ -m7 ˆ;m†Ѵ;vĺ (;vv;Ѵ 7b-l;|;uv;vঞl-|;7=uol|_;-m]bo]u-ll-‹mo|u;Y;1||_;;mঞu; Ѵ†lbm-Ѵ7b-l;|;uķvbm1;|_;ˆ-v1†Ѵ-|†u;‰-vbl-];7†vbm]Y†ou;v1;m|Ѵ‹ Ѵ-0;Ѵ;77;Š|u-m‰_b1_Ѵ-0;Ѵv=u;;Yo‰bm]rѴ-vl-‰b|_o†|v|-bmbm]|_;

"ĺƒƓķƒƔ_{ "bm1; |_; u_;oѴo]b1-Ѵ 7;v1ubrঞomv †v;7 bm |_; vbl†Ѵ-ঞom}

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ƏĺƔμlĺƒƓ_{ †;|oѴblb|-ঞomvbmu;voѴ†ঞom-m7u;-7o†|u-|;o=|_;$}

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ƒՊ|Պ!"&$"

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ƒĺƑՊ|Պ;v;m|;u‹7-|-Ōomv|u†1ঞm]bm=oul-ঞˆ;

rubou7bv|ub0†ঞomv

b7Ŋv;]l;m|ru;vv†u;-m7v;]l;m|_;l-|o1ub|ˆv7b-l;|;u-u;v_o‰m bm b]†u;ƕĸlo7;Ѵvbl†Ѵ-ঞomv-u;v_o‰m=oulb7Ŋv;]l;m|ru;vv†u; -m7 ;Šr;ubl;m|-Ѵ l;-v†u;l;m|v -v ‰;ѴѴ -v lo7;Ѵ vbl†Ѵ-ঞomv =ou _;l-|o1ub|ĺ);o0v;uˆ;1omvb7;u-0Ѵ;_;|;uo];m;b|‹bmlb7Ŋv;]l;m| ru;vv†u;=ou-]bˆ;mv;]l;m|7b-l;|;u=ou0o|_-u|;uboѴ;v-m71-rbѴѴ-uŊ b;vķ‰_;u;-vˆ;mo†vru;vv†u;v-u;lou;_olo];m;o†vĺu;vv†u;vbm -u|;uboѴ;vՈ;m†Ѵ;vőbm1u;-v;Ő7;1u;-v;ő‰b|_|_;bu7b-l;|;uĺo|;|_-| |_;vѴb]_|bm1u;-v;bm1-rbѴѴ-u‹lb7Ŋv;]l;m|ru;vv†u;‰b|_7b-l;|;ubv v†rrou|;70‹omѴ‹u;Ѵ-ঞˆ;Ѵ‹=;‰o0v;uˆ-ঞomvĺ;l-|o1ub|bvu;Ѵ-ঞˆ;Ѵ‹ _;|;uo];m;o†v ‰b|_bm v;]l;m| 1Ѵ-vv;v -m7 bm1u;-v;v ‰b|_ 7b-l;|;u =ou-ѴѴv;]l;m|1Ѵ-vv;vĺ -v;7om|_;v;o0v;uˆ-ঞomvķ‰;7;ubˆ;7;lrbub1-Ѵu;Ѵ-ঞomv_brv |_-|7;v1ub0;0o|_ru;vv†u;-m7_;l-|o1ub|-v-=†m1ঞomo=v;]l;m| 7b-l;|;ubmou7;u|o1omv|u†1|bm=oul-ঞˆ;rubou7bv|ub0†ঞomvĺu;vv†u; 0;_-ˆ;77b@;u;m|Ѵ‹-v-=†m1ঞomo=7b-l;|;u-1uovvv;]l;m|1Ѵ-vv;vķ -m7|_u;;v;r-u-|;C|v‰;u;|_;u;=ou;-7or|;7|o7;v1ub0;ru;vv†u; =ou |_; |_u;; v;]l;m| |‹r;vĺ omˆ;uv;Ѵ‹ķ _;l-|o1ub| v_o‰v lou; vblbѴ-u0;_-ˆbou-1uovvv;]l;m|1Ѵ-vvķ-m7-vbm]Ѵ;C||o7-|-rooѴ;7 -1uovvv;]l;m|1Ѵ-vv;v‰-v†v;7ĺ$_;v;;lrbub1-ѴC|vv;uˆ;7-v|_; l;-mˆ-Ѵ†;v]oˆ;umbm]|_;bm=oul-ঞˆ;rubou7bv|ub0†ঞomvĺ$_;1ouu;Ŋ vrom7bm]ˆ-ub-m1;vo=|_;rubou7bv|ub0†ঞomv‰;u;;vঞl-|;7=uol|_; u;vb7†-ѴvŐ7;ˆb-ঞom0;|‰;;m;lrbub1-Ѵlo7;ѴC|v-m7o0v;uˆ-ঞomvőĺ $_;v;l;-mv-m7ˆ-ub-m1;v7;Cm;|_;v_-r;_‹r;uŊr-u-l;|;uvo=|_; bm=oul-ঞˆ;rubou7bv|ub0†ঞomv‰_b1_]oˆ;um0o†m7-u‹1om7bঞomvĺ

ƒĺƒՊ|Պ;v;m|;u‹7-|-Ōo7;Ѵbm=;u;m1;bmv1;m-ubov

‰b|_Ѵblb|;77-|--ˆ-bѴ-0bѴb|‹

);7;Cm;7v†0v;|vo=m;|‰ouhv;]l;m|vbmou7;u|olblb1;Šr;ubŊ l;m|-Ѵv1;m-ubovbm‰_b1_;Šr;ubl;m|-Ѵl;-v†u;l;m|vo=r_‹vboѴo]bŊ 1-Ѵˆ-ub-0Ѵ;vŐ0Ѵoo7Yo‰ˆ;Ѵo1b|‹ķYo‰7bu;1ঞomķ-m7_;l-|o1ub|ő-u; omѴ‹r-uঞ-ѴѴ‹-ˆ-bѴ-0Ѵ;ĺ$_u;;ˆ;vv;Ѵ]uo†rv‰;u;7;Cm;7Ĺ-u|;uboѴ;v ‰b|_7b-l;|;uƻƐƔμlķˆ;m†Ѵ;v‰b|_7b-l;|;uƻƐƔμlķ-m71-rbѴѴ-ub;v Ő b]†u;ѵķőĺ-v;7om|_bvr-uঞঞomķ‰;];m;u-|;7|;m7-|-v;|v‰b|_ ˆ-ubo†v-lo†m|vo=;Šr;ubl;m|-Ѵbm=oul-ঞom-ˆ-bѴ-0Ѵ;ĺ oubm=oul-Ŋ ঞom-0o†||_;v;7-|-v;|vķu;=;u|o b]†u;ƓķѴ;[1oѴ†lmĺ-Ѵb0u-ঞomo= |_;vbl†Ѵ-ঞomlo7;Ѵ‰-v0-v;7omo0v;uˆ-ঞom7-|--ˆ-bѴ-0Ѵ;‰b|_bm ;-1_o=|_;|;m7-|-v;|vĺo7;Ѵru;7b1ঞˆ;r;u=oul-m1;‰-v;ˆ-Ѵ†Ŋ -|;7 0‹ 1olr-ubm] lo7;Ѵ ru;7b1ঞomv |o -ѴѴ o0v;uˆ-ঞomvķ |_;u;0‹ 1omvb7;ubm]1-Ѵb0u-ঞomņbmŊv-lrѴ;r;u=oul-m1;-v‰;ѴѴ-vˆ-Ѵb7-ঞomņ o†|Ŋo=Ŋv-lrѴ;r;u=oul-m1;ĺ$o1omv|u-bm|_;lo7;Ѵbm|_;-0v;m1;o= 1olru;_;mvbˆ;o0v;uˆ-ঞom7-|-bm-ѴѴv;]l;m|vķ‰;†v;7|_;bm=oulŊ -ঞˆ;rubou7bv|ub0†ঞomv7;ubˆ;7=uol|_;bmbঞ-Ѵ-m-Ѵ‹vbv-vrubouv=ou |_;0o†m7-u‹1om7bঞomvĺ‹r;uŊr-u-l;|;uvo=7bv|ub0†ঞomv]oˆ;umŊ bm]0Ѵoo7Yo‰ˆ;Ѵo1b|‹;uuouķ_;l-|o1ub|;uuouķ-m7|_;ruo0-0bѴb|‹o= 1ouu;1| ru;7b1ঞom o= 0Ѵoo7 Yo‰ 7bu;1ঞom ‰;u; v;| -v bm |_; bmbঞ-Ѵ 1-Ѵb0u-ঞom-m-Ѵ‹vbvĺ

†-mঞ|-ঞˆ; l;|ub1v 1olr-ubm] l;-v†u;l;m|v -m7 lo7;Ѵ ru;Ŋ 7b1ঞomv-u;u;rou|;7bm b]†u;Ɠĺ$_;†v;o=-mbm=oul-ঞˆ;rubou‰-v -vvo1b-|;7‰b|_-m;]Ѵb]b0Ѵ;r;u=oul-m1;Ѵovvbm1olr-ubvom‰b|_|_; †v;o=-‰;-hrubouom|_;7-|-v;|‰b|_-ѴѴo0v;uˆ-ঞom-ˆ-bѴ-0Ѵ;=ou 1-Ѵb0u-ঞom ŐCuv| |‰o 0-uv bm bm7bˆb7†-Ѵ rѴo|vőĺ o|-0Ѵ‹ķ lo7;Ѵ r;uŊ =oul-m1;‰b|_ u;vr;1| |o ru;7b1|;7ˆ;Ѵo1b|‹ -m7 Yo‰ 7bu;1ঞom‰-v ];m;u-ѴѴ‹ru;v;uˆ;7-Ѵ|_o†]__;l-|o1ub|l;-v†u;l;m|v‰;u;Ѵ-1hbm]ķ -Ѵ|_o†]_ |_bv o= 1o†uv; Ѵ;-7v |o u;7†1;7 r;u=oul-m1;‰b|_ u;vr;1| |o_;l-|o1ub|ru;7b1ঞomvĺm-77bঞomķ|_;vbl†Ѵ-ঞomlo7;Ѵl-bm|-bmv |_;1-r-0bѴb|‹o=ru;7b1ঞm]ˆ;Ѵo1b|‹;ˆ;m‰_;mo0v;uˆ-ঞomvbmv;]Ŋ l;m| v†0]uo†rv ‰;u; 7bvu;]-u7;7 =uol |_; 1-Ѵb0u-ঞom v|-];ĺ o|; |_-|bm1u;-v;vbm;uuou=ou|_;7bvu;]-u7;7v†0]uo†rv7omo|m;1;vŊ v-ubѴ‹blrѴ‹7;1u;-v;7lo7;Ѵr;u=oul-m1;-vv†1_ķvbm1;|_;v;;uuouv u;ru;v;m| ˆ-Ѵb7-ঞomņo†|Ŋo=Ŋv-lrѴ; ;uuouv u-|_;u |_-m 1-Ѵb0u-ঞomņ bmŊv-lrѴ;;uuouvĺo7;Ѵvbl†Ѵ-ঞomvl-bm|-bm]oo7r;u=oul-m1;-Ѵvo bm7-|-v;|v‰_;u;0Ѵoo7Yo‰ˆ;Ѵo1bঞ;vbml-bm=;;7bm]-m77u-bmbm] ˆ;vv;Ѵv-u;7bvu;]-u7;7bm|_;1-Ѵb0u-ঞomv|-];ĺ

-u]bm-Ѵrov|;ubou7bv|ub0†ঞomv=ou0o†m7-u‹ru;vv†u;-m70o†m7Ŋ -u‹ _;l-|o1ub| bm m;|‰ouh ƒ -u; v_o‰m =ou =o†u o= |_; v1;m-ubov bm b]†u;ƔŐѴ;[1oѴ†lmv_o‰vl;-v†u;l;m|v-ˆ-bѴ-0Ѵ;=oulo7;Ѵ1-Ѵb0u-Ŋ ঞomőĺ$_;u;bvv|uom]1omvbv|;m1‹0;|‰;;m|_;bm=;uu;7ru;vv†u;7bv|ubŊ 0†ঞomv‰_;mbm=;u;m1;bv0-v;7om0uo-7rubouvŐ b]†u;Ɣő-m7lou; bm=oul-ঞˆ; rubouv Ő b]†u;Ɣőĺ o|; |_-| |_;u; bv v†L1b;m| ;ˆb7;m1; bm |_; l;-v†u;l;m|v |o -ѴѴo‰ |_; rov|;ubou 7bv|ub0†ঞomv |o 7bˆ;u]; =uol|_;rubou7bv|ub0†ঞomŐmo7;vƐķƑķƒķƒƐķƒƒķ-m7ƒѵbmr-uঞ1†Ѵ-uőĺ   & !   ѵ Պ (bv†-ѴbŒ-|bomo=|_;vr-|b-Ѵv|u†1|†u;=oul;v;m|;u‹m;|‰ouhƒĺŐőѴѴƔƓѵˆ;vv;Ѵv;]l;m|v1oѴou;7-11ou7bm]|oˆ;vv;Ѵ|‹r; 1Ѵ-vvb=b1-|bomĸ-u|;uboѴ;v-u;u;7ķ1-rbѴѴ-ub;v-u;]u;;mķ-m7ˆ;m†Ѵ;v-u;0Ѵ†;ĺo†m7-u‹mo7;v-u;Ѵ-0;Ѵ;7‰b|_m†l0;uvou7;u;71Ѵo1h‰bv;=uol |_;l-bm=;;7bm]-u|;uboѴ;ŐomѴ‹†m;ˆ;mm†l0;uvv_o‰mőĺŐő(-ub-m|o=1olrѴ;|;m;|‰ouh‰b|_1-rbѴѴ-ub;v_b]_Ѵb]_|;7ĺŐő(-ub-m|o=1olrѴ;|; m;|‰ouh‰b|_-u|;uboѴ;v-m7ˆ;m†Ѵ;v‰b|_7b-l;|;uvƻƐƔμl_b]_Ѵb]_|;7ĺ";]l;m|7b-l;|;uv-u;7o†0Ѵ;7|o;m_-m1;ˆbvb0bѴb|‹

"blbѴ-uѴ‹ķ|_;u;bvv|uom]1omvbv|;m1‹0;|‰;;mrov|;ubou7bv|ub0†ঞomv ]oˆ;umbm]_;l-|o1ub|=ou|_;0uo-7-m7bm=oul-ঞˆ;rubouŐ b]†u;Ɣķ ub]_|1oѴ†lmőĺ=ˆ;Ѵo1b|‹l;-v†u;l;m|vbm-u|;uboѴ;v‰;u;7bvu;]-u7;7 bm 1-Ѵb0u-ঞomķ |_;m |_; rov|;ubou 7bv|ub0†ঞomv o= 0o†m7-u‹ ru;vŊ v†u;v=ou-u|;uboѴ;vŐmo7;vƐ-m7ƒő-rruo-1_|_;rubou7bv|ub0†ঞomv Ő b]†u;Ɣķ őĺ ou1-rbѴѴ-u‹0o†m7-u‹mo7;vŐmo7;vƑķƒƐķƒƒķ-m7ƒѵőķ -ˆ-bѴ-0bѴb|‹o=1-rbѴѴ-u‹Yo‰ˆ;Ѵo1bঞ;vbm|_;1-Ѵb0u-ঞomv|;rѴ;-7v|o- 7;r-u|†u;=uol|_;rubou7bv|ub0†ঞomv=ouru;vv†u;Ő b]†u;Ɣŋőĺo|; |_-|_;l-|o1ub|bv7;1u;-v;7=oumo7;ƒƐķruo0-0Ѵ‹bm-m-‚;lr|0‹|_; lo7;Ѵ|ou;ruo7†1;|_;u;Ѵ-ঞˆ;Ѵ‹_b]_o0v;uˆ;70Ѵoo7Yo‰ˆ;Ѵo1b|‹ o0v;uˆ;7 bm |_;ˆb1bmb|‹ o= mo7; ƒƐĺ b]†u;Ɣ  v_o‰v rov|;ubou 7bvŊ |ub0†ঞomvbm=;uu;7‰_;momѴ‹l;-v†u;l;m|vo=ˆ;mo†vˆ;Ѵo1bঞ;v-m7 vr;1bC1-ঞomo=-u|;uboѴ-uYo‰7bu;1ঞom-u;-ˆ-bѴ-0Ѵ;=oulo7;Ѵ1-Ѵb0u-Ŋ ঞomĺov|rov|;ubou7bv|ub0†ঞomvo=0o†m7-u‹ru;vv†u;v-m7_;l-|oŊ 1ub|Ѵ-u];Ѵ‹u;v;l0Ѵ;|_;rubou7bv|ub0†ঞomvķ‰_;u;-vru;vv†u;vo=Ѵ-u]; ˆ;m†Ѵ;v -u; 1_-u-1|;ubŒ;7 0‹ t†b|; Ѵo1-ѴbŒ;7 rov|;ubou 7bv|ub0†ঞomvĺ ˆ;u-ѴѴķ b]†u;Ɣv_o‰v|_-||_;lo7;Ѵbm]=u-l;‰ouh1-m-7-r||oѴblŊ b|;71-Ѵb0u-ঞom7-|--ˆ-bѴ-0bѴb|‹‰_;mb|bm1Ѵ†7;v|_;bm=oul-ঞˆ;rubouĺ ol0bmbm] -m-Ѵ‹vbv o= ;Šr;ubl;m|-Ѵ l;-v†u;l;m|v ‰b|_ lo7;Ѵ vbl†Ѵ-ঞomv1-mro|;mঞ-ѴѴ‹‹b;Ѵ7lou;bm=oul-ঞom|_-mom;1-m]Ѵ;-m =uolu-‰l;-v†u;l;m|7-|-ĺ$obѴѴ†v|u-|;v†1_-77bঞom-Ѵbm=oul-ঞomķ ‰;7;ubˆ;7Ŋ(0Ѵoo7|u-mvb|ঞl;7bv|ub0†ঞomvŐ b]†u;Ѷőĺˆ;u-ѴѴķ|_; -ˆ;u-];v-m7v|-m7-u77;ˆb-ঞomo=Ŋ(|u-mvb|ঞl;v-]u;;‰b|_ru;ˆbŊ o†vu;rou|vĺ11_{ †u|_;ulou;ķ‰;o0v;uˆ;-7bˆ;uvb|‹o=|_;7bv|ub0†ঞomv}

-1uovv m;|‰ouhv Őv;r-u-|; 1oѴ†lmvőĺ $_; oˆ;u-ѴѴ |u-mvb| ঞl;v |;m7 |o bm1u;-v; -v o0v;uˆ-ঞomv -u; 7bvu;]-u7;7ĸ _o‰;ˆ;uķ |_; 7bˆ;uvb|‹ -1uovv m;|‰ouhv bv ru;v;uˆ;7‰_;m 7bvu;]-u7bm] o0v;uˆ-ঞomv -ˆ-bѴŊ -0Ѵ;=oulo7;Ѵ1-Ѵb0u-ঞomŐ b]†u;Ѷķőĺ

ƒĺƓՊ|Պu-bm1ou|;Š7-|-Ō-u];ˆ-v1†Ѵ-um;|‰ouh-m7

limited measurement availability

&vbm]|_;-‹;vb-m=u-l;‰ouhķo†uvbl†Ѵ-ঞomlo7;Ѵ‰-v1-Ѵb0u-|;7 |o m;|‰ouh 7-|- =uol |_; 0u-bm 1ou|;Š Ő b]†u;Ɩőķ ‰b|_ omѴ‹ - ѴblŊ b|;7m†l0;uo=l;-v†u;l;m|v-ˆ-bѴ-0Ѵ;=ou1-Ѵb0u-ঞomŐ b]†u;Ɩő-m7 1Ѵov;|oѵƏƏ†mhmo‰mru;vv†u;-m7_;l-|o1ub|0o†m7-u‹1om7bঞomv Ő b]†u;Ɩőĺ

b]†u;Ƒv_o‰v|_;;Ѵl-mŊ!†0bm ̂R1omˆ;u];m1;7b-]movঞ1ˆv |_; m†l0;u o= =†m1ঞom ;ˆ-Ѵ†-ঞomvĺ omˆ;u];m1; =ou -ѴѴ r-u-l;|;u 1_-bmv‰-v u;-1_;7 -[;u -rruoŠbl-|;Ѵ‹ ƐƑƏƏƏƏƏ =†m1ঞom ;ˆ-Ѵ†-Ŋ ঞomvķ‰_;u;-v1omˆ;u];m1;=ouƖƖѷo=|_;r-u-l;|;uv‰-vu;-1_;7 -[;u-rruoŠbl-|;Ѵ‹ƔƏƏƏƏƏ=†m1ঞom;ˆ-Ѵ†-ঞomvĺ$_u;;lbѴѴbom=†m1Ŋ ঞom;ˆ-Ѵ†-ঞomv|ooh-0o†|Ɛƒ_ĺ

$_; 1ol0bm;7 -m-Ѵ‹vbv o= lo7;Ѵ vbl†Ѵ-ঞomv -m7 ;Šr;ubl;m|-Ѵ l;-v†u;l;m|v ‹b;Ѵ7v ru;7b1ঞomv o= ru;vv†u;ķ Yo‰ķ -m7 _;l-|o1ub| |_uo†]_o†||_;m;|‰ouhŐ b]†u;Ɩ ŋ őĺo|;|_-||_;-‹;vb-m-m-Ѵ‹Ŋ vbvѴ;-7v|o7bv|ub0†ঞomvoˆ;u|_;v;t†-mঞঞ;v‰_bѴ;|_;rѴo|vv†ll-Ŋ ubŒ;|_;v;7bv|ub0†ঞomv0‹v_o‰bm]|_;bul;-momѴ‹ĺ b]†u;ƐƏ1olr-u;v|_;vbl†Ѵ-ঞomlo7;ѴĽvru;7b1ঞomo=ˆ;Ѵo1b|‹bm -u|;uboѴ;v-m7ˆ;m†Ѵ;vŐ b]†u;Ɩő|o;Šr;ubl;m|-Ѵl;-v†u;l;m|v-v- =†m1ঞomo=7b-l;|;uĺo7;Ѵru;7b1ঞomvt†-Ѵb|-ঞˆ;Ѵ‹-]u;;‰b|_l;-Ŋ v†u;l;m|v-m7v_o‰7;1u;-v;7ˆ;Ѵo1b|‹‰b|_7b-l;|;uĺ77bঞom-ѴѴ‹ķ |_;u;bvt†-mঞ|-ঞˆ;-]u;;l;m|0;|‰;;m|_;lo7;ѴĽvru;7b1ঞomv-m7 -1|†-Ѵ l;-v†u;l;m|vķ ‰_bѴ; |_; †m1;u|-bm|‹ u;Ѵ-|;7 |o |_; lo7;ѴĽv ru;7b1ঞomvv_o‰v-u;Ѵ-ঞˆ;]oo71oˆ;u-];o=l;-v†u;l;m|robm|vĺ

bm-ѴѴ‹ķ b]†u;ƐƐ v_o‰v Ŋ( 0Ѵoo7 |u-mvb| ঞl; 7bv|ub0†ঞomvĺ "blbѴ-u|o|_;l;v;m|;u‹m;|‰ouhvķ‰;o0v;uˆ;-1omvb7;u-0Ѵ;_;|;uoŊ ];m;b|‹bm0Ѵoo7ķ!ķ-m7rѴ-vl-Ŋ(|u-mvb|ঞl;vĺ

mv†ll-u‹ķ|_;-m-Ѵ‹vbvo=|_;0u-bm1ou|;Š7-|-bѴѴ†v|u-|;v|_-|Őbő |_;-m-Ѵ‹vbv=u-l;‰ouh‰ouhv‰;ѴѴomv|-|;Ŋo=Ŋ|_;Ŋ-u|7-|-v;|v‰_b1_ 1om|-bm _†m7u;7v o= †mhmo‰m ru;vv†u; -m7 _;l-|o1ub| 0o†m7-u‹ 1om7bঞomvķŐbbő|_;-m-Ѵ‹vbv=u-l;‰ouh-ѴѴo‰v1-Ѵb0u-ঞomo=vbl†Ѵ-ঞom   & !   ƕ Պ bv|ub0†|bomvo=Őőlb7Ŋv;]l;m|ru;vv†u;-m7Őő v;]l;m|_;l-|o1ub|bm|_;|_u;;l;v;m|;u‹m;|‰ouhvĺu|;uboѴ-u v;]l;m|v-u;u;7ķ1-rbѴѴ-u‹v;]l;m|v-u;]u;;mķ-m7ˆ;m†Ѵ-uv;]l;m|v -u;0Ѵ†;ĺ"1-||;urobm|v1ouu;vrom7|ol;7b-mlo7;Ѵru;7b1|bomv=ou v;]l;m|ru;vv†u;ŐmƷƐƒƑƐv;]l;m|vőķ-m7l;7b-m_;l-|o1ub|0-v;7 om0o|_ru;7b1|bomv-m7l;-v†u;l;m|vŐmƷƑѵƓƑőŐl;-v†u;l;m|v l-uh;7‰b|_‰_b|;7o|vőĺo7;Ѵru;7b1|bomv1ouu;vrom7|o|_; 1-Ѵb0u-|bomv;|†r‰b|_-ѴѴl;-v†u;l;m|v-ˆ-bѴ-0Ѵ;=ou1-Ѵb0u-|bom-m7 ľmomŊbm=oul-|bˆ;Ŀrubouvĺ"oѴb7Ѵbm;v-u;Ѵo1-ѴroѴ‹molb-Ѵu;]u;vvbom =b|vo=|_;7-|-ĺƓƑ_{$_;v;=b|v‰;u;†v;7-vl;-mˆ-Ѵ†;vo=|_;} ľbm=oul-|bˆ;Ŀrubouvķ-m7|_;7-v_;7Ѵbm;vl-uhƖƔr;u1;m|bѴ;vo=|_; rubou7bv|ub0†|bomv

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ƓĺƒՊ|Պo7;Ѵru;7b1ঞomv

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