{"id":6078,"date":"2026-10-19T09:48:26","date_gmt":"2026-10-19T09:48:26","guid":{"rendered":"https:\/\/phd.hi.is\/doktorsvorn\/doktorsvorn-i-tolfraedi-giridhar-r-gopalan\/"},"modified":"2026-10-19T09:48:26","modified_gmt":"2026-10-19T09:48:26","slug":"doktorsvorn-i-tolfraedi-giridhar-r-gopalan","status":"publish","type":"phd_defence","link":"https:\/\/phd.hi.is\/en\/doktorsvorn\/doktorsvorn-i-tolfraedi-giridhar-r-gopalan\/","title":{"rendered":"Doktorsv\u00f6rn \u00ed t\u00f6lfr\u00e6\u00f0i – Giridhar R. Gopalan"},"content":{"rendered":"
\n
\n

Doktorsefni:<\/strong>\u00a0Giridhar R. Gopalan<\/p>\n

Heiti ritger\u00f0ar:<\/strong>\u00a0T\u00f6lfr\u00e6\u00f0il\u00edk\u00f6n fyrir j\u00f6klafr\u00e6\u00f0ig\u00f6gn<\/p>\n

\u00a0Andm\u00e6lendur:\u00a0<\/strong><\/p>\n

Dr. Oksana Chkrebtii, lektor vi\u00f0 Ohio State University
Dr. Hilmar Gu\u00f0mundsson, pr\u00f3fessor vi\u00f0 Northumbria University.<\/p>\n

Lei\u00f0beinandi:<\/strong>\u00a0Dr. Birgir Hrafnkelsson, pr\u00f3fessor vi\u00f0 Raunv\u00edsindadeild H\u00e1sk\u00f3la \u00cdslands.\u00a0<\/strong><\/p>\n

Einnig \u00ed doktorsnefnd:<\/strong>\u00a0Dr. Christopher K. Wikle, pr\u00f3fessor vi\u00f0 University of Missouri.
Dr. Gu\u00f0finna Th A\u00f0algeirsd\u00f3ttir, pr\u00f3fessor vi\u00f0 Jar\u00f0v\u00edsindadeild H\u00e1sk\u00f3la \u00cdslands.<\/p>\n

Doktorsv\u00f6rn st\u00fdrir:<\/strong>\u00a0Dr. Oddur Ing\u00f3lfsson, pr\u00f3fessor og deildarforseti Raunv\u00edsindadeildar H\u00e1sk\u00f3la \u00cdslands<\/p>\n

\u00c1grip<\/strong><\/p>\n

Markmi\u00f0 \u00feessarar ritger\u00f0ar er a\u00f0 \u00fer\u00f3a t\u00edma- og r\u00fdmish\u00e1\u00f0 t\u00f6lfr\u00e6\u00f0ileg l\u00edk\u00f6n fyrir j\u00f6kla me\u00f0 \u00fev\u00ed a\u00f0\u00a0nota stigskipt Bayes\u00edsk l\u00edk\u00f6n. H\u00e9r er s\u00e1 hluti stigskipta Bayes\u00edska l\u00edkansins sem sn\u00fdr a\u00f0 undirliggjandi l\u00edkani fyrir ferli\u00f0 sem er veri\u00f0 a\u00f0 sko\u00f0a, \u00fatf\u00e6r\u00f0ur \u00feannig a\u00f0 t\u00edmara\u00f0irnar sem\u00a0koma fr\u00e1 t\u00f6lulegum hermi (\u00fe.e. fr\u00e1 t\u00f6lulegri lausn \u00e1 hlutaflei\u00f0uj\u00f6fnu e\u00f0a n\u00e1lgun \u00e1 sl\u00edkri t\u00f6lulegri lausn) eru lag\u00f0ar saman vi\u00f0 l\u00edkindafr\u00e6\u00f0ilegt ferli sem hefur \u00fea\u00f0 hlutverk a\u00f0 lei\u00f0r\u00e9tta fyrir\u00a0mismuninn \u00e1 milli t\u00f6lulega hermisins og raunverulega ferlisins, og er n\u00e1tengd hugmyndinni um misr\u00e6mi l\u00edkana.<\/p>\n

\u00deetta l\u00edkindafr\u00e6\u00f0ilega ferli lei\u00f0r\u00e9ttir fyrir r\u00fdmish\u00e1\u00f0 fr\u00e1vik og tekur tillit til a\u00f0\u00a0fr\u00e1vikin safnist upp yfir t\u00edma. Til a\u00f0 fl\u00fdta fyrir \u00fatreikningum \u00fe\u00e1 er l\u00ednuleg algebra fyrir r\u00fdr fylki\u00a0notu\u00f0 til a\u00f0 reikna sennileikafall l\u00edkansins og fyrstu gr\u00e1\u00f0u hermar nota\u00f0ir til a\u00f0 fl\u00fdta fyrir \u00fatreikningum \u00e1 t\u00f6lulegum lausnum hlutaflei\u00f0ujafna e\u00f0a \u00f6\u00f0rum kerfum. A\u00f0 auki er n\u00fd\u00a0reiknisparandi n\u00e1lgun fundin fyrir sennileikafalli\u00f0.<\/p>\n

Fr\u00e6\u00f0ilegar lausnir \u00e1 \u00feunnj\u00f6kla n\u00e1lguninni\u00a0sem byggir \u00e1 j\u00f6fnum Stokes fyrir spennur \u00ed j\u00f6klum, eru nota\u00f0ar til a\u00f0 meta reiknihra\u00f0a og\u00a0n\u00e1kv\u00e6mni t\u00f6lulegra n\u00e1lgana, og hversu vel l\u00edkani\u00f0 fellur a\u00f0 g\u00f6gnunum. A\u00f0 auki er l\u00edk\u00f6nunum og\u00a0a\u00f0fer\u00f0afr\u00e6\u00f0inni \u00ed \u00feessari ritger\u00f0 beitt \u00e1 raunveruleg gagnas\u00f6fn sem Jar\u00f0v\u00edsindastofnun H\u00e1sk\u00f3la\u00a0\u00cdslands hefur sett saman, \u00fear me\u00f0 taldar afkomum\u00e6lingar \u00e1 22-25 f\u00f6stum st\u00f6\u00f0um sem teknar\u00a0eru tvisvar \u00e1 \u00e1ri \u00e1 Langj\u00f6kli yfir 19 \u00e1ra t\u00edmabil, auk h\u00e6\u00f0arkorts sem hefur 100 metra upplausn.<\/p>\n

Aukaafur\u00f0 sem kom til vi\u00f0 sm\u00ed\u00f0i \u00e1 stigskipta Bayes\u00edska l\u00edkaninu, er n\u00fd mismunaa\u00f0fer\u00f0 til a\u00f0\u00a0leysa t\u00f6lulega hlutaflei\u00f0uj\u00f6fnuna fyrir \u00feunnj\u00f6kla n\u00e1lgunina. \u00de\u00f3 svo a\u00f0 a\u00f0fer\u00f0irnar sem h\u00e9r eru\u00a0settar fram s\u00e9u fyrir j\u00f6klafr\u00e6\u00f0i \u00fe\u00e1 m\u00e1 \u00fatf\u00e6ra \u00fe\u00e6r fyrir \u00f6nnur\u00a0 jar\u00f0e\u00f0lisfr\u00e6\u00f0ileg g\u00f6gn og\u00a0tilsvarandi l\u00edk\u00f6n.<\/p>\n

Ritger\u00f0in byggir \u00e1 \u00feremur v\u00edsindagreinum. \u00cd fyrstu greininni er fari\u00f0 yfir \u00feau l\u00edk\u00f6n sem hafa\u00a0veri\u00f0 \u00fer\u00f3u\u00f0 til a\u00f0 l\u00fdsa hreyfingu j\u00f6kla, annarar gr\u00e1\u00f0u mismunaa\u00f0fer\u00f0 til a\u00f0 leysa t\u00f6lulegu\u00a0hlutaflei\u00f0uj\u00f6fnuna fyrir \u00feunnj\u00f6kla n\u00e1lgunina er kynnt sem og stigskipt Bayes\u00edskt l\u00edkan sem notar\u00a0t\u00f6lulegu lausnina, og mat byggt \u00e1 stigskipta Bayes\u00edska l\u00edkaninu er bori\u00f0 saman vi\u00f0 fr\u00e6\u00f0ilega lausn \u00feunnj\u00f6kla n\u00e1lgunarinnar. \u00cd grein tv\u00f6 er fjalla\u00f0 um n\u00e1nari \u00fatf\u00e6rslu \u00e1 t\u00f6lfr\u00e6\u00f0inni og\u00a0\u00fatreikningunum fyrir stigskipta Bayes\u00edska l\u00edkani\u00f0, slembigangur af stigi h\u00e6rra en einn er\u00a0sko\u00f0a\u00f0ur sem l\u00edkindafr\u00e6\u00f0ilegt l\u00edkan fyrir mismuninn \u00e1 milli t\u00f6lulega hermisins og raunveruleikans, s\u00fdnd notkun \u00e1 fyrstu gr\u00e1\u00f0u hermum, og n\u00fd reiknisparandi n\u00e1lgun fyrir sennileikafalli\u00f0 er kynnt. \u00cd \u00feri\u00f0ju greininni er a\u00f0fer\u00f0afr\u00e6\u00f0i fyrstu tveggja greinanna beitt \u00e1 afkomug\u00f6gn og h\u00e6\u00f0arg\u00f6gn fr\u00e1 Langj\u00f6kli. Framlag ritger\u00f0arinnar felst \u00ed: (i) n\u00fdrri annarrar gr\u00e1\u00f0u mismunaa\u00f0fer\u00f0 til a\u00f0 leysa t\u00f6lulegu hlutaflei\u00f0uj\u00f6fnuna fyrir \u00feunnj\u00f6kla n\u00e1lgunina \u00ed tveimur r\u00famv\u00edddum og t\u00edma, (ii) notkun slembigangs til a\u00f0 l\u00fdsa mismuninum \u00e1 milli t\u00f6lulega hermisins og raunverulega ferlisins, (iii) n\u00fdrri reiknisparandi n\u00e1lgun fyrir sennileikafalli\u00f0, (iv) a\u00f0 beita n\u00fdju t\u00edma- og r\u00fdmish\u00e1\u00f0u t\u00f6lfr\u00e6\u00f0ilegu l\u00edkani fyrir j\u00f6kla vi\u00f0 greiningu gagna fr\u00e1 Langj\u00f6kli, einum af st\u00e6rstu j\u00f6klum \u00cdslands.<\/p>\n

Um doktorsefni\u00f0<\/strong><\/p>\n

\u00c1\u00f0ur en Giri h\u00f3f doktorsn\u00e1m vi\u00f0 H\u00e1sk\u00f3la \u00cdslands, lauk hann B.S. gr\u00e1\u00f0u \u00ed hagn\u00fdtri st\u00e6r\u00f0fr\u00e6\u00f0i fr\u00e1 Caltech og meistarapr\u00f3fi \u00ed t\u00f6lfr\u00e6\u00f0i fr\u00e1 Harvard. Eftir n\u00e1m vi\u00f0 Harvard vann Giri vi\u00f0 l\u00edfuppl\u00fdsingat\u00e6kni og gagnafr\u00e6\u00f0i. Giri hyggst vinna \u00e1fram \u00ed h\u00e1sk\u00f3laumhverfinu og halda \u00e1fram ranns\u00f3knum \u00e1 t\u00f6lfr\u00e6\u00f0i fyrir t\u00edma- og r\u00fdmish\u00e1\u00f0 g\u00f6gn, Bayes\u00edskum stigskiptum l\u00edk\u00f6num, og hagn\u00fdtingum fyrir jar\u00f0e\u00f0lisfr\u00e6\u00f0i.<\/p>\n

Vi\u00f0bur\u00f0ur \u00e1 Facebook<\/a><\/p>\n<\/div><\/div>","protected":false},"featured_media":1775,"template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_phd_date_start":"2019-08-30T13:00:00+00:00","_phd_date_end":"2019-08-30T15:00:00+00:00","_phd_location":"A\u00f0albygging H\u00e1t\u00ed\u00f0arsalur","_phd_admission":"A\u00f0gangur \u00f3keypis","_phd_thesis_title":"T\u00f6lfr\u00e6\u00f0il\u00edk\u00f6n fyrir j\u00f6klafr\u00e6\u00f0ig\u00f6gn","_phd_source_url":"https:\/\/gamli.hi.is\/vidburdir\/doktorsvorn_i_tolfraedi_giridhar_r_gopalan","_phd_source_node_id":"322707","_phd_source_type":"vidburdir","_phd_member_id":449,"footnotes":""},"phd_school":[101,93],"phd_discipline":[104],"class_list":["post-6078","phd_defence","type-phd_defence","status-publish","has-post-thumbnail","hentry","phd_school-raunvisindadeild","phd_school-verkfraedi-og-natturuvisindasvid","phd_discipline-phd-i-tolfraedi"],"_links":{"self":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_defence\/6078","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_defence"}],"about":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/types\/phd_defence"}],"version-history":[{"count":0,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_defence\/6078\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/media\/1775"}],"wp:attachment":[{"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/media?parent=6078"}],"wp:term":[{"taxonomy":"phd_school","embeddable":true,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_school?post=6078"},{"taxonomy":"phd_discipline","embeddable":true,"href":"https:\/\/phd.hi.is\/en\/wp-json\/wp\/v2\/phd_discipline?post=6078"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}