{"id":1,"date":"2022-11-15T09:16:15","date_gmt":"2022-11-15T09:16:15","guid":{"rendered":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/?p=1"},"modified":"2023-01-13T15:12:36","modified_gmt":"2023-01-13T15:12:36","slug":"hello-world","status":"publish","type":"post","link":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/2022\/11\/15\/hello-world\/","title":{"rendered":"Gibbs Sampling"},"content":{"rendered":"\n<div class=\"wp-block-cover alignfull is-light has-parallax is-repeated\" style=\"min-height:359px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim\"><\/span><div role=\"img\" class=\"wp-block-cover__image-background wp-image-184 has-parallax is-repeated\" style=\"background-position:27% 50%;background-image:url(http:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-content\/uploads\/sites\/49\/2022\/11\/\u622a\u5c4f2023-01-13-14.16.51-e1673622506124.png)\"><\/div><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-large-font-size wp-block-paragraph\"><\/p>\n<\/div><\/div>\n\n\n\n<blockquote class=\"wp-block-quote is-style-default has-primary-color has-text-color has-system-serif-font-family has-small-font-size is-layout-flow wp-block-quote-is-layout-flow\" style=\"font-style:normal;font-weight:200\">\n<p class=\"has-system-serif-font-family has-small-font-size wp-block-paragraph\">All that mattered was that slowly, by degrees, by left and right then left and right again, he was guiding them towards the destination.<\/p>\n<cite><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hide_and_Seek_(Rankin_novel)\" data-type=\"URL\" data-id=\"https:\/\/en.wikipedia.org\/wiki\/Hide_and_Seek_(Rankin_novel)\" target=\"_blank\" rel=\"noreferrer noopener\">Ian Rankin, Hide and Seek<\/a><\/cite><\/blockquote>\n\n\n\n<p class=\"has-default-sans-font-family has-small-font-size wp-block-paragraph\">There exist a number of algorithms that can give us a proposal density for our Markov chain\u2019s dynamics.&nbsp;By using the Metropolis-Hastings algorithm we can obtain an&nbsp;acceptance probability for each proposed change of state within the&nbsp;Markov Chain. However, in some cases where we only know the conditional distribution between the variables, Gibbs sampling MCMC algorithm will be more efficient and helpful.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-content\/uploads\/sites\/49\/2022\/12\/\u622a\u5c4f2022-12-11-23.51.55-1024x690.png\" alt=\"\" class=\"wp-image-149\" width=\"459\" height=\"308\" srcset=\"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-content\/uploads\/sites\/49\/2022\/12\/\u622a\u5c4f2022-12-11-23.51.55-1024x690.png 1024w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-content\/uploads\/sites\/49\/2022\/12\/\u622a\u5c4f2022-12-11-23.51.55-300x202.png 300w, https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-content\/uploads\/sites\/49\/2022\/12\/\u622a\u5c4f2022-12-11-23.51.55.png 1246w\" sizes=\"auto, (max-width: 459px) 100vw, 459px\" \/><figcaption class=\"wp-element-caption\"><sub><sup>Gibbs Illustration<\/sup><\/sub><\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>All that mattered was that slowly, by degrees, by left and right then left and right again, he was guiding them towards the destination. Ian Rankin, Hide and Seek There exist a number of algorithms that can give us a proposal density for our Markov chain\u2019s dynamics.&nbsp;By using the Metropolis-Hastings algorithm we can obtain an&nbsp;acceptance [&hellip;]<\/p>\n","protected":false},"author":55,"featured_media":184,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[7,6,9],"class_list":["post-1","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","tag-bayesian-stats","tag-mcmc","tag-statistics"],"_links":{"self":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/posts\/1","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/users\/55"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/comments?post=1"}],"version-history":[{"count":10,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/posts\/1\/revisions"}],"predecessor-version":[{"id":219,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/posts\/1\/revisions\/219"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/media\/184"}],"wp:attachment":[{"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/media?parent=1"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/categories?post=1"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/wanchen-yue\/wp-json\/wp\/v2\/tags?post=1"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}