{"id":233355,"date":"2026-03-15T14:08:51","date_gmt":"2026-03-15T19:08:51","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2026\/03\/markov-chain-monte-carlo"},"modified":"2026-03-15T14:08:51","modified_gmt":"2026-03-15T19:08:51","slug":"markov-chain-monte-carlo","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2026\/03\/markov-chain-monte-carlo","title":{"rendered":"Markov chain Monte Carlo"},"content":{"rendered":"<p style=\"padding-right: 20px\"><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/markov-chain-monte-carlo2.jpg\"><\/a><\/p>\n<p>In <a href=\"https:\/\/en.wikipedia.org\/wiki\/Statistics\" title=\"Statistics\">statistics<\/a>, <b>Markov chain Monte Carlo<\/b> (<b>MCMC<\/b>) is a class of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Algorithm\" title=\"Algorithm\">algorithms<\/a> used to draw samples from a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Probability_distribution\" title=\"Probability distribution\">probability distribution<\/a>. Given a probability distribution, one can construct a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Markov_chain\" title=\"Markov chain\">Markov chain<\/a> whose elements\u2019 distribution approximates it \u2013 that is, the Markov chain\u2019s <a href=\"https:\/\/en.wikipedia.org\/wiki\/Discrete-time_Markov_chain#Stationary_distributions\" title=\"Discrete-time Markov chain\">equilibrium distribution<\/a> matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution.<\/p>\n<p>Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too high <a href=\"https:\/\/en.wikipedia.org\/wiki\/N-dimensional_space\" title=\"N-dimensional space\">dimensional<\/a> to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Metropolis%E2%80%93Hastings_algorithm\" title=\"Metropolis&ndash;Hastings algorithm\">Metropolis\u2013Hastings algorithm<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements\u2019 distribution approximates it \u2013 that is, the Markov chain\u2019s equilibrium distribution matches the target distribution. The more steps that are included, the more [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41],"tags":[],"class_list":["post-233355","post","type-post","status-publish","format-standard","hentry","category-information-science"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/233355","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=233355"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/233355\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=233355"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=233355"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=233355"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}