{"id":768,"date":"2025-12-23T10:11:38","date_gmt":"2025-12-23T10:11:38","guid":{"rendered":"https:\/\/alandix.com\/statistics\/?page_id=768"},"modified":"2025-12-23T10:15:42","modified_gmt":"2025-12-23T10:15:42","slug":"chapter-7","status":"publish","type":"page","link":"https:\/\/alandix.com\/statistics\/book\/toc\/chapter-7\/","title":{"rendered":"Chapter 7: Bayesian methods"},"content":{"rendered":"<div class=\"embedurl\" data-url=\"https:\/\/alandix.com\/books\/hcistats\/content1e\/chaps\/chap-7.html\" ><!--  Chapter 7 Bayesian methods   -->\n\n<script>\nvar chapnos = 7;\nvar json_url = \"https:\\\/\\\/alandix.com\\\/books\\\/hcistats\\\/content1e\\\/chaps\\\/chap-7.json\";\n<\/script>\n\n\n\n\n\n\n<h3> Contents <\/h3>\n<div class=\"toc\">\n<dl>\n<dt>7.1&nbsp;&nbsp;Detecting the Martian invasion <\/dt>\n<dt>7.2&nbsp;&nbsp;Quantifying prior belief <\/dt>\n<dt>7.3&nbsp;&nbsp;Bayes for intelligent interfaces <\/dt><dd><dl>\n<dt>7.3.1&nbsp;&nbsp;Bayes as a statistical method <\/dt>\n<\/dl><\/dd>\n<dt>7.4&nbsp;&nbsp;How do you get the prior? <\/dt>\n<dt>7.5&nbsp;&nbsp;Handling multiple evidence <\/dt>\n<dt>7.6&nbsp;&nbsp;Internecine warfare <\/dt>\n<\/dl><\/div>\n\n\n<h3> Glossary items referenced in this chapter <\/h3>\n<div class=\"toc\">\n<strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayes%20factor\">Bayes factor<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayes%20rule\">Bayes rule<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayesian%20analysis\">Bayesian reasoning<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayesian%20approach\">Bayesian reasoning<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayesian%20methods\">Bayesian reasoning<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayesian%20reasoning\">Bayesian reasoning<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/bayesian%20statistics\">Bayesian statistics<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/cauchy%20distribution\">Cauchy distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/coin%20tossing\">coin tossing<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/conditional%20probability\">conditional probability<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/confidence%20interval\">confidence interval<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/confirmation%20bias\">confirmation bias<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/default%20bayesian%20factors\">default Bayesian factors<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/encoded%20as%20a%20probability\">encoding (belief) as probability<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/error%20rate\">error rate<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/fair%20coin\">fair coin<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/hypothesis%20testing\">hypothesis testing<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/independent\">independent<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/independent%20evidence\">independent evidence<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/intelligent%20interfaces\">intelligent interfaces<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/kolomogrov%20laws\">Kolomogrov laws<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/likelihood\">likelihood<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/machine%20learning\">machine learning<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/mathematics\">mathematics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/normal%20distribution\">Normal distribution<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/null%20hypothesis\">null hypothesis<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/odds%20ratio\">odds ratio<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/p-value\">p-value<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/positive%20results\">positive results<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/posterior%20distribution\">posterior distribution<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/prior%20belief\">prior belief<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/prior%20distribution\">prior distribution<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/quantified%20belief\">quantified belief<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/random%20effect\">random effect<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/real%20world\">real world<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/representative%20sample\">representative sample<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/significance%20level\">significance level<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/statistical%20analysis\">statistical analysis<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/statistical%20inference\">statistical inference<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/statistical%20reasoning\">statistical reasoning<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/task%20completion%20time\">task completion time<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/the%20job%20of%20statistics\">the job of statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/traditional%20statistics\">traditional statistics<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/unbounded%20data\">unbounded data<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/uniform%20prior\">uniform prior<\/a><\/div>\n\n\n<!-- ?php\n\tif ( @$page['prolog_examples'] ):\n?>\n<h3> Prolog examples (from 1st ed.) <\/h3>\n<!-- ?php\n\techo $page['prolog_examples'];\n?>\n<!-- ?php\n\tendif; \/\/ @$page['prolog_examples']\n? -->\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":759,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"class_list":["post-768","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/768","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/comments?post=768"}],"version-history":[{"count":2,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/768\/revisions"}],"predecessor-version":[{"id":792,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/768\/revisions\/792"}],"up":[{"embeddable":true,"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/pages\/759"}],"wp:attachment":[{"href":"https:\/\/alandix.com\/statistics\/wp-json\/wp\/v2\/media?parent=768"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}