{"id":808,"date":"2025-12-23T10:35:19","date_gmt":"2025-12-23T10:35:19","guid":{"rendered":"https:\/\/alandix.com\/statistics\/?page_id=808"},"modified":"2025-12-23T10:41:47","modified_gmt":"2025-12-23T10:41:47","slug":"chapter-7","status":"publish","type":"page","link":"https:\/\/alandix.com\/statistics\/second-edition\/toc\/chapter-7\/","title":{"rendered":"Chapter 7: Bayesian methods."},"content":{"rendered":"<div class=\"embedurl\" data-url=\"https:\/\/alandix.com\/books\/hcistats\/content2e\/chaps\/chap-7.html\" ><!--  Chapter 7 Bayesian methods.  -->\n\n<script>\nvar chapnos = 7;\nvar json_url = \"https:\\\/\\\/alandix.com\\\/books\\\/hcistats\\\/content2e\\\/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;Using Bayes Theorem<\/dt><dd><dl>\n<dt>7.3.1&nbsp;&nbsp;Bayes for intelligent interfaces<\/dt>\n<dt>7.3.2&nbsp;&nbsp;Making decisions &ndash; base rates, risk and error costs<\/dt>\n<\/dl><\/dd>\n<dt>7.4&nbsp;&nbsp;Bayes as a statistical method<\/dt>\n<dt>7.5&nbsp;&nbsp;How do you get the prior?<\/dt>\n<dt>7.6&nbsp;&nbsp;Handling multiple evidence<\/dt>\n<dt>7.7&nbsp;&nbsp;Internecine warfare<\/dt>\n<\/dl><\/div>\n\n\n<h3> Glossary items referenced in this chapter <\/h3>\n<div class=\"toc\">\n<a href=\"https:\/\/alandix.com\/glossary\/hcistats\/artificial%20intelligence\">artificial intelligence<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/base%20rate\">base rate<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/base%20rate%20neglect\">base rate neglect<\/a><\/strong>, <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>, <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\/cognitive%20bias\">cognitive bias<\/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\/encoding%20as%20probability\">encoding (belief) as probability<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/error%20costs\">error costs<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/error%20rate\">error rate<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/fair%20coin\">fair coin<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/false%20negative\">false negative<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/false%20positive\">false positive<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/hypothesis%20testing\">hypothesis testing<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/independence\">independence<\/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\/optimal%20decision\">optimal decision<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/p-value\">p-value<\/a>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/population%20base%20rate\">population base rate<\/a><\/strong>, <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>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/presentation%20base%20rate\">presentation base rate<\/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>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/risk\">risk<\/a><\/strong>, <strong><a href=\"https:\/\/alandix.com\/glossary\/hcistats\/sample%20base%20rate\">sample base rate<\/a><\/strong>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/significance%20level\">significance level<\/a>, <a href=\"https:\/\/alandix.com\/glossary\/hcistats\/stakeholders\">stakeholders<\/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\/stratified%20sample\">stratified sample<\/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? 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