{"id":483,"date":"2016-12-10T09:00:00","date_gmt":"2016-12-10T08:00:00","guid":{"rendered":"https:\/\/smalltalks.eu\/blog\/?p=483"},"modified":"2026-09-26T13:52:23","modified_gmt":"2026-09-26T11:52:23","slug":"la-loi-de-bayes-en-deux-videos-monsieur-phi","status":"publish","type":"post","link":"https:\/\/smalltalks.eu\/blog\/2016\/12\/10\/la-loi-de-bayes-en-deux-videos-monsieur-phi\/","title":{"rendered":"La loi de Bayes, en deux vid\u00e9os (Monsieur Phi)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Dans sa s\u00e9rie <em>Argument frappant<\/em>, Monsieur Phi (Thibaut Giraud) consacre deux \u00e9pisodes \u00e0 la <strong>loi de Bayes<\/strong> : l&#8217;outil qui permet de mettre \u00e0 jour nos croyances face \u00e0 une nouvelle information\u2026 et que nous appliquons tr\u00e8s souvent de travers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Partie 1 : la formule<\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"LA LOI DE BAYES (1\/2) - Argument frappant #3\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/3FOrWMDL8CY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Une introduction claire au th\u00e9or\u00e8me de Bayes et aux probabilit\u00e9s conditionnelles : qu&#8217;est-ce que la probabilit\u00e9 de A <em>sachant<\/em> B, et comment la calculer ?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Erratum signal\u00e9 par l&#8217;auteur : \u00e0 8:32, sur la ligne P(B), les deux derniers A devraient \u00eatre surmont\u00e9s d&#8217;un trait (ils le sont, mais mal align\u00e9s) : il s&#8217;agit de l&#8217;\u00e9v\u00e9nement \u00ab non-A \u00bb.<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Partie 2 : les pi\u00e8ges<\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"LA LOI DE BAYES (2\/2) - Argument frappant #3\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/aU7EWwLtiOg?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Les principaux biais qui nous font mal appliquer la loi de Bayes, illustr\u00e9s d&#8217;exemples concrets (et de quelques schtroumpfs). L&#8217;objectif : devenir un peu plus bay\u00e9siens, \u00e7a ne fera pas de mal\u2026<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>La r\u00e8gle pratique \u00e0 retenir<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On part de la formule compl\u00e8te : <code>P(A|B) = P(B|A) \u00d7 P(A) \/ P(B)<\/code>, avec <code>P(B) = P(B|A) \u00d7 P(A) + P(B|non-A) \u00d7 P(non-A)<\/code>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Quand B se pr\u00e9sente comme une <em>preuve<\/em> de A (P(B|A) proche de 1), et que la probabilit\u00e9 a priori de A est faible, nettement plus faible que la probabilit\u00e9 de faux positif, la formule se simplifie :<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>P(A|B) \u2248 P(A) \/ P(B|non-A)<\/strong><br>probabilit\u00e9 a priori \u00f7 probabilit\u00e9 de faux positif<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Exemple :<\/strong> vous estimez a priori que A a 1 % de chances d&#8217;\u00eatre vrai. On vous apporte une information B cens\u00e9e le prouver, mais qui aurait encore 20 % de chances d&#8217;appara\u00eetre si A \u00e9tait faux. Alors la probabilit\u00e9 de A sachant B vaut environ 1 % \u00f7 20 %, soit 5 %. Autrement dit, la \u00ab preuve \u00bb a multipli\u00e9 la probabilit\u00e9 par 5\u2026 mais A reste tr\u00e8s improbable. Et cette estimation a m\u00eame tendance \u00e0 \u00eatre un peu trop haute.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Avec cette petite m\u00e9thode en t\u00eate, vous \u00e9viterez beaucoup de pi\u00e8ges bay\u00e9siens !<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Pour aller plus loin<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>En fran\u00e7ais : <a href=\"https:\/\/sciencetonnante.wordpress.com\/2012\/10\/08\/les-probabilites-conditionnelles-bayes-level-1\/\">les probabilit\u00e9s conditionnelles, sur le blog Science \u00e9tonnante<\/a> de David Louapre<\/li>\n\n\n\n<li>En anglais : <a href=\"https:\/\/www.lesswrong.com\/w\/bayes-rule?l=1zq\">Bayes&#8217; rule<\/a>, un guide tr\u00e8s complet (ex-Arbital, d\u00e9sormais sur LessWrong)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Vid\u00e9os de la cha\u00eene <a href=\"https:\/\/www.youtube.com\/@MonsieurPhi\">Monsieur Phi<\/a> (novembre et d\u00e9cembre 2016). Le blog : <a href=\"https:\/\/monsieurphi.com\">monsieurphi.com<\/a>, soutenir la cha\u00eene sur <a href=\"https:\/\/www.tipeee.com\/monsieurphi\">Tipeee<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dans sa s\u00e9rie Argument frappant, Monsieur Phi (Thibaut Giraud) consacre deux \u00e9pisodes \u00e0 la loi de Bayes : l&#8217;outil qui permet de mettre \u00e0 jour nos croyances face \u00e0 une nouvelle information\u2026 et que nous appliquons tr\u00e8s souvent de travers. Partie 1 : la formule Une introduction claire au th\u00e9or\u00e8me de Bayes et aux probabilit\u00e9s conditionnelles : qu&#8217;est-ce que la probabilit\u00e9 de A sachant B, et comment la calculer ? Erratum signal\u00e9 par l&#8217;auteur : \u00e0 8:32, sur la ligne&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/smalltalks.eu\/blog\/2016\/12\/10\/la-loi-de-bayes-en-deux-videos-monsieur-phi\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[115,167,166],"tags":[],"class_list":["post-483","post","type-post","status-publish","format-standard","hentry","category-monsieur-phi","category-theme-esprit-critique","category-thibaut-giraud"],"_links":{"self":[{"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/posts\/483","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/comments?post=483"}],"version-history":[{"count":1,"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/posts\/483\/revisions"}],"predecessor-version":[{"id":484,"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/posts\/483\/revisions\/484"}],"wp:attachment":[{"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/media?parent=483"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/categories?post=483"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/smalltalks.eu\/blog\/wp-json\/wp\/v2\/tags?post=483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}