[{"data":1,"prerenderedAt":1342},["ShallowReactive",2],{"article-alternates":3,"article-\u002Fde\u002Fmarketing\u002Fbayesian-ab-test-h":13},{"i18nKey":4,"paths":5},"marketing-002-2026-05",{"de":6,"en":7,"es":8,"fr":9,"it":10,"ru":11,"tr":12},"\u002Fde\u002Fmarketing\u002Fbayesian-ab-test-h","\u002Fen\u002Fmarketing\u002Fbayesian-ab-test-hizli-karar-verme","\u002Fes\u002Fmarketing\u002Fbayesian-ab-test-hizli-karar","\u002Ffr\u002Fmarketing\u002Fbayesian-ab-test-ile-hizli-karar-verme","\u002Fit\u002Fmarketing\u002Ftest-bayesian-decisione-rapida","\u002Fru\u002Fmarketing\u002Fbayesian-ab-testy-dlya-bystrogo-prinyatiya-reshenij","\u002Ftr\u002Fmarketing\u002Fbayesian-a-b-test-ile-hizli-karar-verme",{"_path":6,"_dir":14,"_draft":15,"_partial":15,"_locale":16,"title":17,"description":18,"publishedAt":19,"modifiedAt":19,"category":14,"i18nKey":4,"tags":20,"readingTime":26,"author":27,"body":28,"_type":1336,"_id":1337,"_source":1338,"_file":1339,"_stem":1340,"_extension":1341},"marketing",false,"","Bayesian A\u002FB-Test für schnelle Entscheidungen","Überwinde die Grenzen von Frequentist-Tests. Sequential Testing, dynamische Sample-Größe und Bayesian A\u002FB-Test ermöglichen Entscheidungen in der Performance-Marketing innerhalb von Tagen statt Wochen.","2026-05-09",[21,22,23,24,25],"ab-testing","bayesian-statistik","conversion-optimierung","performance-marketing","sequential-testing",9,"Roibase",{"type":29,"children":30,"toc":1324},"root",[31,39,46,51,56,61,67,72,77,82,87,94,681,687,692,712,717,825,830,835,841,846,851,867,873,1236,1241,1247,1252,1257,1262,1267,1273,1294,1299,1304,1309,1313,1318],{"type":32,"tag":33,"props":34,"children":35},"element","p",{},[36],{"type":37,"value":38},"text","Im Performance-Marketing ist Testgeschwindigkeit ein Wettbewerbsvorteil. Bei klassischem Frequentist A\u002FB-Testing wartest du zwei Wochen auf das Confidence Interval, während dein Kampagnen-Budget täglich sinkt. Der Bayesian-Ansatz liefert dir täglich eine aktualisierte Posterior-Verteilung — schon vor Testende kannst du sagen: „Variante B gewinnt mit 73% Wahrscheinlichkeit.\" Dieser Artikel erklärt die mechanik von Bayesian A\u002FB-Testing, Sequential Decision Rules und dynamische Sample-Size-Berechnung. Du ersetzt die Fixed-Horizon-Zwangslage des Frequentist-Verfahrens durch kontinuierliche Entscheidungsaktualisierung im täglichen Datenstrom.",{"type":32,"tag":40,"props":41,"children":43},"h2",{"id":42},"das-fixed-horizon-problem-des-frequentist-tests",[44],{"type":37,"value":45},"Das Fixed-Horizon-Problem des Frequentist-Tests",{"type":32,"tag":33,"props":47,"children":48},{},[49],{"type":37,"value":50},"Das klassische A\u002FB-Testing basiert auf p-Wert und fester Sample-Größe. Du startest mit dem Plan „n=5.000 Visitor benötigt, dauert 14 Tage\" und verpflichtest dich, bis zum 14. Tag nicht zu entscheiden. In dieser Zeit sendest du weiterhin Traffic zur schlechteren Variante — auch wenn die Conversion Rate 2 Punkte niedriger ist, musst du bis zum Test-Abschluss warten. Stoppt man früher, infliert sich der Type-I-Error, Multiple Testing Problem entsteht.",{"type":32,"tag":33,"props":52,"children":53},{},[54],{"type":37,"value":55},"In der Frequentist-Logik liefert p \u003C 0,05 statistische Signifikanz, aber in der Praxis gibt es viele „signifikant, aber praktisch wertlos\"-Szenarien. Ein Lift von 0,5% kann statistisch signifikant sein (wegen großer Sample-Größe), aber geschäftlich irrelevant. Man muss Confidence Interval und Effect Size getrennt bewerten — der Frequentist-Rahmen zeigt das nicht automatisch.",{"type":32,"tag":33,"props":57,"children":58},{},[59],{"type":37,"value":60},"Eine weitere Einschränkung: Sequential Monitoring ist unmöglich. Du berechnest die Sample-Größe vor dem Test, wartest dann darauf, die Sample zu erreichen. Auch wenn eine Variante offensichtlich gewinnt, musst du die Testplanung einhalten, um p-Value-Gültigkeit zu bewahren. Sonst machst du „Peeking\" und ungültigst den p-Wert.",{"type":32,"tag":40,"props":62,"children":64},{"id":63},"bayesian-test-aktuelle-posterior-verteilung",[65],{"type":37,"value":66},"Bayesian-Test: Aktuelle Posterior-Verteilung",{"type":32,"tag":33,"props":68,"children":69},{},[70],{"type":37,"value":71},"Der Bayesian-Ansatz funktioniert nach Prior-Belief + Daten = Posterior-Logik. Vor dem Test definierst du für jede Variante eine Prior-Verteilung der Conversion Rate (meist uninformativ Beta(1,1) oder informativ aus historischen Daten). Mit jedem Besucher wird die Posterior durch das Bayes-Theorem aktualisiert. Bei Besucher 100 hat die Posterior eine bestimmte Form, bei 200 eine andere — kontinuierliche Aktualisierung.",{"type":32,"tag":33,"props":73,"children":74},{},[75],{"type":37,"value":76},"Die Posterior-Verteilung zeigt genau „die Wahrscheinlichkeitsdichte der wahren Conversion Rate dieser Variante\". Beispiel: Beta(25, 75) bedeutet, dass Conversion Rates zwischen 20% und 30% hohe Wahrscheinlichkeitsdichte haben. Vergleichst du die Posterior beider Varianten, kannst du „Wahrscheinlichkeit, dass B besser als A ist\" berechnen — diese P(B > A) Formel ist in der Bayesian-Welt natürlich.",{"type":32,"tag":33,"props":78,"children":79},{},[80],{"type":37,"value":81},"Sequential Testing im Bayesian-Stil: Tägliche Posterior-Aktualisierung, stoppe den Test wenn P(B > A) > 0,95. Dieser Schwellenwert ist deine Risikotoleranz — du könntest auch 0,90 oder 0,99 verwenden. Im Frequentist-Test existiert solch ein Mechanismus nicht; die einzige Entscheidungsregel ist Fixed Horizon. Im Bayesian-Ansatz kannst du jederzeit entscheiden, weil die Posterior-Verteilung vollständige Information liefert.",{"type":32,"tag":33,"props":83,"children":84},{},[85],{"type":37,"value":86},"Im Bayesian-Test gibt es keinen p-Wert. Stattdessen Metriken wie Probability of Superiority (P(B > A)), Expected Loss (erwarteter Lift-Verlust wenn du A wählst), Credible Interval (95%-Bereich der Posterior). Diese sind praktisch interpretierbarer — du sagst: „Variante B gewinnt mit 85% Wahrscheinlichkeit und bringt im Falle des Gewinns durchschnittlich 2,3% Lift.\"",{"type":32,"tag":88,"props":89,"children":91},"h3",{"id":90},"code-posterior-aktualisierung",[92],{"type":37,"value":93},"Code: Posterior-Aktualisierung",{"type":32,"tag":95,"props":96,"children":100},"pre",{"className":97,"code":98,"language":99,"meta":16,"style":16},"language-python shiki shiki-themes github-dark","import numpy as np\nfrom scipy.stats import beta\n\n# Prior: Beta(1,1) = uniform\nprior_alpha, prior_beta = 1, 1\n\n# Eingehende Daten: Variante A, 50 Conversions, 200 Visits\nconversions_A = 50\nvisits_A = 200\nfailures_A = visits_A - conversions_A\n\n# Posterior: Beta(alpha + conversions, beta + failures)\npost_alpha_A = prior_alpha + conversions_A\npost_beta_A = prior_beta + failures_A\n\n# Sample aus Posterior-Verteilung ziehen\nsamples_A = beta.rvs(post_alpha_A, post_beta_A, size=10000)\n\n# Dasselbe für Variante B\nconversions_B = 60\nvisits_B = 200\nfailures_B = visits_B - conversions_B\npost_alpha_B = prior_alpha + conversions_B\npost_beta_B = prior_beta + failures_B\nsamples_B = beta.rvs(post_alpha_B, post_beta_B, size=10000)\n\n# P(B > A) berechnen\nprob_B_wins = (samples_B > samples_A).mean()\nprint(f\"P(B > A): {prob_B_wins:.2%}\")  # Beispiel: 0.82 = B gewinnt mit 82% Wahrscheinlichkeit\n","python",[101],{"type":32,"tag":102,"props":103,"children":104},"code",{"__ignoreMap":16},[105,133,156,166,176,206,214,223,241,258,286,294,303,330,357,365,374,412,420,429,447,464,491,516,542,576,584,593,621],{"type":32,"tag":106,"props":107,"children":110},"span",{"class":108,"line":109},"line",1,[111,117,123,128],{"type":32,"tag":106,"props":112,"children":114},{"style":113},"--shiki-default:#F97583",[115],{"type":37,"value":116},"import",{"type":32,"tag":106,"props":118,"children":120},{"style":119},"--shiki-default:#E1E4E8",[121],{"type":37,"value":122}," numpy ",{"type":32,"tag":106,"props":124,"children":125},{"style":113},[126],{"type":37,"value":127},"as",{"type":32,"tag":106,"props":129,"children":130},{"style":119},[131],{"type":37,"value":132}," np\n",{"type":32,"tag":106,"props":134,"children":136},{"class":108,"line":135},2,[137,142,147,151],{"type":32,"tag":106,"props":138,"children":139},{"style":113},[140],{"type":37,"value":141},"from",{"type":32,"tag":106,"props":143,"children":144},{"style":119},[145],{"type":37,"value":146}," scipy.stats ",{"type":32,"tag":106,"props":148,"children":149},{"style":113},[150],{"type":37,"value":116},{"type":32,"tag":106,"props":152,"children":153},{"style":119},[154],{"type":37,"value":155}," 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",{"type":32,"tag":106,"props":202,"children":203},{"style":192},[204],{"type":37,"value":205},"1\n",{"type":32,"tag":106,"props":207,"children":209},{"class":108,"line":208},6,[210],{"type":32,"tag":106,"props":211,"children":212},{"emptyLinePlaceholder":162},[213],{"type":37,"value":165},{"type":32,"tag":106,"props":215,"children":217},{"class":108,"line":216},7,[218],{"type":32,"tag":106,"props":219,"children":220},{"style":172},[221],{"type":37,"value":222},"# Eingehende Daten: Variante A, 50 Conversions, 200 Visits\n",{"type":32,"tag":106,"props":224,"children":226},{"class":108,"line":225},8,[227,232,236],{"type":32,"tag":106,"props":228,"children":229},{"style":119},[230],{"type":37,"value":231},"conversions_A ",{"type":32,"tag":106,"props":233,"children":234},{"style":113},[235],{"type":37,"value":189},{"type":32,"tag":106,"props":237,"children":238},{"style":192},[239],{"type":37,"value":240}," 50\n",{"type":32,"tag":106,"props":242,"children":243},{"class":108,"line":26},[244,249,253],{"type":32,"tag":106,"props":245,"children":246},{"style":119},[247],{"type":37,"value":248},"visits_A ",{"type":32,"tag":106,"props":250,"children":251},{"style":113},[252],{"type":37,"value":189},{"type":32,"tag":106,"props":254,"children":255},{"style":192},[256],{"type":37,"value":257}," 200\n",{"type":32,"tag":106,"props":259,"children":261},{"class":108,"line":260},10,[262,267,271,276,281],{"type":32,"tag":106,"props":263,"children":264},{"style":119},[265],{"type":37,"value":266},"failures_A ",{"type":32,"tag":106,"props":268,"children":269},{"style":113},[270],{"type":37,"value":189},{"type":32,"tag":106,"props":272,"children":273},{"style":119},[274],{"type":37,"value":275}," visits_A ",{"type":32,"tag":106,"props":277,"children":278},{"style":113},[279],{"type":37,"value":280},"-",{"type":32,"tag":106,"props":282,"children":283},{"style":119},[284],{"type":37,"value":285}," conversions_A\n",{"type":32,"tag":106,"props":287,"children":289},{"class":108,"line":288},11,[290],{"type":32,"tag":106,"props":291,"children":292},{"emptyLinePlaceholder":162},[293],{"type":37,"value":165},{"type":32,"tag":106,"props":295,"children":297},{"class":108,"line":296},12,[298],{"type":32,"tag":106,"props":299,"children":300},{"style":172},[301],{"type":37,"value":302},"# Posterior: Beta(alpha + conversions, beta + failures)\n",{"type":32,"tag":106,"props":304,"children":306},{"class":108,"line":305},13,[307,312,316,321,326],{"type":32,"tag":106,"props":308,"children":309},{"style":119},[310],{"type":37,"value":311},"post_alpha_A ",{"type":32,"tag":106,"props":313,"children":314},{"style":113},[315],{"type":37,"value":189},{"type":32,"tag":106,"props":317,"children":318},{"style":119},[319],{"type":37,"value":320}," prior_alpha ",{"type":32,"tag":106,"props":322,"children":323},{"style":113},[324],{"type":37,"value":325},"+",{"type":32,"tag":106,"props":327,"children":328},{"style":119},[329],{"type":37,"value":285},{"type":32,"tag":106,"props":331,"children":333},{"class":108,"line":332},14,[334,339,343,348,352],{"type":32,"tag":106,"props":335,"children":336},{"style":119},[337],{"type":37,"value":338},"post_beta_A ",{"type":32,"tag":106,"props":340,"children":341},{"style":113},[342],{"type":37,"value":189},{"type":32,"tag":106,"props":344,"children":345},{"style":119},[346],{"type":37,"value":347}," prior_beta ",{"type":32,"tag":106,"props":349,"children":350},{"style":113},[351],{"type":37,"value":325},{"type":32,"tag":106,"props":353,"children":354},{"style":119},[355],{"type":37,"value":356}," failures_A\n",{"type":32,"tag":106,"props":358,"children":360},{"class":108,"line":359},15,[361],{"type":32,"tag":106,"props":362,"children":363},{"emptyLinePlaceholder":162},[364],{"type":37,"value":165},{"type":32,"tag":106,"props":366,"children":368},{"class":108,"line":367},16,[369],{"type":32,"tag":106,"props":370,"children":371},{"style":172},[372],{"type":37,"value":373},"# Sample aus Posterior-Verteilung ziehen\n",{"type":32,"tag":106,"props":375,"children":377},{"class":108,"line":376},17,[378,383,387,392,398,402,407],{"type":32,"tag":106,"props":379,"children":380},{"style":119},[381],{"type":37,"value":382},"samples_A ",{"type":32,"tag":106,"props":384,"children":385},{"style":113},[386],{"type":37,"value":189},{"type":32,"tag":106,"props":388,"children":389},{"style":119},[390],{"type":37,"value":391}," beta.rvs(post_alpha_A, post_beta_A, ",{"type":32,"tag":106,"props":393,"children":395},{"style":394},"--shiki-default:#FFAB70",[396],{"type":37,"value":397},"size",{"type":32,"tag":106,"props":399,"children":400},{"style":113},[401],{"type":37,"value":189},{"type":32,"tag":106,"props":403,"children":404},{"style":192},[405],{"type":37,"value":406},"10000",{"type":32,"tag":106,"props":408,"children":409},{"style":119},[410],{"type":37,"value":411},")\n",{"type":32,"tag":106,"props":413,"children":415},{"class":108,"line":414},18,[416],{"type":32,"tag":106,"props":417,"children":418},{"emptyLinePlaceholder":162},[419],{"type":37,"value":165},{"type":32,"tag":106,"props":421,"children":423},{"class":108,"line":422},19,[424],{"type":32,"tag":106,"props":425,"children":426},{"style":172},[427],{"type":37,"value":428},"# Dasselbe für Variante B\n",{"type":32,"tag":106,"props":430,"children":432},{"class":108,"line":431},20,[433,438,442],{"type":32,"tag":106,"props":434,"children":435},{"style":119},[436],{"type":37,"value":437},"conversions_B ",{"type":32,"tag":106,"props":439,"children":440},{"style":113},[441],{"type":37,"value":189},{"type":32,"tag":106,"props":443,"children":444},{"style":192},[445],{"type":37,"value":446}," 60\n",{"type":32,"tag":106,"props":448,"children":450},{"class":108,"line":449},21,[451,456,460],{"type":32,"tag":106,"props":452,"children":453},{"style":119},[454],{"type":37,"value":455},"visits_B ",{"type":32,"tag":106,"props":457,"children":458},{"style":113},[459],{"type":37,"value":189},{"type":32,"tag":106,"props":461,"children":462},{"style":192},[463],{"type":37,"value":257},{"type":32,"tag":106,"props":465,"children":467},{"class":108,"line":466},22,[468,473,477,482,486],{"type":32,"tag":106,"props":469,"children":470},{"style":119},[471],{"type":37,"value":472},"failures_B 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",{"type":32,"tag":106,"props":501,"children":502},{"style":113},[503],{"type":37,"value":189},{"type":32,"tag":106,"props":505,"children":506},{"style":119},[507],{"type":37,"value":320},{"type":32,"tag":106,"props":509,"children":510},{"style":113},[511],{"type":37,"value":325},{"type":32,"tag":106,"props":513,"children":514},{"style":119},[515],{"type":37,"value":490},{"type":32,"tag":106,"props":517,"children":519},{"class":108,"line":518},24,[520,525,529,533,537],{"type":32,"tag":106,"props":521,"children":522},{"style":119},[523],{"type":37,"value":524},"post_beta_B ",{"type":32,"tag":106,"props":526,"children":527},{"style":113},[528],{"type":37,"value":189},{"type":32,"tag":106,"props":530,"children":531},{"style":119},[532],{"type":37,"value":347},{"type":32,"tag":106,"props":534,"children":535},{"style":113},[536],{"type":37,"value":325},{"type":32,"tag":106,"props":538,"children":539},{"style":119},[540],{"type":37,"value":541}," 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",{"type":32,"tag":106,"props":561,"children":562},{"style":394},[563],{"type":37,"value":397},{"type":32,"tag":106,"props":565,"children":566},{"style":113},[567],{"type":37,"value":189},{"type":32,"tag":106,"props":569,"children":570},{"style":192},[571],{"type":37,"value":406},{"type":32,"tag":106,"props":573,"children":574},{"style":119},[575],{"type":37,"value":411},{"type":32,"tag":106,"props":577,"children":579},{"class":108,"line":578},26,[580],{"type":32,"tag":106,"props":581,"children":582},{"emptyLinePlaceholder":162},[583],{"type":37,"value":165},{"type":32,"tag":106,"props":585,"children":587},{"class":108,"line":586},27,[588],{"type":32,"tag":106,"props":589,"children":590},{"style":172},[591],{"type":37,"value":592},"# P(B > A) berechnen\n",{"type":32,"tag":106,"props":594,"children":596},{"class":108,"line":595},28,[597,602,606,611,616],{"type":32,"tag":106,"props":598,"children":599},{"style":119},[600],{"type":37,"value":601},"prob_B_wins ",{"type":32,"tag":106,"props":603,"children":604},{"style":113},[605],{"type":37,"value":189},{"type":32,"tag":106,"props":607,"children":608},{"style":119},[609],{"type":37,"value":610}," (samples_B ",{"type":32,"tag":106,"props":612,"children":613},{"style":113},[614],{"type":37,"value":615},">",{"type":32,"tag":106,"props":617,"children":618},{"style":119},[619],{"type":37,"value":620}," samples_A).mean()\n",{"type":32,"tag":106,"props":622,"children":624},{"class":108,"line":623},29,[625,630,635,640,646,651,656,661,666,671,676],{"type":32,"tag":106,"props":626,"children":627},{"style":192},[628],{"type":37,"value":629},"print",{"type":32,"tag":106,"props":631,"children":632},{"style":119},[633],{"type":37,"value":634},"(",{"type":32,"tag":106,"props":636,"children":637},{"style":113},[638],{"type":37,"value":639},"f",{"type":32,"tag":106,"props":641,"children":643},{"style":642},"--shiki-default:#9ECBFF",[644],{"type":37,"value":645},"\"P(B > A): ",{"type":32,"tag":106,"props":647,"children":648},{"style":192},[649],{"type":37,"value":650},"{",{"type":32,"tag":106,"props":652,"children":653},{"style":119},[654],{"type":37,"value":655},"prob_B_wins",{"type":32,"tag":106,"props":657,"children":658},{"style":113},[659],{"type":37,"value":660},":.2%",{"type":32,"tag":106,"props":662,"children":663},{"style":192},[664],{"type":37,"value":665},"}",{"type":32,"tag":106,"props":667,"children":668},{"style":642},[669],{"type":37,"value":670},"\"",{"type":32,"tag":106,"props":672,"children":673},{"style":119},[674],{"type":37,"value":675},")  ",{"type":32,"tag":106,"props":677,"children":678},{"style":172},[679],{"type":37,"value":680},"# Beispiel: 0.82 = B gewinnt mit 82% Wahrscheinlichkeit\n",{"type":32,"tag":40,"props":682,"children":684},{"id":683},"dynamische-sample-größe-und-early-stopping",[685],{"type":37,"value":686},"Dynamische Sample-Größe und Early Stopping",{"type":32,"tag":33,"props":688,"children":689},{},[690],{"type":37,"value":691},"Im Bayesian-Test ist die Sample-Größe nicht festgelegt. Du kannst eine Mindestgrenze setzen (z.B. „mindestens 1.000 Visitor\", damit Posterior nicht zu breit wird), aber die Obergrenze ist dynamisch. Erreichst du P(B > A) > 0,95, stoppt der Test — das könnte beim 500. oder beim 5.000. Besucher sein.",{"type":32,"tag":33,"props":693,"children":694},{},[695,697,703,705,710],{"type":37,"value":696},"Expected Loss ist hervorragend für frühe Entscheidungen. Formel: ",{"type":32,"tag":102,"props":698,"children":700},{"className":699},[],[701],{"type":37,"value":702},"E[Loss] = E[max(0, CR_winner - CR_chosen)]",{"type":37,"value":704},". Das heißt: wenn du A wählst, aber B ist besser, wie viel Lift verlierst du im Erwartungswert. Setze einen Loss-Schwellenwert, z.B. „E",{"type":32,"tag":106,"props":706,"children":707},{},[708],{"type":37,"value":709},"Loss",{"type":37,"value":711}," \u003C 0,5%\", dann hast du die Garantie „im schlimmsten Fall verliere ich 0,5% Lift\" und kannst testen stoppen. Diese Metrik macht risikoaverse Entscheidung leicht.",{"type":32,"tag":33,"props":713,"children":714},{},[715],{"type":37,"value":716},"Beispiel Sequential Stopping Rule:",{"type":32,"tag":718,"props":719,"children":720},"table",{},[721,745],{"type":32,"tag":722,"props":723,"children":724},"thead",{},[725],{"type":32,"tag":726,"props":727,"children":728},"tr",{},[729,735,740],{"type":32,"tag":730,"props":731,"children":732},"th",{},[733],{"type":37,"value":734},"Metrik",{"type":32,"tag":730,"props":736,"children":737},{},[738],{"type":37,"value":739},"Schwellenwert",{"type":32,"tag":730,"props":741,"children":742},{},[743],{"type":37,"value":744},"Aktion",{"type":32,"tag":746,"props":747,"children":748},"tbody",{},[749,768,785,807],{"type":32,"tag":726,"props":750,"children":751},{},[752,758,763],{"type":32,"tag":753,"props":754,"children":755},"td",{},[756],{"type":37,"value":757},"P(B > A)",{"type":32,"tag":753,"props":759,"children":760},{},[761],{"type":37,"value":762},"> 0,95",{"type":32,"tag":753,"props":764,"children":765},{},[766],{"type":37,"value":767},"B als Winner deklarieren",{"type":32,"tag":726,"props":769,"children":770},{},[771,776,780],{"type":32,"tag":753,"props":772,"children":773},{},[774],{"type":37,"value":775},"P(A > B)",{"type":32,"tag":753,"props":777,"children":778},{},[779],{"type":37,"value":762},{"type":32,"tag":753,"props":781,"children":782},{},[783],{"type":37,"value":784},"A als Winner deklarieren",{"type":32,"tag":726,"props":786,"children":787},{},[788,797,802],{"type":32,"tag":753,"props":789,"children":790},{},[791,793],{"type":37,"value":792},"E",{"type":32,"tag":106,"props":794,"children":795},{},[796],{"type":37,"value":709},{"type":32,"tag":753,"props":798,"children":799},{},[800],{"type":37,"value":801},"\u003C 0,005",{"type":32,"tag":753,"props":803,"children":804},{},[805],{"type":37,"value":806},"Unterlegene Variante schließen",{"type":32,"tag":726,"props":808,"children":809},{},[810,815,820],{"type":32,"tag":753,"props":811,"children":812},{},[813],{"type":37,"value":814},"Mindest-Visits",{"type":32,"tag":753,"props":816,"children":817},{},[818],{"type":37,"value":819},"\u003C 1.000",{"type":32,"tag":753,"props":821,"children":822},{},[823],{"type":37,"value":824},"Noch keine Entscheidung",{"type":32,"tag":33,"props":826,"children":827},{},[828],{"type":37,"value":829},"Mit diesen Regeln sinkt die Test-Dauer durchschnittlich um 30-40% (laut Google Optimize und VWO Bayesian-Motor-Daten). Bei großem Effect Size kannst du in 3 Tagen mit 95% Confidence entscheiden — frequentist brauchte 14 Tage.",{"type":32,"tag":33,"props":831,"children":832},{},[833],{"type":37,"value":834},"Unterschied zu Multi-Armed Bandits: Bayesian A\u002FB-Test führt noch kein Exploration-Exploitation Tradeoff durch, sondern nur Posterior-Aktualisierung und Stopping Rule. Bandit-Algorithmen (z.B. Thompson Sampling) optimieren die Traffic-Verteilung dynamisch (mehr Traffic zur Gewinner-Variante). Bayesian-Test behält feste Split (50\u002F50) bei, stoppt aber schneller. Bandit aggressiver — jeder Impression ändert die Verteilung, Bayesian konservativer — Split fix, Entscheidung schnell.",{"type":32,"tag":40,"props":836,"children":838},{"id":837},"informative-prior-und-incrementality-tests",[839],{"type":37,"value":840},"Informative Prior und Incrementality Tests",{"type":32,"tag":33,"props":842,"children":843},{},[844],{"type":37,"value":845},"Prior-Wahl ist der kritischste Punkt im Bayesian-Test. Uninformative Prior (Beta(1,1)) ignoriert Vorwissen, Posterior ist rein datengetrieben. Informative Prior kommt aus historischen Test-Daten oder Segment-Baselines. Beispiel: mobile Segmente hatten in 50 vergangenen Tests durchschnittlich 12% Conversion, also Beta(60, 440) Prior (approximiert 12% Mean, aber mit Streuung). Dieser Prior gibt der neuen Test-Posterior einen „vernünftigen Startpunkt\".",{"type":32,"tag":33,"props":847,"children":848},{},[849],{"type":37,"value":850},"Vorteil informativ Prior: Sample-Size-Anforderung sinkt, weil Posterior-Update nicht bei Null startet. Nachteil: Falscher Prior erzeugt Bias. Wenn sich das Segment geändert hat oder Saisonalität wirkt, führt alter Prior zu Fehler. Daher: Prior-Sensitivitätsanalyse — teste mit verschiedenen Priors und prüfe ob Ergebnisse ändern.",{"type":32,"tag":33,"props":852,"children":853},{},[854,856,865],{"type":37,"value":855},"Im ",{"type":32,"tag":857,"props":858,"children":862},"a",{"href":859,"rel":860},"https:\u002F\u002Fwww.roibase.com.tr\u002Fde\u002Fcro",[861],"nofollow",[863],{"type":37,"value":864},"Conversion Rate Optimierung",{"type":37,"value":866},"-Prozess vereinfacht Bayesian-Test Incrementality-Messung. Incrementality braucht Holdout-Gruppe oder Geo-Split. Vergleichst du mit Bayesian Holdout-Posterior mit Test-Posterior, erhältst du Lift-Distribution. Statt klassischem t-Test berechnest du P(Lift > 0) — interpretierbarer: „neue Kampagne hat 78% Wahrscheinlichkeit für Incrementality, erwarteter Lift 1,2–2,8%\".",{"type":32,"tag":88,"props":868,"children":870},{"id":869},"prior-wahl-vergleich",[871],{"type":37,"value":872},"Prior-Wahl Vergleich",{"type":32,"tag":95,"props":874,"children":876},{"className":97,"code":875,"language":99,"meta":16,"style":16},"# Uninformative Prior\nprior_uninf = beta(1, 1)\n\n# Informative Prior: historisch 12% conversion, n=500 sample\n# Beta mean = alpha \u002F (alpha + beta) → 60\u002F500 = 0.12\nprior_inf = beta(60, 440)\n\n# Posterior mit 20 Conversions, 100 Visits\nconversions, visits = 20, 100\npost_uninf = beta(1 + conversions, 1 + (visits - conversions))\npost_inf = beta(60 + conversions, 440 + (visits - conversions))\n\n# Posterior-Mittelwerte\nprint(f\"Uninformative posterior mean: {post_uninf.mean():.2%}\")  # ~20%\nprint(f\"Informative posterior mean: {post_inf.mean():.2%}\")      # ~13,3%\n",[877],{"type":32,"tag":102,"props":878,"children":879},{"__ignoreMap":16},[880,888,922,929,937,945,979,986,994,1020,1072,1120,1127,1135,1185],{"type":32,"tag":106,"props":881,"children":882},{"class":108,"line":109},[883],{"type":32,"tag":106,"props":884,"children":885},{"style":172},[886],{"type":37,"value":887},"# Uninformative Prior\n",{"type":32,"tag":106,"props":889,"children":890},{"class":108,"line":135},[891,896,900,905,910,914,918],{"type":32,"tag":106,"props":892,"children":893},{"style":119},[894],{"type":37,"value":895},"prior_uninf ",{"type":32,"tag":106,"props":897,"children":898},{"style":113},[899],{"type":37,"value":189},{"type":32,"tag":106,"props":901,"children":902},{"style":119},[903],{"type":37,"value":904}," 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alpha \u002F (alpha + beta) → 60\u002F500 = 0.12\n",{"type":32,"tag":106,"props":946,"children":947},{"class":108,"line":208},[948,953,957,961,966,970,975],{"type":32,"tag":106,"props":949,"children":950},{"style":119},[951],{"type":37,"value":952},"prior_inf 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Vorwissen.",{"type":32,"tag":40,"props":1242,"children":1244},{"id":1243},"tradeoff-bayesian-vs-frequentist-vs-bandit",[1245],{"type":37,"value":1246},"Tradeoff: Bayesian vs. Frequentist vs. Bandit",{"type":32,"tag":33,"props":1248,"children":1249},{},[1250],{"type":37,"value":1251},"Bayesian-Test ist nicht überall optimal. Frequentist-Tests sind in regulierten Umgebungen (besonders Medizin\u002FFinanzen) bevorzugt, weil p-Wert-Standard existiert, Peer-Review darauf beruht. Bayesian Prior-Wahl wirkt subjektiv. Wenn Regulierung p-Wert verlangt und Test-Dauer fix ist (z.B. 30 Tage Pflicht), ist Frequentist sinnvoll.",{"type":32,"tag":33,"props":1253,"children":1254},{},[1255],{"type":37,"value":1256},"Bandit-Algorithmen (Thompson Sampling, UCB) optimieren Exploration-Exploitation automatisch, verteilen Traffic dynamisch neu. Bei langen Tests (3+ Wochen) erzielt Bandit bessere Performance als Bayesian, weil unterlegene Varianten weniger Traffic bekommen. Bei kurzen Tests (1-2 Wochen) reicht Bayesian A\u002FB — Bandits Regret-Minimierung macht kurzzeitig keinen Unterschied.",{"type":32,"tag":33,"props":1258,"children":1259},{},[1260],{"type":37,"value":1261},"Ist Sample-Größe sehr klein (100 Besucher\u002FTag), versagen sowohl Bayesian als auch Frequentist. Posterior wird so breit, dass P(B > A) nie 95% erreicht. Dann: Micro-Conversions testen (Click, Add-to-Cart) oder Geo-aggregierte Tests. Bayesian hat bei kleiner Sample keinen Vorteil, nur bessere Interpretierbarkeit.",{"type":32,"tag":33,"props":1263,"children":1264},{},[1265],{"type":37,"value":1266},"Bayesian-Test glänzt in Cross-Channel-Test-Orchestrierung. Paid-Creative-Test + Landing-Page-CRO gleichzeitig? Posterior beider Tests kombinieren (Joint Posterior), Lift-Contribution trennen. Frequentist braucht komplexes ANOVA, Bayesian macht es natürlich via Markov Chain Monte Carlo (MCMC).",{"type":32,"tag":40,"props":1268,"children":1270},{"id":1269},"praktische-implementierung-plattformen-und-tooling",[1271],{"type":37,"value":1272},"Praktische Implementierung: Plattformen und Tooling",{"type":32,"tag":33,"props":1274,"children":1275},{},[1276,1278,1284,1286,1292],{"type":37,"value":1277},"Google Optimize (Dienst eingestellt) nutzte Bayesian-Motor. Heute: Open-Source Python ",{"type":32,"tag":102,"props":1279,"children":1281},{"className":1280},[],[1282],{"type":37,"value":1283},"bayesian-testing",{"type":37,"value":1285}," oder R ",{"type":32,"tag":102,"props":1287,"children":1289},{"className":1288},[],[1290],{"type":37,"value":1291},"bayesAB",{"type":37,"value":1293},". In Production brauchst du Stack — SQL UDF in BigQuery für Posterior-Berechnung oder dbt-Modell als Posterior-Pipeline.",{"type":32,"tag":33,"props":1295,"children":1296},{},[1297],{"type":37,"value":1298},"Beispiel dbt Macro: täglich neue Test-Daten, Macro aktualisiert Posterior alpha\u002Fbeta, berechnet P(B > A). Bei Schwelle überschritten, Slack-Notification. Automatisches Stopping statt manuales Monitoring. Dashboard zeigt Credible Interval und Expected Loss — Stakeholder sieht „B gewinnt jetzt mit 82%\" statt „wann entscheiden wir?\".",{"type":32,"tag":33,"props":1300,"children":1301},{},[1302],{"type":37,"value":1303},"AB-Testing-Plattformen (VWO, Optimizely) fügen Bayesian-Motor hinzu, aber nicht als Default, sondern parallel zu Frequentist. Prior-Wahl ist dein Parameter, kann nicht automatisiert. Plattformen nehmen uninformative Prior an; willst du informativ, brauchst du Setup. Deshalb: großskaliges Bayesian Testing nutzt In-House-Tooling.",{"type":32,"tag":33,"props":1305,"children":1306},{},[1307],{"type":37,"value":1308},"Multi-Variant-Test (A\u002FB\u002FC\u002FD) ist im Bayesian einfacher. Frequentist braucht Multiple-Comparison-Correction (Bonferroni, Holm), Bayesian berechnet jede Variant-Posterior separat — du siehst P(C > A), P(D > B), alle Kombinationen. Winner: höchster Posterior-Mittelwert oder niedrigster Expected Loss.",{"type":32,"tag":1310,"props":1311,"children":1312},"hr",{},[],{"type":32,"tag":33,"props":1314,"children":1315},{},[1316],{"type":37,"value":1317},"Bayesian A\u002FB-Test beschleunigt Entscheidungen in Performance-Marketing. Die Fixed-Horizon-Zwangslage des Frequentist wird durch Sequential Monitoring ersetzt. Posterior bleibt immer aktuell, P(B > A) und Expected Loss ermöglichen kontrollierte risikobewusste Entscheidungen. Mit informativem Prior bringst du historische Test-Daten in neuen Test, reduzierst Sample-Size-Bedarf. Tradeoff: Prior-Wahl subjektiv, Regulierung verlangt vielleicht Frequentist, sehr kleine Samples b",{"type":32,"tag":1319,"props":1320,"children":1321},"style",{},[1322],{"type":37,"value":1323},"html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}",{"title":16,"searchDepth":158,"depth":158,"links":1325},[1326,1327,1330,1331,1334,1335],{"id":42,"depth":135,"text":45},{"id":63,"depth":135,"text":66,"children":1328},[1329],{"id":90,"depth":158,"text":93},{"id":683,"depth":135,"text":686},{"id":837,"depth":135,"text":840,"children":1332},[1333],{"id":869,"depth":158,"text":872},{"id":1243,"depth":135,"text":1246},{"id":1269,"depth":135,"text":1272},"markdown","content:de:marketing:bayesian-ab-test-h.md","content","de\u002Fmarketing\u002Fbayesian-ab-test-h.md","de\u002Fmarketing\u002Fbayesian-ab-test-h","md",1778335430480]