{"id":15525,"date":"2022-04-17T18:56:54","date_gmt":"2022-04-17T17:56:54","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=15525"},"modified":"2024-02-13T13:48:29","modified_gmt":"2024-02-13T12:48:29","slug":"inference-statistique","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/statistical-inference\/","title":{"rendered":"Statistical Inference 101"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"15525\" class=\"elementor elementor-15525\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e76b2fa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e76b2fa\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b4c1238\" data-id=\"b4c1238\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-46078f5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"46078f5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/2020\/04\/03\/theories-and-algorithms-2\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Theory<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1ee0989\" data-id=\"1ee0989\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8530b0f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8530b0f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Home page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-509997f\" data-id=\"509997f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9b0a8f8 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"9b0a8f8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/en.wikipedia.org\/wiki\/Statistical_inference\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-744ed1f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"744ed1f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d130336\" data-id=\"d130336\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dbc9baf elementor-widget elementor-widget-toggle\" data-id=\"dbc9baf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2301\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2301\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">I. Point estimation<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2301\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2301\"><ul><li><a title=\"Estimating equations\" href=\"https:\/\/en.wikipedia.org\/wiki\/Estimating_equations\" target=\"_blank\" rel=\"noopener\">Estimating equations<\/a>\u00a0<ul><li><a class=\"mw-redirect\" title=\"Maximum likelihood\" href=\"https:\/\/en.wikipedia.org\/wiki\/Maximum_likelihood\" target=\"_blank\" rel=\"noopener\">Maximum likelihood<\/a><\/li><li><a title=\"Method of moments (statistics)\" href=\"https:\/\/en.wikipedia.org\/wiki\/Method_of_moments_(statistics)\" target=\"_blank\" rel=\"noopener\">Method of moments<\/a><\/li><li><a title=\"M-estimator\" href=\"https:\/\/en.wikipedia.org\/wiki\/M-estimator\" target=\"_blank\" rel=\"noopener\">M-estimator<\/a><\/li><li><a class=\"mw-redirect\" title=\"Minimum estimated distance\" href=\"https:\/\/en.wikipedia.org\/wiki\/Minimum_distance_estimation\" target=\"_blank\" rel=\"noopener\">minimum distance<\/a><\/li><\/ul><\/li><li><a title=\"Bias of an estimator\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bias_of_an_estimator\" target=\"_blank\" rel=\"noopener\">Unbiased estimators<\/a>\u00a0<ul><li><a title=\"Minimum-variance unbiased estimator\" href=\"https:\/\/en.wikipedia.org\/wiki\/Minimum-variance_unbiased_estimator\" target=\"_blank\" rel=\"noopener\">Mean-unbiased minimum-variance<\/a>\u00a0<ul><li><a title=\"Rao\u2013Blackwell theorem\" href=\"https:\/\/en.wikipedia.org\/wiki\/Rao%E2%80%93Blackwell_theorem\" target=\"_blank\" rel=\"noopener\">Rao\u2013Blackwellization<\/a><\/li><li><a title=\"Lehmann\u2013Scheff\u00e9 theorem\" href=\"https:\/\/en.wikipedia.org\/wiki\/Lehmann%E2%80%93Scheff%C3%A9_theorem\" target=\"_blank\" rel=\"noopener\">Lehmann\u2013Scheff\u00e9 theorem<\/a><\/li><\/ul><\/li><li><a class=\"mw-redirect\" title=\"Median-unbiased estimator\" href=\"https:\/\/en.wikipedia.org\/wiki\/Median-unbiased_estimator\" target=\"_blank\" rel=\"noopener\">Median unbiased<\/a><\/li><\/ul><\/li><li><a class=\"mw-redirect\" title=\"Plug-in principle\" href=\"https:\/\/en.wikipedia.org\/wiki\/Plug-in_principle\" target=\"_blank\" rel=\"noopener\">plugin<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2302\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2302\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">II. Estimation of intervals<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2302\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2302\"><ul><li><a title=\"Confidence interval\" href=\"https:\/\/en.wikipedia.org\/wiki\/Confidence_interval\" target=\"_blank\" rel=\"noopener\">Confidence interval<\/a><\/li><li><a title=\"Pivotal quantity\" href=\"https:\/\/en.wikipedia.org\/wiki\/Pivotal_quantity\" target=\"_blank\" rel=\"noopener\">Pivot<\/a><\/li><li><a class=\"mw-redirect\" title=\"Likelihood interval\" href=\"https:\/\/en.wikipedia.org\/wiki\/Likelihood_interval\" target=\"_blank\" rel=\"noopener\">Likelihood interval<\/a><\/li><li><a title=\"Prediction interval\" href=\"https:\/\/en.wikipedia.org\/wiki\/Prediction_interval\" target=\"_blank\" rel=\"noopener\">Prediction interval<\/a><\/li><li><a title=\"Tolerance interval\" href=\"https:\/\/en.wikipedia.org\/wiki\/Tolerance_interval\" target=\"_blank\" rel=\"noopener\">Tolerance interval<\/a><\/li><li><a title=\"Resampling (statistics)\" href=\"https:\/\/en.wikipedia.org\/wiki\/Resampling_(statistics)\" target=\"_blank\" rel=\"noopener\">Resampling<\/a>\u00a0<ul><li><a title=\"Bootstrapping (statistics)\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bootstrapping_(statistics)\" target=\"_blank\" rel=\"noopener\">Bootstrap<\/a><\/li><li><a title=\"jackknife resampling\" href=\"https:\/\/en.wikipedia.org\/wiki\/Jackknife_resampling\" target=\"_blank\" rel=\"noopener\">Jackknife<\/a><\/li><\/ul><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2303\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-2303\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">III. Hypothesis testing<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2303\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-2303\"><ul><li><a title=\"One- and two-tailed tests\" href=\"https:\/\/en.wikipedia.org\/wiki\/One-_and_two-tailed_tests\" target=\"_blank\" rel=\"noopener\">1- &amp; 2-tails<\/a><\/li><li><a class=\"mw-redirect\" title=\"Power (statistics)\" href=\"https:\/\/en.wikipedia.org\/wiki\/Power_(statistics)\" target=\"_blank\" rel=\"noopener\">Power<\/a>\u00a0<ul><li><a title=\"Uniformly most powerful test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Uniformly_most_powerful_test\" target=\"_blank\" rel=\"noopener\">Uniformly most powerful test<\/a><\/li><\/ul><\/li><li><a title=\"Swap test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Permutation_test\" target=\"_blank\" rel=\"noopener\">Swap test<\/a>\u00a0<ul><li><a class=\"mw-redirect\" title=\"Randomization test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Randomization_test\" target=\"_blank\" rel=\"noopener\">Randomization test<\/a><\/li><\/ul><\/li><li><a class=\"mw-redirect\" title=\"Multiple comparisons\" href=\"https:\/\/en.wikipedia.org\/wiki\/Multiple_comparisons\" target=\"_blank\" rel=\"noopener\">Multiple comparisons<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2304\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-2304\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">IV. Parameter testing<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2304\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-2304\"><ul><li><a title=\"Likelihood ratio test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Likelihood-ratio_test\" target=\"_blank\" rel=\"noopener\">Likelihood ratio<\/a><\/li><li><a title=\"test-score\" href=\"https:\/\/en.wikipedia.org\/wiki\/Score_test\" target=\"_blank\" rel=\"noopener\">Score\/Lagrange multiply<\/a><\/li><li><a title=\"Wald-test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Wald_test\" target=\"_blank\" rel=\"noopener\">Wald<\/a><\/li><li><a title=\"\" href=\"https:\/\/en.wikipedia.org\/wiki\/Z-test\" target=\"_blank\" rel=\"noopener\">Z-test (normal)<\/a><\/li><li><a title=\"Student&#039;s t-test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Student%27s_t-test\" target=\"_blank\" rel=\"noopener\">Student&#039;s\u00a0<i>t<\/i>-test<\/a><\/li><li><a title=\"F test\" href=\"https:\/\/en.wikipedia.org\/wiki\/F-test\" target=\"_blank\" rel=\"noopener\"><i>F<\/i>-test<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2305\" class=\"elementor-tab-title\" data-tab=\"5\" role=\"button\" aria-controls=\"elementor-tab-content-2305\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">V.Fitting<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2305\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"region\" aria-labelledby=\"elementor-tab-title-2305\"><ul><li><a title=\"Chi-squared test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Chi-squared_test\" target=\"_blank\" rel=\"noopener\">Chi-squared<\/a><\/li><li><a title=\"G-test\" href=\"https:\/\/en.wikipedia.org\/wiki\/G-test\" target=\"_blank\" rel=\"noopener\"><i>G<\/i>-test<\/a><\/li><li><a title=\"Kolmogorov\u2013Smirnov test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Kolmogorov%E2%80%93Smirnov_test\" target=\"_blank\" rel=\"noopener\">Kolmogorov\u2013Smirnov<\/a><\/li><li><a title=\"Anderson\u2013Darling test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Anderson%E2%80%93Darling_test\" target=\"_blank\" rel=\"noopener\">Anderson\u2013Darling<\/a><\/li><li><a title=\"Lilliefors test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Lilliefors_test\" target=\"_blank\" rel=\"noopener\">Lilliefors<\/a><\/li><li><a title=\"Jarque\u2013Bera test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Jarque%E2%80%93Bera_test\" target=\"_blank\" rel=\"noopener\">Jarque\u2013Bera<\/a><\/li><li><a title=\"Shapiro\u2013Wilk test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Shapiro%E2%80%93Wilk_test\" target=\"_blank\" rel=\"noopener\">Normality (Shapiro\u2013Wilk)<\/a><\/li><li><a title=\"Likelihood ratio test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Likelihood-ratio_test\" target=\"_blank\" rel=\"noopener\">Likelihood ratio test<\/a><\/li><li><a title=\"Model selection\" href=\"https:\/\/en.wikipedia.org\/wiki\/Model_selection\" target=\"_blank\" rel=\"noopener\">Model selection<\/a>\u00a0<ul><li><a title=\"Cross validation (statistics)\" href=\"https:\/\/en.wikipedia.org\/wiki\/Cross-validation_(statistics)\" target=\"_blank\" rel=\"noopener\">Cross-validation<\/a><\/li><li><a title=\"Akaike information criterion\" href=\"https:\/\/en.wikipedia.org\/wiki\/Akaike_information_criterion\" target=\"_blank\" rel=\"noopener\">AIC<\/a><\/li><li><a title=\"Bayesian information criteria\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bayesian_information_criterion\" target=\"_blank\" rel=\"noopener\">BIC<\/a><\/li><\/ul><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2306\" class=\"elementor-tab-title\" data-tab=\"6\" role=\"button\" aria-controls=\"elementor-tab-content-2306\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">VI. Rank<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2306\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"6\" role=\"region\" aria-labelledby=\"elementor-tab-title-2306\"><ul><li><a title=\"sign-test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Sign_test\" target=\"_blank\" rel=\"noopener\">sign<\/a>\u00a0<ul><li><a class=\"mw-redirect\" title=\"Median sample\" href=\"https:\/\/en.wikipedia.org\/wiki\/Sample_median\" target=\"_blank\" rel=\"noopener\">Median sample<\/a><\/li><\/ul><\/li><li><a title=\"Wilcoxon signed-rank test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Wilcoxon_signed-rank_test\" target=\"_blank\" rel=\"noopener\">Signed rank (Wilcoxon)<\/a>\u00a0<ul><li><a title=\"Hodges\u2013Lehmann estimator\" href=\"https:\/\/en.wikipedia.org\/wiki\/Hodges%E2%80%93Lehmann_estimator\" target=\"_blank\" rel=\"noopener\">Hodges\u2013Lehmann estimator<\/a><\/li><\/ul><\/li><li><a title=\"Mann\u2013Whitney U test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Mann%E2%80%93Whitney_U_test\" target=\"_blank\" rel=\"noopener\">Rank sum (Mann\u2013Whitney)<\/a><\/li><li><a title=\"Nonparametric statistics\" href=\"https:\/\/en.wikipedia.org\/wiki\/Nonparametric_statistics\" target=\"_blank\" rel=\"noopener\">Nonparametric<\/a>\u00a0<a title=\"Analysis of variance\" href=\"https:\/\/en.wikipedia.org\/wiki\/Analysis_of_variance\" target=\"_blank\" rel=\"noopener\">anova<\/a>\u00a0<ul><li><a title=\"Kruskal\u2013Wallis one-way analysis of variance\" href=\"https:\/\/en.wikipedia.org\/wiki\/Kruskal%E2%80%93Wallis_one-way_analysis_of_variance\" target=\"_blank\" rel=\"noopener\">1-way (Kruskal\u2013Wallis)<\/a><\/li><li><a title=\"Friedman test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Friedman_test\" target=\"_blank\" rel=\"noopener\">2-way (Friedman)<\/a><\/li><li><a title=\"Jonckheere&#039;s trend test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Jonckheere%27s_trend_test\" target=\"_blank\" rel=\"noopener\">Ordered alternative (Jonckheere\u2013Terpstra)<\/a><\/li><\/ul><\/li><li><a title=\"Van der Waerden test\" href=\"https:\/\/en.wikipedia.org\/wiki\/Van_der_Waerden_test\" target=\"_blank\" rel=\"noopener\">Van der Waerden test<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2307\" class=\"elementor-tab-title\" data-tab=\"7\" role=\"button\" aria-controls=\"elementor-tab-content-2307\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">VII. Bayesian inference<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2307\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"7\" role=\"region\" aria-labelledby=\"elementor-tab-title-2307\"><ul><li><a title=\"Bayesian probability\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bayesian_probability\" target=\"_blank\" rel=\"noopener\">Bayesian probability<\/a>\u00a0<ul><li><a title=\"Prior probability\" href=\"https:\/\/en.wikipedia.org\/wiki\/Prior_probability\" target=\"_blank\" rel=\"noopener\">prior<\/a><\/li><li><a title=\"Posterior probability\" href=\"https:\/\/en.wikipedia.org\/wiki\/Posterior_probability\" target=\"_blank\" rel=\"noopener\">later<\/a><\/li><\/ul><\/li><li><a title=\"Credible interval\" href=\"https:\/\/en.wikipedia.org\/wiki\/Credible_interval\" target=\"_blank\" rel=\"noopener\">Credible interval<\/a><\/li><li><a title=\"Bayes-factor\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bayes_factor\" target=\"_blank\" rel=\"noopener\">Bayes-factor<\/a><\/li><li><a title=\"Bayes estimator\" href=\"https:\/\/en.wikipedia.org\/wiki\/Bayes_estimator\" target=\"_blank\" rel=\"noopener\">Bayesian estimator<\/a>\u00a0<ul><li><a title=\"Maximum a posteriori estimate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Maximum_a_posteriori_estimation\" target=\"_blank\" rel=\"noopener\">Maximum posterior estimator<\/a><\/li><\/ul><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2308\" class=\"elementor-tab-title\" data-tab=\"8\" role=\"button\" aria-controls=\"elementor-tab-content-2308\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">VIII. Tutorials<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2308\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"8\" role=\"region\" aria-labelledby=\"elementor-tab-title-2308\"><ul><li><a href=\"https:\/\/towardsdatascience.com\/mle-map-and-bayesian-inference-3407b2d6d4d9\" target=\"_blank\" rel=\"noopener\">MLE, MAP and Bayesian inference<\/a><\/li><li><a href=\"https:\/\/medium.com\/data-science-at-microsoft\/causal-inference-part-1-of-3-understanding-the-fundamentals-816f4723e54a\" target=\"_blank\" rel=\"noopener\">Causal inference and packages<\/a><\/li><li><a href=\"https:\/\/medium.com\/data-science-at-microsoft\/causal-inference-part-2-of-3-selecting-algorithms-a966f8228a2d\" target=\"_blank\" rel=\"noopener\">Algorithms for causal inference<\/a><\/li><li><a href=\"https:\/\/medium.com\/data-science-at-microsoft\/causal-inference-part-3-of-3-model-validation-and-applications-c84764156a29\" target=\"_blank\" rel=\"noopener\">Validation of causal inference<\/a><\/li><li><a href=\"https:\/\/neptune.ai\/blog\/cross-validation-mistakes\" target=\"_blank\" rel=\"noopener\">Best practices for cross-validation<\/a><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-25df854 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"25df854\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6e2e713\" data-id=\"6e2e713\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b1d210a elementor-widget elementor-widget-heading\" data-id=\"b1d210a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/statistical-inference\/#Inference-statistique\" >Statistical inference<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Inference-statistique\"><\/span>Statistical inference<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-10c7e9b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"10c7e9b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-08ff80c\" data-id=\"08ff80c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-516bce9 elementor-widget elementor-widget-text-editor\" data-id=\"516bce9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Statistical inference is the process of using the<a href=\"https:\/\/complex-systems-ai.com\/en\/data-analysis\/\">data analysis<\/a> to infer properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.<\/p><p>Inferential statistics can be compared to descriptive statistics. Descriptive statistics are concerned only with the properties of the observed data and do not rely on the assumption that the data comes from a larger population.<\/p><p>In machine learning, the term inference is sometimes used instead to mean &quot;to make a prediction, by evaluating an already trained model&quot; In this context, the deduction of model properties is called training or learning (rather than inference ), and the use of a model because the prediction is called inference (instead of prediction); see also predictive inference.<\/p><p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-15528 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/telechargement.png\" alt=\"statistical inference\" width=\"412\" height=\"122\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/telechargement.png 412w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/telechargement-300x89.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/telechargement-18x5.png 18w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Theory Homepage Wiki I. Point estimation Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao\u2013Blackwellization Lehmann\u2013Scheff\u00e9 theorem \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15525","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/15525","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=15525"}],"version-history":[{"count":13,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/15525\/revisions"}],"predecessor-version":[{"id":20646,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/15525\/revisions\/20646"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=15525"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}