diff --git a/module2/exo5/exo5_fr.ipynb b/module2/exo5/exo5_fr.ipynb index d9256b489607cbde5df5b2163a67fecc8aa47929..125422fbe64b1db64c6095b21353e3b72a6c3bcd 100644 --- a/module2/exo5/exo5_fr.ipynb +++ b/module2/exo5/exo5_fr.ipynb @@ -40,7 +40,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -287,7 +287,7 @@ "22 1/12/86 6 58 200 1" ] }, - "execution_count": 12, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -322,7 +322,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -425,7 +425,7 @@ "22 1/12/86 6 58 200 1" ] }, - "execution_count": 13, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -462,7 +462,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -514,7 +514,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -541,7 +541,7 @@ " Date: Sun, 28 Jan 2024 Deviance: 3.0144 \n", "\n", "\n", - " Time: 17:21:21 Pearson chi2: 5.00 \n", + " Time: 17:39:06 Pearson chi2: 5.00 \n", "\n", "\n", " No. Iterations: 6 Covariance Type: nonrobust\n", @@ -570,7 +570,7 @@ "Link Function: logit Scale: 1.0000\n", "Method: IRLS Log-Likelihood: -3.9210\n", "Date: Sun, 28 Jan 2024 Deviance: 3.0144\n", - "Time: 17:21:21 Pearson chi2: 5.00\n", + "Time: 17:39:06 Pearson chi2: 5.00\n", "No. Iterations: 6 Covariance Type: nonrobust\n", "===============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", @@ -581,7 +581,7 @@ "\"\"\"" ] }, - "execution_count": 15, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -592,9 +592,9 @@ "data[\"Success\"]=data.Count-data.Malfunction\n", "data[\"Intercept\"]=1\n", "\n", - "logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n", + "logmodelT=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n", "\n", - "logmodel.summary()" + "logmodelT.summary()" ] }, { @@ -606,6 +606,213 @@ "un impact conséquent sur l'apparition de dysfonctionnements.\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Estimation de l'influence de la pression\n", + "\n", + "\n", + "Vérifions maintenant l'influence de la pression. \n", + "\n", + "Supposons que chacun des 6 joints toriques est endommagé avec la même\n", + "probabilité et indépendamment des autres et que cette probabilité ne\n", + "dépend que de la pression. Si on note $p(p)$ cette probabilité, le\n", + "nombre de joints $D$ dysfonctionnant lorsque l'on effectue le vol à\n", + "pression $p$ suit une loi binomiale de paramètre $n=6$ et\n", + "$p=p(p)$. Pour relier $p(p)$ à $p$, on va donc effectuer une\n", + "régression logistique." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "
Generalized Linear Model Regression Results
Dep. Variable: Frequency No. Observations: 23
Model: GLM Df Residuals: 21
Model Family: Binomial Df Model: 1
Link Function: logit Scale: 1.0000
Method: IRLS Log-Likelihood: -4.2246
Date: Sun, 28 Jan 2024 Deviance: 3.6216
Time: 17:39:09 Pearson chi2: 3.94
No. Iterations: 6 Covariance Type: nonrobust
\n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "
coef std err z P>|z| [0.025 0.975]
Intercept -4.3835 3.487 -1.257 0.209 -11.219 2.452
Pressure 0.0102 0.019 0.549 0.583 -0.026 0.047
" + ], + "text/plain": [ + "\n", + "\"\"\"\n", + " Generalized Linear Model Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Frequency No. Observations: 23\n", + "Model: GLM Df Residuals: 21\n", + "Model Family: Binomial Df Model: 1\n", + "Link Function: logit Scale: 1.0000\n", + "Method: IRLS Log-Likelihood: -4.2246\n", + "Date: Sun, 28 Jan 2024 Deviance: 3.6216\n", + "Time: 17:39:09 Pearson chi2: 3.94\n", + "No. Iterations: 6 Covariance Type: nonrobust\n", + "==============================================================================\n", + " coef std err z P>|z| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "Intercept -4.3835 3.487 -1.257 0.209 -11.219 2.452\n", + "Pressure 0.0102 0.019 0.549 0.583 -0.026 0.047\n", + "==============================================================================\n", + "\"\"\"" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "logmodelP=sm.GLM(data['Frequency'], data[['Intercept','Pressure']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n", + "\n", + "logmodelP.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "L'estimateur le plus probable du paramètre de pression est 0.0102, ce qui est très faible, et l'erreur standard de cet estimateur est de 0.019. La pression semble avoir peu d'impact sur l'apparition de dysfonctionnements." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Influences conjointes de la temperature et la pression\n", + "\n", + "Vérifions les faits qui semblent ressortir de nos premières analyses, dans lesquelles nous n'avons fait varier qu'un seul paramètre à la fois. Nous effectuons maintenant une regression logistique sur les deux paramètres à la fois : température et pression, en utilisant toujours les hypothèses de loi binomiale identique pour tous les joints à une pression et un température donnée." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "
Generalized Linear Model Regression Results
Dep. Variable: Frequency No. Observations: 23
Model: GLM Df Residuals: 20
Model Family: Binomial Df Model: 2
Link Function: logit Scale: 1.0000
Method: IRLS Log-Likelihood: -3.7926
Date: Sun, 28 Jan 2024 Deviance: 2.7576
Time: 17:46:06 Pearson chi2: 4.19
No. Iterations: 6 Covariance Type: nonrobust
\n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "
coef std err z P>|z| [0.025 0.975]
Intercept 2.5202 8.541 0.295 0.768 -14.220 19.260
Pressure 0.0085 0.019 0.451 0.652 -0.028 0.045
Temperature -0.0983 0.110 -0.894 0.371 -0.314 0.117
" + ], + "text/plain": [ + "\n", + "\"\"\"\n", + " Generalized Linear Model Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Frequency No. Observations: 23\n", + "Model: GLM Df Residuals: 20\n", + "Model Family: Binomial Df Model: 2\n", + "Link Function: logit Scale: 1.0000\n", + "Method: IRLS Log-Likelihood: -3.7926\n", + "Date: Sun, 28 Jan 2024 Deviance: 2.7576\n", + "Time: 17:46:06 Pearson chi2: 4.19\n", + "No. Iterations: 6 Covariance Type: nonrobust\n", + "===============================================================================\n", + " coef std err z P>|z| [0.025 0.975]\n", + "-------------------------------------------------------------------------------\n", + "Intercept 2.5202 8.541 0.295 0.768 -14.220 19.260\n", + "Pressure 0.0085 0.019 0.451 0.652 -0.028 0.045\n", + "Temperature -0.0983 0.110 -0.894 0.371 -0.314 0.117\n", + "===============================================================================\n", + "\"\"\"" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "logmodelPT=sm.GLM(data['Frequency'], data[['Intercept','Pressure', 'Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n", + "\n", + "logmodelPT.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "L'estimateur le plus probable pour la température est -0.0983 et celui pour la pression est 0.0085, avec des erreurs standart respectives de 0.110 et 0.019. La température semble donc avoir un impact substanciellement plus important que la pression sur l'apparition de dysfonctionnements.\n", + "\n", + "Il est donc raisonnable de considérer que seule la température influence le fonctionnement des joints, ce que nous considérerons pour l'estimation de la probabilité de défaillance durant le vol (ne connaissant pas la pression ce jour-là)." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -618,8 +825,10 @@ }, { "cell_type": "code", - "execution_count": 16, - "metadata": {}, + "execution_count": 41, + "metadata": { + "scrolled": true + }, "outputs": [ { "data": { @@ -637,7 +846,7 @@ "source": [ "%matplotlib inline\n", "data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})\n", - "data_pred['Frequency'] = logmodel.predict(data_pred[['Intercept','Temperature']])\n", + "data_pred['Frequency'] = logmodelT.predict(data_pred[['Intercept','Temperature']])\n", "data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n", "plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n", "plt.grid(True)" @@ -656,8 +865,79 @@ " avec un autre, la probabilité de défaillance d'une paire \n", " est $p^2 = 0.64$. La probabilité de défaillance d'un des\n", "lançeur est donc de $1-(1-p^2)^3 \\approx 0.95%$. La navette \n", - "a toutes les chances d'exploser !!\n", - "\n", + "a toutes les chances d'exploser !!\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vérifions maintenant la dépendance du résultat sur la température à partir de notre loi jointe en température et pression : " + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "for pressure in [50, 100, 200]:\n", + " data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Pressure':pressure, 'Intercept': 1})\n", + " data_pred['Frequency'] = logmodelPT.predict(data_pred[['Intercept', 'Pressure', 'Temperature']])\n", + " data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n", + " plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"], label=\"pressure={:.0f}\".format(pressure))\n", + " plt.grid(True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "La pression influence fortement le résultat. Cependant, pour toutes les pressions prises en compte, la probabilité de dysfonctionnememt d'un joint est supérieur à 0.5, donc la probabilité de défaillance de la navette est supérieure à 0.58. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "Le lendemain, la navette Challenger explosera et emportera\n", "avec elle ses sept membres d'équipages. L'opinion publique est\n", "fortement touchée et lors de l'enquête qui suivra, la fiabilité des\n",