module3/exo3/exercice.jmd

@@ -613,15 +613,15 @@ négligeable. L'incertitude sur $\beta$ est en particulier de nature à engendre
 une perte de prédictibilité du modèle en temps long.
 
 ```julia; echo=false; results="raw"
-data.theta_pred = predict(model, data)
+pred = predict(model, data, interval=:prediction, level=0.95)
+data.theta_pred = pred.prediction
+data.theta_pred1 = pred.prediction .- pred.lower
+data.theta_pred2 = pred.upper .- pred.prediction
 
 plot(xlabel="Date", ylabel="CO2 [ppm]")
 plot!(data_raw.date, data_raw.co2, label="mesures")
-plot!(data.date, data.theta_pred, label="modèle theta", linewidth=3)
-plot!(data.date, α .+ β1 * data.date_num .+ γ*data.date_num.^2,
-      linecolor="red", label="modèle theta (IC 95% sur beta)")
-plot!(data.date, α .+ β2 * data.date_num .+ γ*data.date_num.^2,
-      linecolor="red", label=nothing)
+plot!(data.date, data.theta_pred, label="modèle theta",
+      ribbon = (data.theta_pred1, data.theta_pred2))
 disp()
 ```
 
@@ -654,7 +654,11 @@ Le modèle `GLM` précédemment calibré est utilisé pour prédire $\theta(t)$.
 ajoute la fonction de forme annuelle $\phi(t)$ par périodicité.
 
 ```julia; results="raw"
-prediction.theta = predict(model, prediction)
+pred = predict(model, prediction, interval=:prediction, level=0.95)
+prediction.theta  = pred.prediction
+prediction.theta1 = pred.prediction .- pred.lower
+prediction.theta2 = pred.upper .- pred.prediction
+
 prediction = join(prediction, avg, on=:day)
 
 prediction.co2 = prediction.theta .+ prediction.phi_mean
@@ -670,8 +674,10 @@ d'extrapolation ; on observe un décalage significatif et croissant ensuite.
 idx = data_raw.date .> Date(lastyear)
 plot(xlabel="Date", ylabel="CO2 [ppm]")
 plot!(data_raw.date[idx], data_raw.co2[idx], label="mesures")
-plot!(prediction.date, prediction.theta,     label="tendance", linewidth=2)
-plot!(prediction.date, prediction.co2,       label="prédiction", linewidth=2)
+plot!(prediction.date, prediction.theta, label="tendance",
+      linewidth=2,
+      ribbon = (prediction.theta1, prediction.theta2))
+plot!(prediction.date, prediction.co2, label="prédiction", linewidth=2)
 disp()
 ```