## 3 Results
### Prediction Accuracy  
In general, it is advisable in regression analysis to focus on those input variable that are highly linearly correlated with the output variable. As shown before, in the case of methane emissions from our naturally ventilated cattle building under consideration, none of the routinely monitored features fulfilled this criterion. Nevertheless, there are apparently non-linear relations that justify the use of those features in the modeling process. We considered the predictions of the average emission values obtained by multiple models. In row 1 of Figure 3, we present the results obtained by gradient boosting and random forest. The two ensemble methods produced very similar results with a very accurate and robust prediction of the 10-month average emission value. Less than 10% relative error were obtained even for scenarios where only three times 24 h were used for model training. Linear regression with regularization (Ridge, 2 nd row left) and without regularization (LinReg, 2 nd row right) with scenarios with three to four measurement periods resulted in very different emission values. Linear regression without regularization exhibited larger deviations from the actually measured value and particularly a larger variability (partly with relative errors around 25%). The results with scenarios with six measurement periods, were more comparable to the outcome of the ensemble methods. The projected emission values obtained with an artificial neural network with hyperparameter tuning (ANN, left) and a simple neural network with one hidden layer and four nodes (fixAnn, right) are depicted in the third row. The more complex network resulted in general in projections that were closer to the experimental value. In addition, the variance was smaller than obtained from fixANN. However, the complex ANN generally tended to slightly overestimate the  
Figure 2: Scatter plots between the target size (emission) and the input features (year-time, day-time, temperature, squared temperature, wind speed and wind direction). emission values. The deviations from the actually measured mean were typically larger than observed with the machine learning methods in row 1 and 2. The results of the Gaussian process model (GaussProc, right) and the support vector machine (SVM, left) are compared in the last row. The SVM predictions were similar to the results with Ridge. With the Gaussian process the variability was larger and almost all mean values were below the experimental value. Figure 3: Predictions of methane emissions [g h\({}^{-1}\) LU\({}^{-1}\)] averaged over the 10 month measuring period with eight regression methods. The mean over the predictions, based on 30 random realizations of each of the 27 scenarios (as depicted in Figure 1), is highlighted in blue. The associated one-sigma intervals are indicated by the light blue dashed lines. Here, all methods used the features: \(T\) (i.e., outdoor temperature), \(T^{2}\), wind speed, wind direction, time and day-time, scaled with the _RobustScaler_ from Scikit-learn [25]. For comparison, red horizontal lines highlight the mean observed emission (\(E_{n}=11.6\) g h\({}^{-1}\) LU\({}^{-1}\)). Next, we compared the model projections when considering all features versus using only a selection of features for modeling, since the correlation analysis indicated that the linear relation between the methane emission and the considered features is usually very week. In consequence, taking into account all features might reduce the predictive accuracy, particularly in the case of multilinear regression. The results of this empirical study are summarized examplarily for GradBoost, LinReg and Rigde in Table 2. We observed that in the case of multilinear regression (i.e., LinReg and Ridge) neglecting all but the sine and cosine of the day-time indeed improved the prediction accuracy. A similar behavior as with the linear regression was observed using the ANN approach (results not shown).