Conclusion. The outcomes of Experiment 3 are shown in Figure eight. We can see that when l is smaller sized, each RMSE and the uncertainty bounds modify swiftly. While just after it exceeds certain values, each converge. This once more complies with our theoretical conclusions and simulation benefits. We should also notice from Figures 7 and eight that the increment of s f tends to increase the uncertainty, whereas the increment of l tends to decrease the uncertainty. Taking both into consideration, an optimised uncertainty bound can be obtained. two We also conduct an experiment to demonstrate how the noise level n impacts the two to differ from 0.five to 4.five. The outcomes ELBO and UBML. In our experiment, we set n are shown in Figure 9. To make the outcomes distinguishable, we set the vertical axes to log(- ELBO/UBML). To create the logrithm operate, we reverse the indicators of each ELBO and UBML. That is the reason why ELBO is `greater’ than UBML in Figure 9. The Moxifloxacin-d4 Epigenetics complete GPs model 2 is trained by setting n to 1, 7, 13, 19, 25, 31, 37, 43, 49 to receive 9 sets of hyperparameters. 2 For each and every set of them, we then set n to differ from 0.5 to 4.five. The darker the colour in two 2 Figure 9, the smaller n is for model education. We can see that typically, higher n can slow down the convergence speed of both ELBO and UBML, though coaching a model. When the two model is trained, the increment of n can reduced down UBML, which can be the maximum that two ELBO can reach. This implies that the increment of n may cause the failure of a sparse GPs model, as ELBO is deeply related to identify a sparse GPs model. Nevertheless, the experimental outcomes again comply with our theoretical conclusions.0.5 0.45 0.four 0.35 0.3 0.25 60 0.2 40 0.15 20 0.1 5 10 15 20 25 30 five ten 15 20 25Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC180 160 140 120 100Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC(a)900 0.35 0.3 0.25 0.2 0.15 300 0.1 200 0.05Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC(b)800 700 600 500Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC(c)(d)two Figure 7. Relationship of s f on NO prediction RMSE and uncertainty bound: (a) n = 0.5, two = 0.5, (c) 2 = 1.five, (d) two = 1.five. (b) n n nAtmosphere 2021, 12,13 of0.5 0.45 0.four 0.35 0.three 0.25 0.two 0.15 0.1 0.05 50 100 150 200 250Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC220 200 180 160 140 120 one hundred 80 60 40 20 50 one hundred 150Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC(a)3.two 0.45 three 0.four 2.eight 0.35 0.3 0.25 0.2 2 0.15 1.eight 50 100 150 200 250 300 50Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC(b)Pesh-NO-GP Pesh-NO-VFE Pesh-NO-FITC Shef-NO-GP Shef-NO-VFE Shef-NO-FITC2.6 two.4 2.(c)(d)2 2 Figure eight. Connection of l on NO prediction RMSE and uncertainty bound: (a) n = 0.5, (b) n = 0.5, two = 1.5, (d) two = 1.5. (c) n n10 9 eight 7ELBO UBML10 9 8 7ELBO UBML0.1.2.3.four.0.1.two.3.4.(a)(b)two Figure 9. Effects of n on ELBO and UBML: (a) NO in Sheffield, (b) NO in Peshawar.5. Conclusions This paper proposes a common strategy to investigate how the efficiency variation of a Gaussian approach model can be Isophorone Protocol attributed to hyperparameters and measurement noises, etc. The approach is demonstrated by applying it to method particulate matter (e.g., PM2.five ) and gaseous pollutants (e.g., NO, NO2 , and SO2 ) from both Sheffield, UK, and Peshawar, Pakistan. Experimental benefits show that the proposed approach supplies insights on how measurement noises.