## 8 Reliability and Accuracy Analysis
### Discussion  
As can be seen, and as already previewed above, the machine learning technique GRNN usually provides the best results for this dataset and usually outperforming ARIMA, which is traditionally used for predicting ED indicators. However, ARIMA usually comes a close second and actually outperforms GRNN for the Patient Attendances, probably due to the very high variance in this indicator.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Confidence Bands Data Distribution**} \\ \hline \hline \multirow{5}{*}{Patients in Department} & **Residual Quality** & _ARIMA_ & _Prophet_ & _GRNN_ \\ \cline{2-5}  & Very good & 48.8\% & 43.5\% & 48.9\% \\ \cline{2-5}  & Good & 16.4\% & 16.2\% & 19.2\% \\ \cline{2-5}  & Regular & 14.6\% & 15.1\% & 16.3\% \\ \cline{2-5}  & Unreliable & 20.2\% & 25.2\% & 15.6\% \\ \cline{2-5}  & **Reliability** & **79.8\%** & **74.8\%** & **84.4\%** \\ \hline \multirow{5}{*}{Patient Attendances} & Very good & 53.5\% & 50.0\% & 53.3\% \\ \cline{2-5}  & Good & 13.0\% & 12.0\% & 12.4\% \\ \cline{2-5}  & Regular & 15.7\% & 15.8\% & 15.0\% \\ \cline{2-5}  & Unreliable & 17.8\% & 22.2\% & 18.3\% \\ \cline{2-5}  & **Reliability** & **82.2\%** & **77.8\%** & **80.7\%** \\ \hline \multirow{5}{*}{Unallocated Patients with DTA} & Very good & 32.1\% & 28.7\% & 36.2\% \\ \cline{2-5}  & Good & 15.7\% & 15.0\% & 16.0\% \\ \cline{2-5}  & Regular & 10.5\% & 11.6\% & 11.1\% \\ \cline{2-5}  & Unreliable & 41.7\% & 45.0\% & 36.7\% \\ \cline{2-5}  & **Reliability** & **58.3\%** & **55.0\%** & **63.3\%** \\ \cline{2-5}  & Very good & 53.5\% & 44.0\% & 53.4\% \\ \cline{2-5}  & Good & 19.3\% & 17.4\% & 22.3\% \\ \cline{2-5}  & Regular & 10.7\% & 14.6\% & 13.1\% \\ \cline{2-5}  & Unreliable & 16.4\% & 24.1\% & 10.2\% \\ \cline{2-5}  & **Reliability** & **83.5\%** & **76.0\%** & **88.8\%** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Reliability comparison of ARIMA, Prophet and GRNN.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**RMSE (Root Mean Square Deviation)**} \\ \hline \hline  & **ARIMA** & **Prophet** & **GRNN** \\ \hline Patients in Department & 18.1091 & 21.5031 & 17.7061 \\ \hline Patient Attendances & 7.1002 & 8.8217 & 7.5965 \\ \hline Unallocated Patients with DTA & 6.6968 & 8.1521 & 6.2153 \\ \hline Medically Fit for Discharge & 35.1270 & 39.2894 & 34.3455 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy comparison of ARIMA, Prophet and GRNN.  
The relative performance is heavily impacted by the ability of GRNN to adapt rapidly to sudden dramatic changes in the data trends and for more stable time-series data, the performance of all three is likely to be closer.  
The COVID-19 pandemic drove just such a change and strongly altered the behaviour of ED indicators, which then presented a challenge to the purely autoregressive models represented by ARIMA and Prophet, which rely solely on abstractions of previous values. GRNN was able to adapt to the change in data patterns promptly, resulting in closer predictions during this change period for all 4 indicators, as seen in Section 7. In addition, when analysing the entire 10 months of data for reliability (Table 2) and accuracy (Table 3), GRNN was the best fit model for 3 out of the 4 indicators, as seen in Section 8.  
Although the difference in both accuracy and reliability are evident and relevant, data analysis suggests that outside of the pandemic period, the improvements in accuracy and reliability are reduced to slim margins. Hence, further simulations with different KPIs and data sample periods are necessary to further validate the findings of this study.