# Prediction and Surveillance Sampling Assessment in Plant Nurseries and Fields
## 3 Results
### Estimation and Prediction from Sampling Assessment  
Having evaluated the effect of choosing random samples under different sampling methods, we observed that the most appropriate sampling method when we have data of this nature is a random samples method with equal percentages of 25%. With these samples, we obtained lower prediction errors. This result seems appropriate since it is an intermediate sampling scheme between a sample percentage recommended by [22] and the 10% reported by most literature on sampling. The proposed modeling approach is able to capture the behavior of the entire dataset when we consider smaller sample sizes. This was not only observed with random samples of 25% but in the maps obtained from the random samples of 10%, 15% and 20%. Similar behavior was obtained in the maps generated from the other sampling methods considered. The modeling is robust in the presence of little data and in the absence of explanatory variables. Once again, we recognized the importance of a random spatial effect and its determining effect on the dynamics of the disease (Figure 5a). The greatest risks are still presented towards the edges of the nursery and the northern and southern borders, where there is greater wind action (Figure 5b). We only show the maps of the spatial effect and the estimated uncertainties of the posterior probabilities for random samples of 25%. By comparing the map obtained with random samples of 25% with the map of the entire nursery, we observed similar behavior between them. That is, the pattern observed in the maps using the entire data is preserved and can be seen in the maps of random samples of 25% (Figure 6a,b). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Block 1** & **Block 2** & **Block 3** & **Total** \\ \hline
100\% & 20\% & 20\% & 10\% & 12.23\% \\ N & 1240 & 1200 & 8480 & 10,920 \\ n & 248 & 240 & 848 & 1336 \\ \hline
100\% & 25\% & 25\% & 15\% & 16.67\% \\ N & 1240 & 1200 & 8480 & 10,920 \\ n & 310 & 300 & 1211 & 1821 \\ \hline
100\% & 30\% & 30\% & 20\% & 22.97\% \\ N & 1240 & 1200 & 8480 & 10,920 \\ n & 413 & 400 & 1696 & 2509 \\ \hline
100\% & 35\% & 35\% & 25\% & 30.58\% \\ N & 1240 & 1200 & 8480 & 10,920 \\ n & 620 & 600 & 2120 & 3340 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Percentages used in the stratified random sampling method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measure** & **20\%, 20\%, 10\%** & **25\%, 25\%, 15\%** & **30\%, 30\%, 20\%** & **35\%, 35\%, 25\%** \\ \hline \(\kappa\) & 0.0042 & 0.0031 & 0.0024 & 0.0091 \\ \(\phi\) (cm) & 6.98 & 10.36 & 14.68 & 9.35 \\ \(\tau\) (cm) & 9.82 & 3.80 & 3.917 & 2.91 \\ \hline MSE & 8.2617 & 4.0836 & 3.4858 & 3.0376 \\ ABSE & 0.0195 & 0.0140 & 0.0130 & 0.0124 \\ CV & 0.3985 & 0.3264 & 0.2969 & 0.2505 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Posterior distribution of the parameters and prediction errors in the stratified random samples considered. Following the definitions for the range \(\phi\) and the total variance of the spatial effect \(\sigma_{W}^{2}\), we have, respectively, that the spatial correlation maximum is reached in approximately 975.32, i.e., in 9.75 cm, while the variability equals 0.041. Comparing these estimates with those obtained using the entire dataset for the nursery, we have that both the range (\(\phi\)) and the spatial variance (\(\sigma_{W}^{2}\)) are lower in random samples of 25%. This result seems logical and is a product of the sampling method. However, despite these differences, we can say that the range continues to describe the existence of a pattern of contagion among nearby salings, i.e., between salings located in the same row. This behaviour is observed especially in those rows located to the north and south of the nursery. The validity of the modeling is verified through the effective number of parameters \(p_{D}\) derived from calculation of the DIC and predictive measures generated from the main calculations of INLA. In particular, the predictive measure evaluated was the probability integral transform (PIT).