## 2 Materials and Methods
### Agreement Techniques  
The study of agreement comprises of two important parts. The first part is to quantify the extent of agreement between two measurement methods/instruments/or procedures and to determine whether this is sufficient so that they can be used 'interchangeably'. The second part is to compare important characteristics of the measurement methods such as bias and precision [39]. The first goal of our study is the quantification of the difference between the core and the surface temperature. The second goal is the comparison of important characteristics such as bias and precision of the measurements since the bias reveals the trend of the difference along various ranges of temperature between the core and surface temperature of the fruit. The precision might reveal possible fluctuations of the temperature readings probably due to difference in temperature fluctuations in the two points of interest. The official and valid approach used to compare two different measurement methods or instruments lies in the field of statistical agreement [39]. We followed the approach proposed by [PERSON] [40] and [PERSON] et al. [41] based on measurement error models that predict the true latent trait using an empirical Bayes approach. An R package is available for the implementation of the method [42]. A graphical illustration of the estimated bias between measurement approaches and the precision of each is allowed as well. Since the package focuses on recalibration of the two methods the source code of the package is modified to remove the recalibration step, which is not relevant in our case. The adapted code is presented in detail in Supplementary Materials S2. The model used is the following [40]:  
\[y_{1 ij}=\beta_{0}+\beta_{1}x_{ij}+\varepsilon_{1 ij}\,,\,\varepsilon_{1 ij}|x_{i }\sim N\Big{(}0,\sigma_{\varepsilon_{1i}}^{2}(x_{ij};\theta_{1})\Big{)} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & 2 \({}^{\circ}\)C & 5 \({}^{\circ}\)C & 15 \({}^{\circ}\)C & 20 \({}^{\circ}\)C & 25 \({}^{\circ}\)C & 27 \({}^{\circ}\)C & 34 \({}^{\circ}\)C & 43 \({}^{\circ}\)C \\ \hline Mean & 3.663 & 5.897 & 15.439 & 18.8 & 26.948 & 33.931 & 31.414 & 43.289 \\ \hline Standard Deviation & 1.88 & 0.954 & 0.049 & 0.237 & 0.376 & 0.554 & 0.554 & 1.156 \\ \hline \end{tabular}
\end{table} 
Table 1: The means and standard deviations of the reference temperatures measured by the external temperature sensor per fixed condition. \[y_{2 ij}=x_{ij}+\varepsilon_{2 ij},\ \varepsilon_{2 ij}\big{|}x_{i}\sim N\Big{(}0, \sigma_{\varepsilon_{2j}}^{2}(x_{ij};\theta_{2})\Big{)} \tag{2}\]  
\[x_{i}\sim f_{x}\Big{(}\mu_{x},\sigma_{x}^{2}\Big{)}\]  
where \(y_{1 ij}\) is the proxy surface measurement for \(i=1,\ldots,8\) subjects, \(j=1,\ldots,15\) is the number of replications per subject, \(y_{2 ij}\) is the reference measurement (fruit core temperature in our case). The parameters \(\beta_{0}\) and \(\beta_{1}\) are the differential and proportional biases, respectively, while \(x_{ij}\) is a latent variable with density \(f_{x}\) representing the true unknown trait value, true temperature for individual \(i\) in our case. As a result, \(x_{ij}\equiv x_{i}\). Method by subject interactions are absorbed into the measurement error terms. The quantities \(\varepsilon_{1 ij}\), \(\varepsilon_{2 ij}\) represent measurement errors for measurements at the surface (1) and the core (2), respectively. It is assumed that the variances of these errors are heteroscedastic and increase/decrease with the level of the true latent trait \(x_{ij}\) in a way that depends on the parameter \(\theta_{1}\) and \(\theta_{2}\). These parameters quantify the trend of the variance's fluctuation.