Over the 50 years of its existence, Baarda’s concept of reliability has been used as a standard practice for the quality control in geodesy and surveying. In this study, we analysed the pioneering work of Baarda (Publ Geod New Ser 2(4) 1967; Publ Geod New Ser 2(5) 1968) and recent studies on the subject. We highlighted that the advent of personal computers with powerful processors has rendered Monte Carlo method as an attractive and cost-effective approach for quality control purposes. We also provided an overview of the latest advances in the reliability theory for geodesy, with particular emphasis on Monte Carlo method.

An iterative outlier elimination procedure based on hypothesis testing, commonly known as Iterative Data Snooping (IDS) among geodesists, is often used for the quality control of modern measurement systems in geodesy and surveying. The test statistic associated with IDS is the extreme normalised least-squares residual. It is well-known in the literature that critical values (quantile values) of such a test statistic cannot be derived from well-known test distributions but must be computed numerically by means of Monte Carlo. This paper provides the first results on the Monte Carlo-based critical value inserted into different scenarios of correlation between outlier statistics. From the Monte Carlo evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, over-identifications and statistical overlap associated with IDS in the presence of a single outlier. On the basis of such probability levels, we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for cases in which IDS is in play. The MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances in which the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection but the lower the rates of outlier identification. In such a case, the larger the Type I Error, the larger the ratio between the MIB and MDB. We also highlight that an outlier becomes identifiable when the contributions of the measures to the wrong exclusion rate decline simultaneously. In this case, we verify that the effect of the correlation between outlier statistics on the wrong exclusion rate becomes insignificant for a certain outlier magnitude, which increases the probability of identification.

The goal of this paper is to evaluate the outlier identification performance of iterative Data Snooping (IDS) and L₁-norm in levelling networks by considering the redundancy of the network, number and size of the outliers. For this purpose, several Monte-Carlo experiments were conducted into three different levelling networks configurations. In addition, a new way to compare the results of IDS based on Least Squares (LS) residuals and robust estimators such as the L₁-norm has also been developed and presented. From the perspective of analysis only according to the success rate, it is shown that L₁-norm performs better than IDS for the case of networks with low redundancy $(\overline{r}<0.5)$, especially for cases where more than one outlier is present in the dataset. In the relationship between false positive rate and outlier identification success rate, however, IDS performs better than L₁-norm, independently of the levelling network configuration, number and size of outliers.

The relationship between the fires occurrences and diseases is an essential issue for making public health policy and environment protecting strategy. Thanks to the Internet, today, we have a huge amount of health data and fire occurrence reports at our disposal. The challenge, therefore, is how to deal with 4 Vs (volume, variety, velocity and veracity) associated with these data. To overcome this problem, in this paper, we propose a method that combines techniques based on Data Mining and Knowledge Discovery from Databases (KDD) to discover spatial and temporal association between diseases and the fire occurrences. Here, the case study was addressed to Malaria, Leishmaniasis and respiratory diseases in Brazil. Instead of losing a lot of time verifying the consistency of the database, the proposed method uses Decision Tree, a machine learning-based supervised classification, to perform a fast management and extract only relevant and strategic information, with the knowledge of how reliable the database is. Namely, States, Biomes and period of the year (months) with the highest rate of fires could be identified with great success rates and in few seconds. Then, the K-means, an unsupervised learning algorithms that solves the well-known clustering problem, is employed to identify the groups of cities where the fire occurrences is more expressive. Finally, the steps associated with KDD is perfomed to extract useful information from mined data. In that case, Spearman’s rank correlation coefficient, a nonparametric measure of rank correlation, is computed to infer the statistical dependence between fire occurrences and those diseases. Moreover, maps are also generated to represent the distribution of the mined data. From the results, it was possible to identify that each region showed a susceptible behaviour to some disease as well as some degree of correlation with fire outbreak, mainly in the drought period.

We present a numerical simulation method for designing geodetic networks. The quality criterion considered is based on the power of the test of data snooping testing procedure. This criterion expresses the probability of the data snooping to identify correctly an outlier. In general, the power of the test is defined theoretically. However, with the advent of the fast computers and large data storage systems, it can be estimated using numerical simulation. Here, the number of experiments in which the data snooping procedure identifies the outlier correctly is counted using Monte Carlos simulations. If the network configuration does not meet the reliability criterion at some part, then it can be improved by adding required observation to the surveying plan. The method does not use real observations. Thus, it depends on the geometrical configuration of the network; the uncertainty of the observations; and the size of outlier. The proposed method is demonstrated by practical application of one simulated leveling network. Results showed the needs of five additional observations between adjacent stations. The addition of these new observations improved the internal reliability of approximately 18%. Therefore, the final designed network must be able to identify and resist against the undetectable outliers - according to the probability levels.

Geodetic networks provide accurate three-dimensional control points for mapping activities, geoinformation, and infrastructure works. Accurate computation and adjustment are necessary, as all data collection is vulnerable to outliers. Applying a Least Squares (LS) process can lead to inaccuracy over many points in such conditions. Robust Estimator (RE) methods are less sensitive to outliers and provide an alternative to conventional LS. To solve the RE functions, we propose a new metaheuristic (MH), based on the Vortex Search (IVS) algorithm, along with a novel search space definition scheme. Numerous scenarios for a Global Navigation Satellite Systems (GNSS)-based network are generated to compare and analyze the behavior of several known REs. A classic iterative RE and an LS process are also tested for comparison. We analyze the median and trim position of several estimators, in order to verify their impact on the estimates. The tests show that IVS performs better than the original algorithm; therefore, we adopted it in all subsequent RE computations. Regarding network adjustments, outcomes in the parameter estimation show that REs achieve better results in large-scale outliers’ scenarios. For detection, both LS and REs identify most outliers in schemes with large outliers.