# A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

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Graduate Program in Remote Sensing, Federal University of Rio Grande do Sul, Porto Alegre 91501970, Brazil

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Institute of Geography, Federal University of Uberlandia, Monte Carmelo 38500-000, Brazil

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Graduate Program in Agriculture and Geospatial Information, Federal University of Uberlândia, Monte Carmelo 38500-000, Brazil

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Graduate Program in Applied Computing, Unisinos University, Av. Unisinos, 950, São Leopoldo 93022-000, Brazil

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Department of Civil Construction, Federal Institute of Santa Catarina, Florianopolis 88020-300, Brazil

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Graduate Program in Geodetic Sciences, Federal University of Paraná, Curitiba 81531-990, Brazil

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Author to whom correspondence should be addressed.

Received: 24 January 2020 / Revised: 25 February 2020 / Accepted: 4 March 2020 / Published: 6 March 2020

(This article belongs to the Section Engineering Remote Sensing)

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.