An Attempt to Analyse Baarda’s Iterative Data Snooping Procedure based on Monte Carlo Simulation

Rofatto, Vinicius Francisco; Matsuoka, Marcelo Tomio; Klein, Ivandro

doi:10.4314/sajg.v6i3.11

Cited by 15 publications

(18 citation statements)

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“…Rofatto et al [12,55] showed how to compute the probability levels associated with the IDS procedure. They introduced two new classes of wrong decisions for IDS, namely, over-identification positive and over-identification negative.…”

Section: On the Probability Levels Of Iterative Outlier Elimination Amentioning

confidence: 99%

“…Recent studies by Rofatto et al [12,55] provide an algorithm based on Monte Carlo to determine the probability levels associated with IDS. In that case, five classes of decisions for IDS are described, namely, the probability of correct identification (P CI ), the probability of missed detection (P MD ), the probability of wrong exclusion (P WE ), the probability of over-identification positive (P over+ ), and the probability of over-identification negative (P over− ), defined as follows:…”

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confidence: 99%

“…However, the procedure used by these authors [12,55] does not allow the user to control the Type I decision error (denoted by α ). The probability level α (known as the significance level of a test) defines the size of a test and is often called the "false alarm probability".…”

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confidence: 99%

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A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

et al. 2020

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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.

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Section: On the Probability Levels Of Iterative Outlier Elimination Amentioning

confidence: 99%

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confidence: 99%

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A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

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“…Thus, we suggest to the user to analyze the best scenario with different levels of significance (e.g. Rofatto et al, 2017). The analysis of the significance level is outside the scope of this paper and it will be addressed in a future research.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Therefore, the confidence level and the power of the test are the probabilities of the test result leading to correct decisions, as opposed to the occurrence of type I, II and III errors (see, for example, Förstner, 1983;Teunissen, 2006;Klein et al, 2015b). In addition to these probabilities, the DS can identify more observations than real number of outliers (Rofatto et al, 2017).…”

Section: Preliminary Conceptsmentioning

confidence: 99%

Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

2018

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Abstract: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.Keywords: Reliability, Outlier, Numerical Simulation, Monte Carlo, Design of geodetic networks. Resumo:Nós apresentamos um método de simulação numérica para planejamento de redes geodésicas. O critério de qualidade considerado é baseado no poder do teste do procedimento estatístico data snooping. Esse critério expressa a probabilidade do procedimento data snooping de identificar corretamente um outlier. Em geral, o valor do poder do teste é sempre desconhecido na prática (definido na teoria). Porém, com o advento de computadores mais rápidos e sistemas de armazenamento de dados de maior capacidade, o poder do teste pode ser estimado por meio de simulações numéricas. O número de experimentos que o procedimento data snooping identifica corretamente um outlier é quantificado por meio do método Monte Carlo de simulação. Se a configuração inicial da rede não atender o critério de confiabilidade, então uma nova observação é adicionada no projeto da rede. O método não faz uso de observações reais coletadas em campo, dependendo apenas da configuração geométrica da rede, das incertezas das observações e da magnitude dos outliers. A eficiência do método é verificada por meio de um exemplo numérico de uma rede de nivelamento geométrico simulada. Os resultados mostraram a necessidade de cinco observações adicionais entre os pontos adjacentes. A adição destas novas observações melhorou a confiabilidade interna da rede de aproximadamente 18%. Portanto, a rede é projetada de modo que seja capaz de identificar outliers e ainda resistir a outilers não identificados nas observações -de acordo com os níveis de probabilidade.

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Adaptive Quasi-Monte Carlo method for nonlinear function error propagation and its application in geodetic measurement

Wang

Luo

2021

Measurement

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An Attempt to Analyse Baarda’s Iterative Data Snooping Procedure based on Monte Carlo Simulation

Abstract: William Sealy Gosset, otherwise known as " Student", Fisher's disciple, was

Cited by 15 publications

References 22 publications

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

Adaptive Quasi-Monte Carlo method for nonlinear function error propagation and its application in geodetic measurement

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