Distributional theory for the DIA method

Teunissen, Peter

doi:10.1007/s00190-017-1045-7

Cited by 113 publications

(102 citation statements)

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“…When q = n − u, an overall model test is performed. For more details about the overall model test, see, for example, [46,47].…”

Section: Binary Hypothesis Testing Versus Multiple Hypothesis Testingmentioning

confidence: 99%

“…Note that the decision rule (10) says that if the Baarda's w-test statistic is larger than some critical value k, i.e., a percentile of its probability distribution, then we reject the null hypothesis in favour of the alternative hypothesis. This is a special case of testing the null hypothesis H 0 against only one single alternative hypothesis H (i) A , and therefore, the rejection of the null hypothesis automatically implies the acceptance of the alternative hypothesis and vice versa [46,47]. In other words, the outlier detection automatically implies outlier identification and vice versa.…”

Section: Binary Hypothesis Testingmentioning

confidence: 99%

“…Of particular importance for quality control purposes are decision probabilities. Probability levels have already been described in the literature for the case in which data snooping is run once (i.e., only one single estimation and testing), as well as for the case in which the outlier is parameterised in the model (see, e.g., [2,[19][20][21]23,37,46,47]). For such cases, the probability of correct detection (P CD ) and correct identification (P CI ) and their corresponding Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) have already been described for data snooping [37,46].…”

mentioning

confidence: 99%

“…The evaluation of the probability levels associated with IDS is not a trivial task. When used for data snooping for a single run, the probabilities of IDS are multivariate integrals over complex regions [2,47]. This complexity is due to the fact that IDS is not only based on multiple hypothesis testing but also on multiple rounds of estimation, testing and exclusion.…”

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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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“…When q = n − u, an overall model test is performed. For more details about the overall model test, see, for example, [46,47].…”

Section: Binary Hypothesis Testing Versus Multiple Hypothesis Testingmentioning

confidence: 99%

Section: Binary Hypothesis Testingmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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A Monte Carlo-Based Outlier Diagnosis Method for Sensitivity Analysis

et al. 2020

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“…Many of the relevant probabilities in this contribution are multivariate integrals over complex regions (Teunissen, 2017). They therefore need to be computed by means of numerical simulation such as MCS.…”

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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How Abnormal Are the PDFs of the DIA Method: A Quality Description in the Context of GNSS

Zaminpardaz

Teunissen

2019

IX Hotine-Marussi Symposium on Mathematical Geodesy

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The DIA-method, for the detection, identification and adaptation of modeling errors, has been widely used in a broad range of applications including the quality control of geodetic networks and the integrity monitoring of GNSS models. The DIA-method combines two key statistical inference tools, estimation and testing. Through the former, one seeks estimates of the parameters of interest, whereas through the latter, one validates these estimates and corrects them for biases that may be present. As a result of this intimate link between estimation and testing, the quality of the DIA outcome Nx must also be driven by the probabilistic characteristics of both estimation and testing. In practice however, the evaluation of the quality of Nx is never carried out as such. Instead, use is made of the probability density function (PDF) of the estimator under the identified hypothesis, say Ox i , thereby thus neglecting the conditioning process that led to the decision to accept the i th hypothesis. In this contribution, we conduct a comparative study of the probabilistic properties of Nx and O x i . Our analysis will be carried out in the framework of GNSS-based positioning. We will also elaborate on the circumstances under which the distribution of the estimator Ox i provides either poor or reasonable approximations to that of the DIA-estimator Nx.

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Distributional theory for the DIA method

Cited by 113 publications

References 30 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

How Abnormal Are the PDFs of the DIA Method: A Quality Description in the Context of GNSS

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