Centre de documentation
scientifique

Bayesian statistics and Monte Carlo methods / Karl Rudolf Koch in Journal of geodetic science, vol 8 n° 1 (January 2018)  

Public [article]  inJournal of geodetic science > vol 8 n° 1 (January 2018) . - pp 18 - 29 Titre : Bayesian statistics and Monte Carlo methods Type de document : Article/Communication Auteurs : Karl Rudolf Koch, Auteur Année de publication : 2018 Article en page(s) : pp 18 - 29 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Statistiques [Termes IGN] matrice de covariance [Termes IGN] méthode de Monte-Carlo [Termes IGN] propagation d'erreur [Termes IGN] théorème de Bayes [Termes IGN] variable aléatoire [Termes IGN] vecteur aléatoire multidimensionnel Résumé : (Auteur) The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes’ theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. The Monte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum. Numéro de notice : A2018-613 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1515/jogs-2018-0003 Date de publication en ligne : 02/03/2018 En ligne : https://doi.org/10.1515/jogs-2018-0003 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=92646 [article]

Systematic effects in laser scanning and visualization by confidence regions / Karl Rudolf Koch in Journal of applied geodesy, vol 10 n° 4 (December 2016)  

Public [article]  inJournal of applied geodesy > vol 10 n° 4 (December 2016) . - pp 247 – 257 Titre : Systematic effects in laser scanning and visualization by confidence regions Type de document : Article/Communication Auteurs : Karl Rudolf Koch, Auteur ; Jan Martin Brockmann, Auteur Année de publication : 2016 Article en page(s) : pp 247 – 257 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Lasergrammétrie [Termes IGN] carte de confiance [Termes IGN] covariance [Termes IGN] densité de probabilité [Termes IGN] distribution de Gauss [Termes IGN] données lidar [Termes IGN] données localisées 3D [Termes IGN] ellipsoïde (géodésie) [Termes IGN] itération [Termes IGN] matrice de covariance [Termes IGN] mesure géométrique [Termes IGN] méthode de Monte-Carlo [Termes IGN] série temporelle [Termes IGN] visualisation Résumé : (auteur) A new method for dealing with systematic effects in laser scanning and visualizing them by confidence regions is derived. The standard deviations of the systematic effects are obtained by repeatedly measuring three-dimensional coordinates by the laser scanner. In addition, autocovariance and cross-covariance functions are computed by the repeated measurements and give the correlations of the systematic effects. The normal distribution for the measurements and the multivariate uniform distribution for the systematic effects are applied to generate random variates for the measurements and random variates for the measurements plus systematic effects. Monte Carlo estimates of the expectations and the covariance matrix of the measurements with systematic effects are computed. The densities for the confidence ellipsoid for the measurements and the confidence region for the measurements with systematic effects are obtained by relative frequencies. They only depend on the size of the rectangular volume elements for which the densities are determined. The problem of sorting the densities is solved by sorting distances together with the densities. This allows a visualization of the confidence ellipsoid for the measurements and the confidence region for the measurements with systematic effects. Numéro de notice : A2016-975 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article DOI : 10.1515/jag-2016-0012 En ligne : https://doi.org/10.1515/jag-2016-0012 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=83682 [article]

Minimal detectable outliers as measures of reliability / Karl Rudolf Koch in Journal of geodesy, vol 89 n° 5 (May 2015)  

Public [article]  inJournal of geodesy > vol 89 n° 5 (May 2015) . - pp 483-490 Titre : Minimal detectable outliers as measures of reliability Type de document : Article/Communication Auteurs : Karl Rudolf Koch, Auteur Année de publication : 2015 Article en page(s) : pp 483-490 Note générale : Bibliographe Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] B-Spline [Termes IGN] erreur systématique [Termes IGN] fiabilité des données [Termes IGN] méthode de Monte-Carlo [Termes IGN] réseau géodésique [Termes IGN] valeur aberrante Résumé : (auteur) The concept of reliability was introduced into geodesy by Baarda (A testing procedure for use in geodetic networks. Publications on Geodesy, vol. 2. Netherlands Geodetic Commission, Delft, 1968). It gives a measure for the ability of a parameter estimation to detect outliers and leads in case of one outlier to the MDB, the minimal detectable bias or outlier. The MDB depends on the non-centrality parameter of the χ2-distribution, as the variance factor of the linear model is assumed to be known, on the size of the outlier test of an individual observation which is set to 0.001 and on the power of the test which is generally chosen to be 0.80. Starting from an estimated variance factor, the F-distribution is applied here. Furthermore, the size of the test of the individual observation is a function of the number of outliers to keep the size of the test of all observations constant, say 0.05. The power of the test is set to 0.80. The MDBs for multiple outliers are derived here under these assumptions. The method is applied to the reconstruction of a bell-shaped surface measured by a laser scanner. The MDBs are introduced as outliers for the alternative hypotheses of the outlier tests. A Monte Carlo method reveals that due to the way of introducing the outliers, the false null hypotheses cannot be rejected on the average with a power of 0.80 if the MDBs are not enlarged by a factor. Numéro de notice : A2015-348 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-015-0793-5 Date de publication en ligne : 12/02/2015 En ligne : https://doi.org/10.1007/s00190-015-0793-5 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=76722 [article]

Robust estimations for the nonlinear Gauss Helmert model by the expectation maximization algorithm / Karl Rudolf Koch in Journal of geodesy, vol 88 n° 3 (March 2014)  

Public [article]  inJournal of geodesy > vol 88 n° 3 (March 2014) . - pp 263 - 271 Titre : Robust estimations for the nonlinear Gauss Helmert model by the expectation maximization algorithm Type de document : Article/Communication Auteurs : Karl Rudolf Koch, Auteur Année de publication : 2014 Article en page(s) : pp 263 - 271 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] covariance [Termes IGN] modèle de Gauss-Helmert [Termes IGN] modèle linéaire [Termes IGN] télémètre laser à balayage Résumé : (Auteur) For deriving the robust estimation by the EM (expectation maximization) algorithm for a model, which is more general than the linear model, the nonlinear Gauss Helmert (GH) model is chosen. It contains the errors-in-variables model as a special case. The nonlinear GH model is difficult to handle because of the linearization and the Gauss Newton iterations. Approximate values for the observations have to be introduced for the linearization. Robust estimates by the EM algorithm based on the variance-inflation model and the mean-shift model have been derived for the linear model in case of homoscedasticity. To derive these two EM algorithms for the GH model, different variances are introduced for the observations and the expectations of the measurements defined by the linear model are replaced by the ones of the GH model. The two robust methods are applied to fit by the GH model a polynomial surface of second degree to the measured three-dimensional coordinates of a laser scanner. This results in detecting more outliers than by the linear model. Numéro de notice : A2014-135 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-013-0681-9 Date de publication en ligne : 15/12/2013 En ligne : https://doi.org/10.1007/s00190-013-0681-9 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=33040 [article]

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-2014031	SL	Revue	Centre de documentation	Revues en salle	Disponible

Optimal regularization for geopotential model GOCO02S by Monte Carlo methods and multi-scale representation of density anomalies / Karl Rudolf Koch in Journal of geodesy, vol 86 n° 8 (August 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 8 (August 2012) . - pp 647 - 660 Titre : Optimal regularization for geopotential model GOCO02S by Monte Carlo methods and multi-scale representation of density anomalies Type de document : Article/Communication Auteurs : Karl Rudolf Koch, Auteur ; J. Brockmann, Auteur ; W.D. Schuh, Auteur Année de publication : 2012 Article en page(s) : pp 647 - 660 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] analyse de variance [Termes IGN] B-Spline [Termes IGN] données GOCE [Termes IGN] méthode de Monte-Carlo [Termes IGN] modèle de géopotentiel [Termes IGN] ondelette Résumé : (Auteur) GOCO02S is a combined satellite-only geopotential model, regularized from degrees 180 to 250 of the expansion into spherical harmonics. To investigate the start of the regularization, the normal equations of GOCO02S have been used to compute additional geopotential models by regularizations beginning at degrees 160, 200, 220 and with no regularization. Three different methods are applied to determine where to start the regularization. The simplest one considers the decrease of the degree variances of the not regularized solution. The second one tests for the same solution the hypothesis that the square root of the degree variance is equal to the value computed by the estimated harmonic coefficients. If the hypothesis has to be rejected for a certain degree, the error degree variance is so large that the estimated harmonic coefficients cannot be trusted anymore so that the regularization has to start at that degree. The third method uses the density anomalies by which the disturbing potential is caused resulting from the geopotential model. The density anomalies are well suited to visualize the effects of the higher degree harmonics. In contrast to the base functions of the harmonic coefficients with global support, the density anomalies are expressed by a B-spline surface with local support. Multi-scale representations were applied and the hypotheses tested that the wavelet coefficients are equal to zero. Accepting the hypotheses means that nonsignificant wavelet coefficients were determined which lead to nonsignificant density anomalies. By comparing these anomalies for different regularizations, the degree where to start the regularization is determined. It turns out that beginning the regularization at degree 180, as was done for GOCO02S, is a correct choice. Numéro de notice : A2012-377 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-012-0546-7 Date de publication en ligne : 24/02/2012 En ligne : https://doi.org/10.1007/s00190-012-0546-7 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31823 [article]

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
266-2012081	RAB	Revue	Centre de documentation	En réserve L003	Disponible

Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances / Karl Rudolf Koch in Journal of geodesy, vol 84 n° 6 (June 2010)  

Permalink

Bayesian inference with geodetic applications / Karl Rudolf Koch (1990)

Permalink

Model computations for different solutions of the geodetic boundary-value problem / Karl Rudolf Koch (1968)

Permalink

Solution of the geodetic boundary-value problem in case of a reference ellipsoide / Karl Rudolf Koch (1968)

Permalink