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Dresden, Germany

Lehmann R.,FH Dresden | Neitzel F.,Sudan University of Science and Technology
Journal of Geodesy | Year: 2013

Geodetic adjustment models are often set up in a way that the model parameters need to fulfil certain constraints. The normalized Lagrange multipliers have been used as a measure of the strength of constraint in such a way that if one of them exceeds in magnitude a certain threshold then the corresponding constraint is likely to be incompatible with the observations and the rest of the constraints. We show that these and similar measures can be deduced as test statistics of a likelihood ratio test of the statistical hypothesis that some constraints are incompatible in the same sense. This has been done before only for special constraints (Teunissen in Optimization and Design of Geodetic Networks, pp. 526-547, 1985). We start from the simplest case, that the full set of constraints is to be tested, and arrive at the advanced case, that each constraint is to be tested individually. Every test is worked out both for a known as well as for an unknown prior variance factor. The corresponding distributions under null and alternative hypotheses are derived. The theory is illustrated by the example of a double levelled line. © 2013 Springer-Verlag Berlin Heidelberg. Source

Meffert P.J.,TU Berlin | Dziock F.,FH Dresden
Biological Conservation | Year: 2012

Bird species of cultivated landscapes have been declining dramatically for decades. The main cause for this decline is intensified agricultural practice. At the same time, worldwide urbanisation increases and has severe impacts on land use. Urban wastelands, i.e., unused land within urban agglomerations, are known to provide habitat for endangered animals, but to date systematic research on birds is rare. We aim at assessing environmental characteristics of urban wastelands that meet the requirements of rare and declining bird species. In the city of Berlin, Germany, we surveyed birds on 55 wasteland sites dominated by sparse vegetation. Our analysis includes quantitative measurements of residential human density and degree of sealing at different spatial scales, a detailed vegetation mapping, and data on human intrusion. Boosted regression trees were used to model the occurrence of eight bird Species of European Conservation concern (SPEC). Overall we found 12 SPEC species; for eight data were sufficient to built models. Our findings reveal that the occurrence of endangered bird species depends most strongly on area size and vegetation structure and to a lesser extent on the composition of the urban matrix. On-site features accounted for roughly two third of the explained variance and degree of urbanisation in the surroundings for the remaining one third. Intrusion of humans or dogs had no measurable negative effect on species occurrence. As a rule of thumb, plots above 5. ha harbour SPEC species, those above 7. ha are valuable for several sensitive open-land bird species. We show that wasteland habitats have potential for nature conservation that should be considered by urban planners and landscape architects. Knowledge about crucial habitat features (few trees and shrubs, sparse vegetation) enables us to create and maintain urban green spaces that enhance protection of rare and declining species. Urban wastelands may not have the potential to fully compensate for changes and population declines outside urban areas, but they may help to offset the loss of biodiversity in the countryside. © 2012 Elsevier Ltd. Source

Lehmann R.,FH Dresden
Studia Geophysica et Geodaetica | Year: 2015

To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution, we compare the Akaike information criterion (AIC) and the Anderson-Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test. © 2015 Institute of Geophysics of the ASCR, v.v.i Source

We investigate extreme studentized and normalized residuals as test statistics for outlier detection in the Gauss-Markov model possibly not of full rank. We show how critical values (quantile values) of such test statistics are derived from the probability distribution of a single studentized or normalized residual by dividing the level of error probability by the number of residuals. This derivation neglects dependencies between the residuals. We suggest improving this by a procedure based on the Monte Carlo method for the numerical computation of such critical values up to arbitrary precision. Results for free leveling networks reveal significant differences to the values used so far. We also show how to compute those critical values for non-normal error distributions. The results prove that the critical values are very sensitive to the type of error distribution. © 2012 Springer-Verlag. Source

Lehmann R.,FH Dresden
Journal of Geodesy | Year: 2014

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide. © 2014, Springer-Verlag Berlin Heidelberg. Source

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