| 1. |
- Kiriliouk, Anna, et al.
(author)
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Peaks over thresholds modelling with multivariate generalized Pareto distributions
- 2016
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Other publication (other academic/artistic)abstract
- The multivariate generalized Pareto distribution arises as the limit of a suitably normalized vector conditioned upon at least one component of that vector being extreme. Statistical modelling using multivariate generalized Pareto distributions constitutes the multivariate analogue of peaks over thresholds modelling with the univariate generalized Pareto distribution. We introduce a construction device which allows us to develop a variety of new and existing parametric tail dependence models. A censored likelihood procedure is proposed to make inference on these models, together with a threshold selectionprocedure and several goodness-of-fit diagnostics. We illustrate our methods on two data applications, one concerning the financial risk stemming from the stock prices of four large banks in the United Kingdom, and one aiming at estimating the yearly probability of a rainfall which could cause a landslide in northern Sweden.
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| 2. |
- Renner, Johan, 1977-
(author)
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Towards Subject Specific Aortic Wall Shear Stress : a combined CFD and MRI approach
- 2011
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Doctoral thesis (other academic/artistic)abstract
- The cardiovascular system is an important part of the human body since it transports both energy and oxygen to all cells throughout the body. Diseases in this system are often dangerous and cardiovascular diseases are the number one killer in the western world. Common cardiovascular diseases are heart attack and stroke, which origins from obstructed blood flow. It is generally important to understand the causes for these cardiovascular diseases. The main causes for these diseases are atherosclerosis development in the arteries (hardening and abnormal growth). This transform of the arterial wall is believed to be influenced by the mechanical load from the flowing blood on the artery and especially the tangential force the wall shear stress. To retrieve wall shear stress information in arteries invivo is highly interesting due to the coupling to atherosclerosis and indeed a challenge. The goal of this thesis is to develop, describe and evaluate an in-vivo method for subject specific wall shear stress estimations in the human aorta, the largest artery in the human body. The method uses an image based computational fluid dynamics approach in order to estimate the wall shear stress. To retrieve in-vivo geometrical descriptions of the aorta magnetic resonance imaging capabilities is used which creates image material describing the subject specific geometry of the aorta. Magnetic resonance imaging is also used to retrieve subject specific blood velocity information in the aorta. Both aortic geometry and velocity is gained at the same time. Thereafter the image material is interpreted using level-set segmentation in order to get a three-dimensional description of the aorta. Computational fluid dynamics simulations is applied on the subject specific aorta in order to calculate time resolved wall shear stress distribution at the entire aortic wall included in the actual model.This work shows that it is possible to estimate subject specific wall shear stress in the human aorta. The results from a group of healthy volunteers revealed that the arterial geometry is very subject specific and the different wall shear stress distributions have general similarities but the level and local distribution are clearly different. Sensitivity (on wall shear stress) to image modality, the different segmentation methods and different inlet velocity profiles have been tested, which resulted in these general conclusions:The aortic diameter from magnetic resonance imaging became similar to the reference diameter measurement method.The fast semi-automatic level-set segmentation method gave similar geometry and wall shear stress results when compared to a reference segmentation method.Wall shear stress distribution became different when comparing a simplified uniform velocity profile inlet boundary condition with a measured velocity profile.The method proposed in this thesis has the possibility to produce subject specific wall shear stress distribution in the human aorta. The method can be used for further medical research regarding atherosclerosis development and has the possibility for usage in clinical work.
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| 3. |
- Rootzén, Holger, 1945, et al.
(author)
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Multivariate generalized Pareto distributions: Parametrizations, representations, and properties
- 2018
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In: Journal of Multivariate Analysis. - : Elsevier BV. - 0047-259X .- 1095-7243. ; 165, s. 117-131
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Journal article (peer-reviewed)abstract
- © 2017 Elsevier Inc. Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized and represented in a number of different ways. Moreover, generalized Pareto distributions enjoy a number of interesting stability properties. An overview of the main features of such distributions is given, expressed compactly in several parametrizations, giving the potential user of these distributions a convenient catalogue of ways to handle and work with generalized Pareto distributions.
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