| 1. |
- Drees, Holger, et al.
(author)
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Limit Theorems for Empirical Processes of Cluster Functionals
- 2010
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In: Annals of statistics. - 0090-5364. ; 38:4, s. 2145-2186
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Journal article (peer-reviewed)abstract
- Let (X-n, i) 1 <= i <= n,m is an element of N be a triangular array of row-wise stationary R-d-valued random variables. We use a "blocks method" to define clusters of extreme values: the rows of (X-n, i) are divided into m(n) blocks (Y-n, j), and if a block contains at least one extreme value, the block is considered to contain a cluster. The cluster starts at the first extreme value in the block and ends at the last one. The main results are uniform central limit theorems for empirical processes Z(n)(f) := 1/root nv(n) Sigma(mn)(j=1) (f(Y-n,Y- j) - Ef(Y-n,Y- j)), for v(n) = P{X-n,X- i not equal 0} and f belonging to classes of cluster functionals, that is, functions of the blocks Y-n,Y- j which only depend on the cluster values and which are equal to 0 if Y-n,Y- j does not contain a cluster. Conditions for finite-dimensional convergence include beta-mixing, suitable Lindeberg conditions and convergence of covariances. To obtain full uniform convergence, we use either "bracketing entropy" or bounds on covering numbers with respect to a random semi-metric. The latter makes it possible to bring the powerful Vapnik-Cervonenkis theory to bear. Applications include multivariate tail empirical processes and empirical processes of cluster values and of order statistics in clusters. Although our main field of applications is the analysis of extreme values, the theory can be applied more generally to rare events occurring, for example, in nonparametric curve estimation.
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| 3. |
- Belzile, L. R., et al.
(author)
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Human mortality at extreme age
- 2021
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In: Royal Society Open Science. - : The Royal Society. - 2054-5703. ; 8:9
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Journal article (peer-reviewed)abstract
- We use a combination of extreme value statistics, survival analysis and computer-intensive methods to analyse the mortality of Italian and French semi-supercentenarians. After accounting for the effects of the sampling frame, extreme-value modelling leads to the conclusion that constant force of mortality beyond 108 years describes the data well and there is no evidence of differences between countries and cohorts. These findings are consistent with use of a Gompertz model and with previous analysis of the International Database on Longevity and suggest that any physical upper bound for the human lifespan is so large that it is unlikely to be approached. Power calculations make it implausible that there is an upper bound below 130 years. There is no evidence of differences in survival between women and men after age 108 in the Italian data and the International Database on Longevity, but survival is lower for men in the French data.
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| 4. |
- Belzile, Léo R., et al.
(author)
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Is There a Cap on Longevity? A Statistical Review
- 2022
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In: Annual Review of Statistics and Its Application. - : Annual Reviews. - 2326-8298 .- 2326-831X. ; 9, s. 21-45
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Research review (peer-reviewed)abstract
- There is sustained and widespread interest in understanding the limit, if there is any, to the human life span. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social security systems. A central question is whether the endpoint of the underlying lifetime distribution is finite. Recent analyses of data on the oldest human lifetimes have led to competing claims about survival and to some controversy, due in part to incorrect statistical analysis. This article discusses the particularities of such data, outlines correct ways of handling them, and presents suitable models and methods for their analysis. We provide a critical assessment of some earlier work and illustrate the ideas through reanalysis of semisupercentenarian lifetime data. Our analysis suggests that remaining life length after age 109 is exponentially distributed and that any upper limit lies well beyond the highest lifetime yet reliably recorded. Lower limits to 95% confidence intervals for the human life span are about 130 years, and point estimates typically indicate no upper limit at all.
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| 5. |
- Eriksson Barman, Sandra, 1985, et al.
(author)
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New characterization measures of pore shape and connectivity applied to coatings used for controlled drug release
- 2021
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In: Journal of Pharmaceutical Sciences. - : Elsevier BV. - 1520-6017 .- 0022-3549. ; 110:7, s. 2753-2764
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Journal article (peer-reviewed)abstract
- Pore geometry characterization-methods are important tools for understanding how pore structure influences properties such as transport through a porous material. Bottlenecks can have a large influence on transport and related properties. However, existing methods only catch certain types of bottleneck effects caused by variations in pore size. We here introduce a new measure, geodesic channel strength, which captures a different type of bottleneck effect caused by many paths coinciding in the same pore. We further develop new variants of pore size measures and propose a new way of visualizing 3-D characterization results using layered images. The new measures together with existing measures were used to characterize and visualize properties of 3-D FIB-SEM images of three leached ethyl-cellulose/hydroxypropyl-cellulose films. All films were shown to be anisotropic, and the strongest anisotropy was found in the film with lowest porosity. This film had very tortuous paths and strong geodesic channel-bottlenecks, while the paths through the other two films were relatively straight with well-connected pore networks. The geodesic channel strength was shown to give important new visual and quantitative insights about connectivity, and the new pore size measures provided useful information about anisotropies and inhomogeneities in the pore structures. The methods have been implemented in the freely available software MIST.
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| 6. |
- Eriksson Barman, Sandra, 1985, et al.
(author)
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Prediction of diffusive transport through polymer films from characteristics of the pore geometry
- 2019
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In: Aiche Journal. - : Wiley. - 0001-1541 .- 1547-5905. ; 65:1, s. 446-457
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Journal article (peer-reviewed)abstract
- Diffusive transport through porous materials is to a large extent determined by the microstructure of the material. To design materials with controlled transport properties, it is hence important to connect properties of the pore geometry to diffusive transport rates. Different kinds of microstructures from a stochastic model are generated and multiplicative regression is used to find relationships between geometric measures of the microstructures and numerically simulated diffusive transport. The main results are that the geodesic tortuosity explains a large part of the transport variation, and that the standard deviations we introduce further improves prediction. It was found that it is best to compute the tortuosity using the whole pore space, instead of using only the inlet, as is commonly done. The effects of calculating the measures using small samples of the pore structure were investigated, and a method for minimizing errors resulting from boundary effects was proposed.
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| 7. |
- Fager, Cecilia, 1990, et al.
(author)
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3D high spatial resolution visualisation and quantification of interconnectivity in polymer films
- 2020
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In: International Journal of Pharmaceutics. - : Elsevier B.V.. - 0378-5173 .- 1873-3476. ; 587
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Journal article (peer-reviewed)abstract
- A porous network acts as transport paths for drugs through films for controlled drug release. The interconnectivity of the network strongly influences the transport properties. It is therefore important to quantify the interconnectivity and correlate it to transport properties for control and design of new films. This work presents a novel method for 3D visualisation and analysis of interconnectivity. High spatial resolution 3D data on porous polymer films for controlled drug release has been acquired using a focused ion beam (FIB) combined with a scanning electron microscope (SEM). The data analysis method enables visualisation of pore paths starting at a chosen inlet pore, dividing them into groups by length, enabling a more detailed quantification and visualisation. The method also enables identification of central features of the porous network by quantification of channels where pore paths coincide. The method was applied to FIB-SEM data of three leached ethyl cellulose (EC)/hydroxypropyl cellulose (HPC) films with different weight percentages. The results from the analysis were consistent with the experimentally measured release properties of the films. The interconnectivity and porosity increase with increasing amount of HPC. The bottleneck effect was strong in the leached film with lowest porosity.
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| 10. |
- Guerin, Charles-Antoine, et al.
(author)
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Empirical testing of the infinite source poisson data traffice model
- 2003
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In: Stochastic models. ; 19, s. 156-196
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Journal article (peer-reviewed)abstract
- The infinite source Poisson model is a fluid queue approximation of network data transmission that assumes that sources begin constant rate transmissions of data at Poisson time points for random lengths of time. This model has been a popular one as analysts attempt to provide explanations for observed features in telecommunications data such as self-similarity, long range dependence and heavy tails. We survey some features of this model in cases where transmission length distributions have (a) tails so heavy that means are infinite, (b) heavy tails with finite mean and infinite variance and (c) finite variance. We survey the self-similarity properties of various descriptor processes in this model and then present analyses of four data sets which show that certain features of the model are consistent with the data while others are contradicted. The data sets are 1) the Boston University 1995 study of web sessions, 2) the UC Berkeley home IP HTTP data collected in November 1996, 3) traces collected in end of 1997 at a Customer Service Switch in Munich, and 4) detailed data from a corporate Ericsson WWW server from October 1998.
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