149 research outputs found
Stochastic models which separate fractal dimension and Hurst effect
Fractal behavior and long-range dependence have been observed in an
astonishing number of physical systems. Either phenomenon has been modeled by
self-similar random functions, thereby implying a linear relationship between
fractal dimension, a measure of roughness, and Hurst coefficient, a measure of
long-memory dependence. This letter introduces simple stochastic models which
allow for any combination of fractal dimension and Hurst exponent. We
synthesize images from these models, with arbitrary fractal properties and
power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure
Conditional Sampling for Max-Stable Processes with a Mixed Moving Maxima Representation
This paper deals with the question of conditional sampling and prediction for
the class of stationary max-stable processes which allow for a mixed moving
maxima representation. We develop an exact procedure for conditional sampling
using the Poisson point process structure of such processes. For explicit
calculations we restrict ourselves to the one-dimensional case and use a finite
number of shape functions satisfying some regularity conditions. For more
general shape functions approximation techniques are presented. Our algorithm
is applied to the Smith process and the Brown-Resnick process. Finally, we
compare our computational results to other approaches. Here, the algorithm for
Gaussian processes with transformed marginals turns out to be surprisingly
competitive.Comment: 35 pages; version accepted for publication in Extremes. The final
publication is available at http://link.springer.co
Mark correlations: relating physical properties to spatial distributions
Mark correlations provide a systematic approach to look at objects both
distributed in space and bearing intrinsic information, for instance on
physical properties. The interplay of the objects' properties (marks) with the
spatial clustering is of vivid interest for many applications; are, e.g.,
galaxies with high luminosities more strongly clustered than dim ones? Do
neighbored pores in a sandstone have similar sizes? How does the shape of
impact craters on a planet depend on the geological surface properties? In this
article, we give an introduction into the appropriate mathematical framework to
deal with such questions, i.e. the theory of marked point processes. After
having clarified the notion of segregation effects, we define universal test
quantities applicable to realizations of a marked point processes. We show
their power using concrete data sets in analyzing the luminosity-dependence of
the galaxy clustering, the alignment of dark matter halos in gravitational
-body simulations, the morphology- and diameter-dependence of the Martian
crater distribution and the size correlations of pores in sandstone. In order
to understand our data in more detail, we discuss the Boolean depletion model,
the random field model and the Cox random field model. The first model
describes depletion effects in the distribution of Martian craters and pores in
sandstone, whereas the last one accounts at least qualitatively for the
observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics,
second Wuppertal conference "Spatial statistics and statistical physics
Proposta de um teste de hipótese para a existência de dependência espacial em dados geoestatÃsticos
A avaliação da significância da dependência espacial é importante para que se possa realizar uma inferência formal sobre a hipótese nula de não existência de dependência espacial em GeoestatÃstica. Com o presente estudo, objetivou-se construir um teste de significância para a hipótese nula de ausência de dependência espacial, para uma melhor decisão sobre a existência ou não de dependência em dados geoestatÃsticos. Para a construção do teste de dependência espacial levou-se em consideração as caracterÃsticas dos modelos ajustados ao semivariograma e, para a construção do teste de hipótese, inicialmente, foram definidos a hipótese nula e uma estatÃstica de teste gerada a partir do conceito de área de dependência espacial obtida no semivariograma. O teste foi construÃdo com base em simulações de fenômenos geoestatÃsticos apresentando caracterÃstica de efeito pepita puro, ou seja, fenômenos em que a hipótese nula foi verdadeira. Por fim, foi estudado o poder do teste para diferentes graus de dependência espacial simulados. O teste apresentou bom poder, sendo que este tendeu a 100% quando aumentou o grau de dependência espacial dos fenômenos geoestatÃsticos simulados
A copula model for marked point processes
The final publication (Diao, Liqun, Richard J. Cook, and Ker-Ai Lee. (2013) A copula model for marked point processes. Lifetime Data Analysis, 19(4): 463-489) is available at Springer via http://dx.doi.org/10.1007/s10985-013-9259-3Many chronic diseases feature recurring clinically important events. In addition, however, there
often exists a random variable which is realized upon the occurrence of each event reflecting the
severity of the event, a cost associated with it, or possibly a short term response indicating the
effect of a therapeutic intervention. We describe a novel model for a marked point process which
incorporates a dependence between continuous marks and the event process through the use of a
copula function. The copula formulation ensures that event times can be modeled by any intensity
function for point processes, and any multivariate model can be specified for the continuous
marks. The relative efficiency of joint versus separate analyses of the event times and the marks is
examined through simulation under random censoring. An application to data from a recent trial
in transfusion medicine is given for illustration.Natural Sciences and Engineering Research Council of Canada (RGPIN 155849); Canadian Institutes for Health Research (FRN 13887); Canada Research Chair (Tier 1) – CIHR funded (950-226626
Irradiated Male Tsetse from a 40-Year-Old Colony Are Still Competitive in a Riparian Forest in Burkina Faso
Background Tsetse flies are the cyclical vectors of African trypanosomosis that constitute a major constraint to development in Africa. Their control is an important component of the integrated management of these diseases, and among the techniques available, the sterile insect technique (SIT) is the sole that is efficient at low densities. The government of Burkina Faso has embarked on a tsetse eradication programme in the framework of the PATTEC, where SIT is an important component. The project plans to use flies from a Glossina palpalis gambiensis colony that has been maintained for about 40 years at the Centre International de Recherche-Développement sur l'Elevage en zone Subhumide (CIRDES). It was thus necessary to test the competitiveness of the sterile males originating from this colony. Methodology/Principal Findings During the period January-February 2010, 16,000 sterile male G. p. gambiensis were released along a tributary of the Mouhoun river. The study revealed that with a mean sterile to wild male ratio of 1.16 (s.d. 0.38), the abortion rate of the wild female flies was significantly higher than before (p = 0.026) and after (p = 0.019) the release period. The estimated competitiveness of the sterile males (Fried index) was 0.07 (s.d. 0.02), indicating that a sterile to wild male ratio of 14.4 would be necessary to obtain nearly complete induced sterility in the female population. The aggregation patterns of sterile and wild male flies were similar. The survival rate of the released sterile male flies was similar to that observed in 1983-1985 for the same colony. Conclusions/Significance We conclude that gamma sterilised male G. p. gambiensis derived from the CIRDES colony have a competitiveness that is comparable to their competitiveness obtained 35 years ago and can still be used for an area-wide integrated pest management campaign with a sterile insect component in Burkina Faso. (Résumé d'auteur
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