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 $N$-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 geoestatísticos

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 Geoestatística. 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 geoestatísticos. Para a construção do teste de dependência espacial levou-se em consideração as características dos modelos ajustados ao semivariograma e, para a construção do teste de hipótese, inicialmente, foram definidos a hipótese nula e uma estatística de teste gerada a partir do conceito de área de dependência espacial obtida no semivariograma. O teste foi construído com base em simulações de fenômenos geoestatísticos apresentando característica 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 geoestatísticos 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