Exploring the bayesian hierarchical approach for the statistical modeling of spatial structures: application in population ecology

Sophie Ancelet
Abstract : For most ecological questions, the random processes studied are spatially structured and come from the combined effect of several observed or unobserved random variables interacting at various scales. In practice, when data can't be directly treated with traditional spatial structures, observations are often considered as independent. Moreover, the usual models are often based on hypotheses that are too simple with regards to the complexity of the studied phenomena. In the present work, the hierarchical modelling framework is combined with some spatial statistics tools to build specific functional random structures for complex and spatially structured phenomena in population ecology. Model inference is done under the bayesian framework using MCMC algorithms. In the first part, a spatial hierarchical model (called Geneclust) is developed to identify genetically homogeneous populations when genetic diversity varies continuously in space. A hidden Markov random field, used to model the spatial structure of genetic diversity, is combined with a bivariate model for the occurrence of genotypes to take into account the possible occurrence of inbreeding in some natural populations. In the second part of the thesis, a particular compound Poisson process, called law of leaks, is presented from the hierarchical point of view. The goal was to describe the process of sampling living organisms. This approach explicitly confronts the technical issue of modelling continuous zero-inflated data from sampling characterized many zero values and variable sampling effort. This model is combined with different area-based models to add spatial dependencies between geographical units then with a bivariate gaussian random field built by process convolutions to model the joint spatial distribution of two species. The fitting and predictive capacities of the different hierarchical models are compared to the traditional models from simulated and real data (Scandinavian brown bears, epibenthic invertebrates in Saint-Lawrence Gulf (Canada)
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Submitted on : Tuesday, March 24, 2009 - 8:00:00 AM
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Sophie Ancelet. Exploring the bayesian hierarchical approach for the statistical modeling of spatial structures: application in population ecology. Mathematics [math]. AgroParisTech, 2008. English. ⟨NNT : 2008AGPT0044⟩. ⟨pastel-00004396⟩

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