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A Bayesian tutorial for data assimilation
 Physica D
, 2007
"... Abstract Data assimilation is the process by which observational data are fused with scientific information. The Bayesian paradigm provides a coherent probabilistic approach for combining information, and thus is an appropriate framework for data assimilation. Viewing data assimilation as a problem ..."
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Abstract Data assimilation is the process by which observational data are fused with scientific information. The Bayesian paradigm provides a coherent probabilistic approach for combining information, and thus is an appropriate framework for data assimilation. Viewing data assimilation as a problem in Bayesian statistics is not new. However, the field of Bayesian statistics is rapidly evolving and new approaches for model construction and sampling have been utilized recently in a wide variety of disciplines to combine information. This article includes a brief introduction to Bayesian methods. Paying particular attention to data assimilation, we review linkages to optimal interpolation, kriging, Kalman filtering, smoothing, and variational analysis. Discussion is provided concerning Monte Carlo methods for implementing Bayesian analysis, including importance sampling, particle filtering, ensemble Kalman filtering, and Markov chain Monte Carlo sampling. Finally, hierarchical Bayesian modeling is reviewed. We indicate how this approach can be used to incorporate significant physically based prior information into statistical models, thereby accounting for uncertainty. The approach is illustrated in a simplified advectiondiffusion model.
7. Author(s)
, 2005
"... The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Governm ..."
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The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the contents or use of the information contained in this document. This report does not constitute a standard, specification, or regulation. The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers’ names appear in this report only because they are considered essential to the objective of the document. About the PCC Center/CTRE
8 Modeling Disease Dynamics: Cholera As a Case Study
"... Disease dynamics are modeled at a population level in order to create a conceptual framework to think about the spread and prevention of disease, to make forecasts and policy decisions, and to ask and answer scientific questions concerning disease mechanisms such as discovering relevant covariates. ..."
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Disease dynamics are modeled at a population level in order to create a conceptual framework to think about the spread and prevention of disease, to make forecasts and policy decisions, and to ask and answer scientific questions concerning disease mechanisms such as discovering relevant covariates. Population models draw on
Mechanicalstatistical modelling in ecology: from outbreak detections to pest dynamics
, 2008
"... Abstract. Knowledge about largescale and longterm dynamics of (natural) populations is required to assess the efficiency of control strategies, the potential for longterm persistence, and the adaptability to global changes such as habitat fragmentation and global warming. For most natural populat ..."
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Abstract. Knowledge about largescale and longterm dynamics of (natural) populations is required to assess the efficiency of control strategies, the potential for longterm persistence, and the adaptability to global changes such as habitat fragmentation and global warming. For most natural populations, such as pest populations, largescale and longterm surveys cannot be carried out at a high resolution. For instance, for population dynamics characterised by irregular abundance explosions, i.e. outbreaks, it is common to report detected outbreaks rather than measuring the population density at every location and time event. Here, we propose a mechanicalstatistical model for analysing such outbreak occurrence data and making inference about population dynamics. This spatiotemporal model contains the main mechanisms of the dynamics and describes the observation process. This construction enables us to account for the discrepancy between the phenomenon scale and the sampling scale. We propose the Bayesian method to estimate model parameters, pest densities and hidden factors, i.e. variables involved in the dynamics but not observed. The model was specified and used to learn about the dynamics of the European pine sawfly (Neodiprion sertifer Geoffr., an insect causing major defoliation of pines in northern Europe) based on Finnish sawfly data covering the years 1961–1990. In this application, a dynamical BevertonHolt model including a hidden regime variable was incorporated into the model to deal with large variations in the population densities.
A unified statistical approach for simulation, modelling, analysis and mapping of environmental data
 Simulation
, 2010
"... In this paper, hierarchical models are proposed as a general approach for spatiotemporal problems, including dynamical mapping, and the analysis of the outputs from complex environmental modeling chains. In this frame, it is easy to define various model components concerning both model outputs and ..."
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In this paper, hierarchical models are proposed as a general approach for spatiotemporal problems, including dynamical mapping, and the analysis of the outputs from complex environmental modeling chains. In this frame, it is easy to define various model components concerning both model outputs and empirical data and to cover with both spatial and temporal correlation. Moreover, special sensitivity analysis techniques are developed for understanding both model components and mapping capability. The motivating application is the dynamical mapping of airborne particulate matters for risk monitoring using data from both a monitoring network and a computer model chain, which includes an emission, a meteorological and a chemicaltransport module. Model estimation is determined by the ExpectationMaximization (EM) algorithm associated with simulationbased spatiotemporal parametric bootstrap. Applying sensitivity analysis techniques to the same hierarchical model provides interesting insights into the computer model chain.
Spatiotemporal modeling of environmental processes: nitrogen oxides concentrations in the Tuscany region
, 2009
"... ..."
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"... Summary Hierarchical biological scales permeate research in tree physiology and represent multiple sources of variation. We discuss the importance of matching the sampling and analysis scales to biological scales in the data. The advantages of statistical hierarchical modeling are demonstrated usin ..."
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Summary Hierarchical biological scales permeate research in tree physiology and represent multiple sources of variation. We discuss the importance of matching the sampling and analysis scales to biological scales in the data. The advantages of statistical hierarchical modeling are demonstrated using the relationship between specific conductivity and tracheid diameter of secondary xylem as an example. The structure and results of three statistical models were compared within a Bayesian context: a simple linear regression (SLR); a repeated measures analysis (REP); and a hierarchical model (HM). The models share similar mean structures but differ in how variation is partitioned among scales: the SLR model assumes independence among observations (variation came from only a single scale); the REP allows multiple observations of each tree to be correlated; and the HM incorporates features of the REP with an additional variance structure that partitions variation across a broader scale. Our data included hierarchical scales of position on the tree, tree, fertilization treatment and species (Pseudotsuga menziesii (Mirb.) Franco). The HM gave more precise estimates for model parameters, was more robust to outliers, provided a more detailed description of covariances within the data at multiple scales compared with the SLR and REP and increased our ability to detect differences among positions on the tree. The proper statistical analyses increase the value of research by allowing the most exact interpretation.
The Strengths and Limitations of Hierarchical Statistical Modeling
, 2007
"... Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process error are often the only sources of uncertainty confronted ..."
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Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process error are often the only sources of uncertainty confronted when addressing complex ecological problems, yet analyses need to account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework for accounting for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and nonBayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline of notation and technology from which discussion on hierarchical statistical modeling in ecology can emanate. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable uncertainties, even if practicalities sometimes necessitate pragmatic compromises. 1.
THESE Pour obtenir le grade de
, 2013
"... Dynamique et assemblage des communautés adventices: Approche par modélisation statistique ..."
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Dynamique et assemblage des communautés adventices: Approche par modélisation statistique