Literatura académica sobre el tema "Spatio-temporal random fields"
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Artículos de revistas sobre el tema "Spatio-temporal random fields":
1
Descombes, X., F. Kruggel y D. Y. Von Cramon. "Spatio-temporal fMRI analysis using Markov random fields". IEEE Transactions on Medical Imaging 17, n.º 6 (1998): 1028–39. http://dx.doi.org/10.1109/42.746636.
2
De Iaco, S. y D. Posa. "Predicting spatio-temporal random fields: Some computational aspects". Computers & Geosciences 41 (abril de 2012): 12–24. http://dx.doi.org/10.1016/j.cageo.2011.11.014.
3
Piatkowski, Nico, Sangkyun Lee y Katharina Morik. "Spatio-temporal random fields: compressible representation and distributed estimation". Machine Learning 93, n.º 1 (25 de julio de 2013): 115–39. http://dx.doi.org/10.1007/s10994-013-5399-7.
4
Ip, Ryan H. L. y W. K. Li. "Matérn cross-covariance functions for bivariate spatio-temporal random fields". Spatial Statistics 17 (agosto de 2016): 22–37. http://dx.doi.org/10.1016/j.spasta.2016.04.004.
5
Salvaña, Mary Lai O. y Marc G. Genton. "Nonstationary cross-covariance functions for multivariate spatio-temporal random fields". Spatial Statistics 37 (junio de 2020): 100411. http://dx.doi.org/10.1016/j.spasta.2020.100411.
6
Fontanella, L., L. Ippoliti, R. J. Martin y S. Trivisonno. "Interpolation of spatial and spatio-temporal Gaussian fields using Gaussian Markov random fields". Advances in Data Analysis and Classification 2, n.º 1 (abril de 2008): 63–79. http://dx.doi.org/10.1007/s11634-008-0019-2.
7
Das, Sonjoy, Roger Ghanem y Steven Finette. "Polynomial chaos representation of spatio-temporal random fields from experimental measurements". Journal of Computational Physics 228, n.º 23 (diciembre de 2009): 8726–51. http://dx.doi.org/10.1016/j.jcp.2009.08.025.
8
Western, Luke M., Zhe Sha, Matthew Rigby, Anita L. Ganesan, Alistair J. Manning, Kieran M. Stanley, Simon J. O'Doherty, Dickon Young y Jonathan Rougier. "Bayesian spatio-temporal inference of trace gas emissions using an integrated nested Laplacian approximation and Gaussian Markov random fields". Geoscientific Model Development 13, n.º 4 (28 de abril de 2020): 2095–107. http://dx.doi.org/10.5194/gmd-13-2095-2020.
Resumen
Abstract. We present a method to infer spatially and spatio-temporally correlated emissions of greenhouse gases from atmospheric measurements and a chemical transport model. The method allows fast computation of spatial emissions using a hierarchical Bayesian framework as an alternative to Markov chain Monte Carlo algorithms. The spatial emissions follow a Gaussian process with a Matérn correlation structure which can be represented by a Gaussian Markov random field through a stochastic partial differential equation approach. The inference is based on an integrated nested Laplacian approximation (INLA) for hierarchical models with Gaussian latent fields. Combining an autoregressive temporal correlation and the Matérn field provides a full spatio-temporal correlation structure. We first demonstrate the method on a synthetic data example and follow this using a well-studied test case of inferring UK methane emissions from tall tower measurements of atmospheric mole fraction. Results from these two test cases show that this method can accurately estimate regional greenhouse gas emissions, accounting for spatio-temporal uncertainties that have traditionally been neglected in atmospheric inverse modelling.
9
Jadaliha, Mahdi, Jinho Jeong, Yunfei Xu, Jongeun Choi y Junghoon Kim. "Fully Bayesian Prediction Algorithms for Mobile Robotic Sensors under Uncertain Localization Using Gaussian Markov Random Fields". Sensors 18, n.º 9 (30 de agosto de 2018): 2866. http://dx.doi.org/10.3390/s18092866.
Resumen
In this paper, we present algorithms for predicting a spatio-temporal random field measured by mobile robotic sensors under uncertainties in localization and measurements. The spatio-temporal field of interest is modeled by a sum of a time-varying mean function and a Gaussian Markov random field (GMRF) with unknown hyperparameters. We first derive the exact Bayesian solution to the problem of computing the predictive inference of the random field, taking into account observations, uncertain hyperparameters, measurement noise, and uncertain localization in a fully Bayesian point of view. We show that the exact solution for uncertain localization is not scalable as the number of observations increases. To cope with this exponentially increasing complexity and to be usable for mobile sensor networks with limited resources, we propose a scalable approximation with a controllable trade-off between approximation error and complexity to the exact solution. The effectiveness of the proposed algorithms is demonstrated by simulation and experimental results.
10
Ghosh, Debraj y Anup Suryawanshi. "Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition". Communications in Computational Physics 16, n.º 1 (julio de 2014): 75–95. http://dx.doi.org/10.4208/cicp.201112.191113a.
Resumen
AbstractA new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loève (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.
Tesis sobre el tema "Spatio-temporal random fields":
1
Dai, Luyan. "Topics in objective bayesian methodology and spatio-temporal models". Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/6084.
Resumen
Thesis (Ph. D.)--University of Missouri-Columbia, 2008.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 4, 2009) Vita. Includes bibliographical references.
2
Jiang, Huijing. "Statistical computation and inference for functional data analysis". Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37087.
Resumen
My doctoral research dissertation focuses on two aspects of functional data analysis (FDA): FDA under spatial interdependence and FDA for multi-level data.
The first part of my thesis focuses on developing modeling and inference procedure for functional data under spatial dependence. The methodology introduced in this part is motivated by a research study on inequities in accessibility to financial services.
The first research problem in this part is concerned with a novel model-based method for clustering random time functions which are spatially interdependent. A cluster consists of time functions which are similar in shape. The time functions are decomposed into spatial global and time-dependent cluster effects using a semi-parametric model. We also assume that
the clustering membership is a realization from a Markov random field. Under these model assumptions, we borrow information across curves from nearby locations resulting in enhanced estimation accuracy of the cluster effects and of the cluster membership. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small number of time points, high noise level and varying dependence structures. Over all simulation settings, the spatial-functional clustering method outperforms existing model-based clustering methods. In the case study presented in this project, we focus on estimates and classifies service accessibility patterns varying over a large geographic area (California and Georgia) and over a period of 15 years. The focus of this study is on financial services but it generally applies to any other service operation.
The second research project of this part studies an association analysis of space-time varying processes, which is rigorous, computational feasible and implementable with standard software. We introduce general measures to model different aspects of the temporal and spatial association between processes varying in space and time. Using a nonparametric spatiotemporal model, we show that the proposed association estimators are asymptotically unbiased and consistent. We complement the point association estimates with simultaneous confidence bands to assess the uncertainty in the point estimates. In a simulation study, we evaluate the accuracy of the association estimates with respect to the sample size as well as the coverage of the confidence bands. In the case study in this project, we investigate the association between service accessibility and income level. The primary objective of this association analysis is to assess whether there are significant changes in the income-driven equity of financial service accessibility over time and to identify potential under-served markets.
The second part of the thesis discusses novel statistical methodology for analyzing multilevel functional data including a clustering method based on a functional ANOVA model and a spatio-temporal model for functional data with a nested hierarchical structure. In this part, I introduce and compare a series of clustering approaches for multilevel functional data. For brevity, I present the clustering methods for two-level data: multiple samples of random functions, each sample corresponding to a case and each random function within a sample/case corresponding to a measurement type. A cluster consists of cases which have similar within-case means (level-1 clustering) or similar between-case means (level-2 clustering). Our primary focus is to evaluate a model-based clustering to more straightforward hard clustering methods. The clustering model is based on a multilevel functional principal component analysis. In a simulation study, we assess the estimation accuracy of our clustering algorithm under a series of settings: small vs. moderate number of time points, high noise level and small number of measurement types. We demonstrate the applicability of the clustering analysis to a real data set consisting of time-varying sales for multiple products sold by a large retailer in the U.S.
My ongoing research work in multilevel functional data analysis is developing a statistical model for estimating temporal and spatial associations of a series of time-varying variables with an intrinsic nested hierarchical structure. This work has a great potential in many real applications where the data are areal data collected from different data sources and over geographic regions of different spatial resolution.
3
Sánchez, Jiménez Oscar. "On the stochastic response of rotor-blade models with Floquet modal theory : applications to time-dependent reliability of tidal turbine blades". Electronic Thesis or Diss., Normandie, 2023. http://www.theses.fr/2023NORMIR39.
Resumen
Le sujet d'étude est la réponse d’un système mécanique déterministe en rotation et soumis à des sollicitations stochastiques. Pour cela, un modèle mécano-probabiliste est développé, résultant de la combinaison de deux éléments : le système mécanique au comportement dit non-standard, et les sollicitations, représentées par un champ stochastique corrélé. L'application vise l'analyse fiabiliste d’une hydrolienne, décrite par un modèle mécanique d’ordre réduit. Plusieurs méthodes sont présentées, comparées et leurs limitations sont mises en évidence. Les résultats obtenus sont contrastés avec ceux de la bibliographie. En particulier, l’aspect innovant se trouve dans le type de quantité mécanique modélisée, le traitement et l'interprétation des quantités modales, et le type de processus stochastique considéré comme sollicitation. Plus précisément, le modèle dynamique développé décrit une classe de systèmes mécaniques de type rotor-pale. Il a été construit par une combinaison judicieuse de résultats des domaines de l'éolien, l'hydrolien, la dynamique des rotors et des vibrations mécaniques. La formulation lagrangienne de la mécanique analytique est utilisée pour obtenir les équations du système dynamique. L'assemblage obtenu avec des composants élastiques linéaires, introduits avec leur comportement modal, produit des termes instationnaires, résultant dans des équations différentielles ordinaires à coefficients périodiques. Pour l'analyse de ce problème mécanique déterministe, l’analyse modale numérique traditionnelle est ici étendue grâce à la théorie de Floquet. La réponse du système est formulée en termes des exposants caractéristiques du système et des vecteurs propres de Floquet, ou vecteurs propres périodiques, permettant une représentation modale de la matrice de transition de Floquet. Diverses méthodes peuvent alors être appliquées pour l'analyse modale du système et on propose une nouvelle méthode basée sur la représentation temps-fréquence grâce aux ondelettes périodiques généralisées. Pour considérer les sollicitations aléatoires instationnaires et non-gaussiennes, on utilise une écriture innovante pour la propagation des moments. L’avantage de cette technique vient de l’aspect pratique et systématique des développements, ce qui est particulièrement avantageux lorsqu'elle est appliquée à des champs spatio-temporels instationnaires. En combinant cette technique avec une méthode d’estimation de la densité de probabilité basée sur le principe d’entropie maximale, nous arrivons à l’estimation de la distribution des valeurs extrêmes de la réponse cherchée en considérant le problème de dépassement d’un seuil par ce processus instationnaire, permettant ainsi la résolution du problème posé en termes de fiabilité dépendante du tempsThe response of a deterministic rotating mechanical system under stochastic excitation is studied. A mechanical-probabilistic model is developed to combine the relevant characteristics of both aspects of the study: the behavior of this non-standard class of mechanical system and the random properties of correlated stochastic fields describing load processes. The results are applied to a reliability analysis of a reduced order model of a tidal turbine. Semi-analytic and empirical ( in the Monte-Carlo simulation sense) results are obtained, compared and contrasted. The results are framed with respect to the existing literature, and it is found that they provide an innovative treatment of the problem, in terms of the dynamical choices reflected in the model, in the presentation and interpretation of the modal aspects of the system, and in the type of stochastic inputs considered. We develop a dynamical model describing a broad class of mechanical system that models a rotor-blade structure. The model is informed by careful consideration of previous results, with the aim of constructing a reduced model that captures essential characteristics of the vibratory behavior of the structure. Lagrangian formalism is utilized to obtain the equations of motion. The presence of elastic components, which are discretized in a modal way, results in a system of ordinary differential equations with periodic coefficients. The Floquet theory of Linear time-periodic systems is applied on the deterministic dynamical model to synthesize an extension of traditional modal analysis to systems with periodic coefficients. The response of the system is formulated in terms of Floquet exponents and the associated Floquet periodic eigenvectors, from which the Floquet State Transition Matrix can be obtained. Several methods are applied to the modal study of the system, and a new time-frequency approach is proposed based on PGHW wavelets and its associated scalogram. Using an innovative notation to describe probabilistic moments of stochastic quantities, a moment propagation scheme is presented and exploited. The advantages of the treatment, particularly in the case of spatio-temporal stochastic fields, is in its applicability and systematic structure of development. This moment propagation strategy is coupled with a maximum entropy formulation to reconstruct the probability density function of the response and obtain important descriptors of the response, such as the Extreme Value Distribution. The moment propagation technique presented is applied to nonstationary processes. The results from Modal Floquet theory are integrated into this analysis. The problem of crossings of a certain threshold is considered for this type of nonstationary stochastic process. Their response is shown to yield a time-dependent reliability problem, which is resolved using the estimated EVD and then by numerical simulation
4
Zhuang, Lili. "Bayesian Dynamical Modeling of Count Data". The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1315949027.
5
Low, Choy Samantha Jane. "Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour". Thesis, Queensland University of Technology, 2001. https://eprints.qut.edu.au/37098/12/Samantha%20Low%20Choy%20Thesis.pdf.
Resumen
This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions.
The essence of the thesis can be described as follows.
Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this.
Two main approaches to modelling and inference are investigated in this thesis.
The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors.
The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics.
Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method.
Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7.
Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time.
Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.
6
Deregnaucourt, Thomas. "Prédiction spatio-temporelle de surfaces issues de l'imagerie en utilisant des processus stochastiques". Thesis, Université Clermont Auvergne (2017-2020), 2019. http://www.theses.fr/2019CLFAC088.
Resumen
La prédiction de surface est désormais une problématique importante dans de multiples domaines, tels que la vision par ordinateur, la simulation d'avatars en cinématographie ou dans les jeux vidéo, etc. Une surface pouvant être statique ou dynamique, c'est-à-dire évoluant dans le temps, le problème peut être séparé en deux catégories : un problème de prédiction spatial et un problème de prédiction spatio-temporel. Afin de proposer une nouvelle approche à chacune de ces problématiques, ce travail de thèse a été séparé en deux parties.Nous avons d'abord cherché à prédire une surface statique, qui est supposée cylindrique, en la connaissant partiellement sous la forme de courbes. L'approche que nous avons proposée consiste à déformer un cylindre sur les courbes connues afin de reconstruire la surface d'intérêt. Tout d'abord, une correspondance entre les courbes connues et le cylindre est générée à l'aide d'outils d'analyse de forme. Une fois cette étape effectuée, une interpolation du champ de déformation, qui a été supposé gaussien, a été estimée en se basant sur le maximum de vraisemblance d'une part, et par inférence bayésienne d'autre part. La méthodologie a par la suite été appliquée à des données réelles provenant de deux domaines de l'imagerie : l'imagerie médicale et l'infographie. Les divers résultats obtenus montrent que la méthode proposée surpasse les méthodes existantes dans la littérature, avec de meilleurs résultats en utilisant l'inférence bayésienne.Dans un second temps, nous nous sommes intéressés à la prédiction spatio-temporelle de surfaces dynamiques. L'objectif était de prédire entièrement une surface dynamique à partir de sa surface initiale. La prédiction nécessitant une phase d'apprentissage à partir d'observations connues, nous avons tout d'abord développé un outil d'analyse spatio-temporel de surfaces. Cette analyse se base sur des outils d'analyse de forme, et permet un meilleur apprentissage pour la prédiction. Une fois cette étape préliminaire effectuée, nous avons estimé la déformation temporelle de la surface dynamique à prédire. Plus précisément, une adaptation, applicable sur l'espace des surfaces, des estimateurs couramment utilisés en statistique a été utilisée. En appliquant la déformation estimée sur la surface initiale, une estimation de la surface dynamique a ainsi été créée. Cette méthodologie a par la suite été utilisée pour prédire des expressions 4D du visage, ce qui permet de générer des expressions visuellement convaincantesThe prediction of a surface is now an important problem due to its use in multiple domains, such as computer vision, the simulation of avatars for cinematography or video games, etc. Since a surface can be static or dynamic, i.e. evolving with time, this problem can be separated in two classes: a spatial prediction problem and a spatio-temporal one. In order to propose a new approach for each of these problems, this thesis works have been separated in two parts.First of all, we have searched to predict a static surface, which is supposed cylindrical, knowing it partially from curves. The proposed approach consisted in deforming a cylinder on the known curves in order to reconstruct the surface of interest. First, a correspondence between known curves and the cylinder is generated with the help of shape analysis tools. Once this step done, an interpolation of the deformation field, which is supposed Gaussian, have been estimated using maximum likelihood and Bayesian inference. This methodology has then been applied to real data from two domains of imaging: medical imaging and infography. The obtained results show that the proposed approach exceeds the existing methods in the literature, with better results using Bayesian inference.In a second hand, we have been interested in the spatio-temporal prediction of dynamic surfaces. The objective was to predict a dynamic surface based on its initial surface. Since the prediction needs to learn on known observations, we first have developed a spatio-temporal surface analysis tool. This analysis is based on shape analysis tools, and allows a better learning. Once this preliminary step done, we have estimated the temporal deformation of the dynamic surface of interest. More precisely, an adaptation, with is usable on the space of surfaces, of usual statistical estimators has been used. Using this estimated deformation on the initial surface, an estimation of the dynamic surface has been created. This process has then been applied for predicting 4D expressions of faces, which allow us to generate visually convincing expressions
7
Salvaña, Mary Lai O. "Lagrangian Spatio-Temporal Covariance Functions for Multivariate Nonstationary Random Fields". Thesis, 2021. http://hdl.handle.net/10754/669674.
Resumen
In geostatistical analysis, we are faced with the formidable challenge of specifying a valid
spatio-temporal covariance function, either directly or through the construction of processes.
This task is di cult as these functions should yield positive de nite covariance matrices. In
recent years, we have seen a
ourishing of methods and theories on constructing spatiotemporal
covariance functions satisfying the positive de niteness requirement. The current
state-of-the-art when modeling environmental processes are those that embed the associated
physical laws of the system. The class of Lagrangian spatio-temporal covariance functions
ful lls this requirement. Moreover, this class possesses the allure that they turn already
established purely spatial covariance functions into spatio-temporal covariance functions by
a direct application of the concept of Lagrangian reference frame. In the three main chapters
that comprise this dissertation, several developments are proposed and new features
are provided to this special class. First, the application of the Lagrangian reference frame
on transported purely spatial random elds with second-order nonstationarity is explored,
an appropriate estimation methodology is proposed, and the consequences of model misspeci
cation is tackled. Furthermore, the new Lagrangian models and the new estimation
technique are used to analyze particulate matter concentrations over Saudi Arabia. Second,
a multivariate version of the Lagrangian framework is established, catering to both secondorder
stationary and nonstationary spatio-temporal random elds. The capabilities of the
Lagrangian spatio-temporal cross-covariance functions are demonstrated on a bivariate reanalysis
climate model output dataset previously analyzed using purely spatial covariance functions. Lastly, the class of Lagrangian spatio-temporal cross-covariance functions with
multiple transport behaviors is presented, its properties are explored, and its use is demonstrated
on a bivariate pollutant dataset of particulate matter in Saudi Arabia. Moreover,
the importance of accounting for multiple transport behaviors is discussed and validated
via numerical experiments. Together, these three extensions to the Lagrangian framework
makes it a more viable geostatistical approach in modeling realistic transport scenarios.
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Qadir, Ghulam A. "Flexible Covariance Models for Spatio-Temporal and Multivariate Spatial Random Fields". Thesis, 2021. http://hdl.handle.net/10754/669402.
Resumen
The modeling of spatio-temporal and multivariate spatial random elds has been
an important and growing area of research due to the increasing availability of spacetime-
referenced data in a large number of scienti c applications. In geostatistics, the
covariance function plays a crucial role in describing the spatio-temporal dependence
in the data and is key to statistical modeling, inference, stochastic simulation and
prediction. Therefore, the development of
exible covariance models, which can accomodate
the inherent variability of the real data, is necessary for an advantageous
modeling of random elds. This thesis is composed of four signi cant contributions
in the development and applications of new covariance models for stationary multivariate
spatial processes, and nonstationary spatial and spatio-temporal processes.
The rst focus of the thesis is on modeling of stationary multivariate spatial
random elds through
exible multivariate covariance functions. Chapter 2 proposes a
semiparametric approach for multivariate covariance function estimation with
exible
speci cation of the cross-covariance functions via their spectral representations. The
proposed method is applied to model and predict the bivariate data of particulate
matter concentration (PM2:5) and wind speed (WS) in the United States. Chapter 3
introduces a parametric class of multivariate covariance functions with asymmetric
cross-covariance functions. The proposed covariance model is applied to analyze the
asymmetry and perform prediction in a trivariate data of PM2:5, WS and relative
humidity (RH) in the United States.
The second focus of the thesis is on nonstationary spatial and spatio-temporal
random elds. Chapter 4 presents a space deformation method which imparts nonstationarity
to any stationary covariance function. The proposed method utilizes
the functional data registration algorithm and classical multidimensional scaling to
estimate the spatial deformation. The application of the proposed method is demonstrated
on a precipitation data. Finally, chapter 5 proposes a parametric class of
time-varying spatio-temporal covariance functions, which are nonstationary in time.
The proposed class is a time-varying generalization of an existing nonseparable stationary
class of spatio-temporal covariance functions. The proposed time-varying
model is then used to study the seasonality e ect and perform space-time predictions
in the daily PM2:5 data from Oregon, United States.
Libros sobre el tema "Spatio-temporal random fields":
1
Wikle, Christopher K. Spatial Statistics. Oxford University Press, 2018. http://dx.doi.org/10.1093/acrefore/9780190228620.013.710.
Resumen
The climate system consists of interactions between physical, biological, chemical, and human processes across a wide range of spatial and temporal scales. Characterizing the behavior of components of this system is crucial for scientists and decision makers. There is substantial uncertainty associated with observations of this system as well as our understanding of various system components and their interaction. Thus, inference and prediction in climate science should accommodate uncertainty in order to facilitate the decision-making process. Statistical science is designed to provide the tools to perform inference and prediction in the presence of uncertainty. In particular, the field of spatial statistics considers inference and prediction for uncertain processes that exhibit dependence in space and/or time. Traditionally, this is done descriptively through the characterization of the first two moments of the process, one expressing the mean structure and one accounting for dependence through covariability.Historically, there are three primary areas of methodological development in spatial statistics: geostatistics, which considers processes that vary continuously over space; areal or lattice processes, which considers processes that are defined on a countable discrete domain (e.g., political units); and, spatial point patterns (or point processes), which consider the locations of events in space to be a random process. All of these methods have been used in the climate sciences, but the most prominent has been the geostatistical methodology. This methodology was simultaneously discovered in geology and in meteorology and provides a way to do optimal prediction (interpolation) in space and can facilitate parameter inference for spatial data. These methods rely strongly on Gaussian process theory, which is increasingly of interest in machine learning. These methods are common in the spatial statistics literature, but much development is still being done in the area to accommodate more complex processes and “big data” applications. Newer approaches are based on restricting models to neighbor-based representations or reformulating the random spatial process in terms of a basis expansion. There are many computational and flexibility advantages to these approaches, depending on the specific implementation. Complexity is also increasingly being accommodated through the use of the hierarchical modeling paradigm, which provides a probabilistically consistent way to decompose the data, process, and parameters corresponding to the spatial or spatio-temporal process.Perhaps the biggest challenge in modern applications of spatial and spatio-temporal statistics is to develop methods that are flexible yet can account for the complex dependencies between and across processes, account for uncertainty in all aspects of the problem, and still be computationally tractable. These are daunting challenges, yet it is a very active area of research, and new solutions are constantly being developed. New methods are also being rapidly developed in the machine learning community, and these methods are increasingly more applicable to dependent processes. The interaction and cross-fertilization between the machine learning and spatial statistics community is growing, which will likely lead to a new generation of spatial statistical methods that are applicable to climate science.
Capítulos de libros sobre el tema "Spatio-temporal random fields":
1
Allard, Denis, Xavier Emery, Céline Lacaux y Christian Lantuéjoul. "Simulation of Stationary Gaussian Random Fields with a Gneiting Spatio-Temporal Covariance". En Springer Proceedings in Earth and Environmental Sciences, 43–49. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-19845-8_4.
Resumen
AbstractThe nonseparable Gneiting covariance has become a standard to model spatio-temporal random fields. Its definition relies on a completely monotone function associated with the spatial structure and a conditionally negative semidefinite function associated with the temporal structure. This work addresses the problem of simulating stationary Gaussian random fields with a Gneiting-type covariance. Two algorithms, in which the simulated field is obtained through a combination of cosine waves are presented and illustrated with synthetic examples. In the first algorithm, the temporal frequency is defined on the basis of a temporal random field with stationary Gaussian increments, whereas in the second algorithm the temporal frequency is drawn from the spectral measure of the covariance conditioned to the spatial frequency. Both algorithms perfectly reproduce the correlation structure with minimal computational cost and memory footprint.
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Kamijo, Shunsuke, Katsushi Ikeuchi y Masao Sakauchi. "Segmentations of Spatio-Temporal Images by Spatio-Temporal Markov Random Field Model". En Lecture Notes in Computer Science, 298–313. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44745-8_20.
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Xu, Wanru, Zhenjiang Miao, Jian Zhang y Yi Tian. "Learning Spatio-Temporal Features for Action Recognition with Modified Hidden Conditional Random Field". En Computer Vision - ECCV 2014 Workshops, 786–801. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16178-5_55.
Actas de conferencias sobre el tema "Spatio-temporal random fields":
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Chandra, Siddhartha, Camille Couprie y Iasonas Kokkinos. "Deep Spatio-Temporal Random Fields for Efficient Video Segmentation". En 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2018. http://dx.doi.org/10.1109/cvpr.2018.00929.
2
Roscher, Ribana, Bernd Uebbing y Jurgen Kusche. "Spatio-temporal altimeter waveform retracking via sparse representation and conditional random fields". En IGARSS 2015 - 2015 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2015. http://dx.doi.org/10.1109/igarss.2015.7325996.
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Hasani, Behzad y Mohammad H. Mahoor. "Spatio-Temporal Facial Expression Recognition Using Convolutional Neural Networks and Conditional Random Fields". En 2017 12th IEEE International Conference on Automatic Face & Gesture Recognition (FG 2017). IEEE, 2017. http://dx.doi.org/10.1109/fg.2017.99.
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Mitra, Adway. "Identifying coherent anomalies in multi-scale spatio-temporal data using Markov random fields". En 2017 IEEE International Conference on Big Data (Big Data). IEEE, 2017. http://dx.doi.org/10.1109/bigdata.2017.8258333.
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Shafiee, M. J., Z. Azimifar, A. Wong y P. Fieguth. "A Novel Hierarchical Model-Based Frame Rate Up-Conversion via Spatio-temporal Conditional Random Fields". En 2011 IEEE International Symposium on Multimedia (ISM). IEEE, 2011. http://dx.doi.org/10.1109/ism.2011.44.
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Georgiou, Ioannis T. "Pattern Characterization in Acceleration Vector Fields Developed in Complex Beam Structures Subject to an Excitation Protocol by Impulsive Forces". En ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70504.
Resumen
Presented are interesting results concerning aspects of the space-time characteristics of coherence patterns of ensembles of impulsive coupled acceleration signals developed in the complex domain of a physical multi-body flexible structure. A modal hammer is used to systematically pulse-interrogate the structure whereas a state of the art piezoelectric tri-axial accelerometer is used to collect at a point time series samples of coupled dynamics. We find the remarkable fact that collocated ensembles of signals of the acceleration vector field are underlain by strong spatio-temporal coherence which is robust under random experimental error introduced in the impulsive force protocol of interrogation. Coherence is characterized-identified optimally in terms of Proper Orthogonal Decomposition (POD) modes. The POD-identified space-time coherence structures, or patterns, feature an unparalleled classical modal-like characterization of coherence of collocated multi-dimensional information. The identified dominant POD spatio-temporal patterns have the space-time modulation characteristics of classical normal modes of vibration of three-dimensional coupled structural dynamics. Exploiting in full the transient dynamics and being model free, this test and evaluation modal-like identification technique can lead to a reliable certification procedure of multi-body flexible structural systems in critical applications.
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Moloney, J. V., P. Ru, R. Indik, S. W. Koch y E. Wright. "Space-Time Dynamics of Semiconductor Lasers: Many-Body Theory and Phenomenological Models". En Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.thb4.
Resumen
The space-time dynamical behaviour of multi-stripe index/gain guided semiconductor laser arrays and broad area lasers is studied using the semiconductor Maxwell-Bloch laser model including transverse diffraction of the counterpropagating optical fields and transverse diffusion of the excited carriers. Our results confirm that evanescently coupled multi-stripe lasers are a fascinating manifestation of spatio-temporal complexity in spatially extended nonlinear systems. Stabilization of the laser output can be achieved by injection-locking the array with a weak external injected signal. The broad area laser shows random intensity filamentation in free-running mode and can be stablized to produce high power output by using the unstable resonator configuration for transverse mode discrimination.
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Madhag, Aqeel y Jongeun Choi. "Distributed Navigation Strategy of Mobile Sensor Networks With Probabilistic Wireless Communication Links". En ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9964.
Resumen
Mobile sensor networks have been widely used to predict spatio-temporal physical phenomena for various scientific and engineering applications. To accommodate the realistic models of mobile sensor networks, we incorporated probabilistic wireless communication links based on packet reception ratio (PRR) with distributed navigation. We then derived models of mobile sensor networks that predict Gaussian random fields from noise-corrupted observations under probabilistic wireless communication links. For the given model with probabilistic wireless communication links, we derived the prediction error variances for further sampling locations. Moreover, we designed a distributed navigation that minimizes the network cost function formulated in terms of the derived prediction error variances. Further, we have shown that the solution of distributed navigation with the probabilistic wireless communication links for mobile sensor networks are uniformly ultimately bounded with respect to that of the distributed one with the R-disk communication model. According to Monte Carlo simulation results, agent trajectories under distributed navigation with the probabilistic wireless communication links are similar to those with the R-disk communication model, which confirming the theoretical analysis.
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Moloney, J. V., P. Ru, R. Indik, S. W. Koch y E. Wright. "Many-Body Semiconductor Laser Theory: A comparison with Phenomenological Theories". En Nonlinear Optics. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.we3.
Resumen
The space-time dynamical behaviour of multi-stripe index/gain guided semiconductor laser arrays and broad area lasers is studied using the coupled Maxwell Semiconductor Bloch equations which include transverse diffraction of the counterpropagating optical fields and many-body effects between the carriers in the active medium. Our results confirm that evanescently coupled multi-stripe and broad area lasers are a fascinating manifestation of spatio-temporal complexity in spatially extended nonlinear systems. Stabilization of the laser output can be achieved by injection-locking the array with a weak external injected signal. The broad area laser shows random intensity filamentation in free-running mode and can be stablized to produce high power output by using an unstable resonator configuration for transverse mode discrimination. A direct comparison is made with phenomenological theories and one of our main conclusions is that these theories can be salvaged in strongly index-guided multistripe structures by appealing to microscopic many-body semiconductor theory to provide the fundamental problem parameters. We note marked differences in predictions of both theories for gain guided structures.
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Chen, Jia y Chi-Keung Tang. "Spatio-Temporal Markov Random Field for Video Denoising". En 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2007. http://dx.doi.org/10.1109/cvpr.2007.383261.