Gaussian Markov Random Fields

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Gaussian Markov Random Fields

Author : Havard Rue
ISBN : 0203492021
Genre : Mathematics
File Size : 39.55 MB
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Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie
Category: Mathematics

Adaptive Gaussian Markov Random Fields With Applications In Human Brain Mapping

Author :
ISBN : OCLC:836295470
Genre :
File Size : 35.1 MB
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Functional magnetic resonance imaging (fMRI) has become the standard technology in human brain mapping. Analyses of the massive spatio-temporal fMRI data sets often focus on parametric or nonparametric modeling of the temporal component, while spatial smoothing is based on Gaussian kernels or random fields. A weakness of Gaussian spatial smoothing is underestimation of activation peaks or blurring of high-curvature transitions between activated and non-activated brain regions. In this paper, we introduce a class of inhomogenous Markov random fields (MRF) with spatially adaptive interaction weights in a space-varying coefficient model for fMRI data. For given weights, the random field is conditionally Gaussian, but marginally it is non-Gaussian. Fully Bayesian inference, including estimation of weights and variance parameters, is carried out through efficient MCMC simulation. An application to fMRI data from a visual stimulation experiment demonstrates the performance of our approach in comparison to Gaussian and robustified non-Gaussian Markov random field models. -- Adaptive weights ; human brain mapping ; inhomogeneous Markov random fields ; MCMC ; space-varying coefficient model ; spatio-temporal modeling

Scalable Bayesian Spatial Analysis With Gaussian Markov Random Fields

Author : Per Sidén
ISBN : 9789179298180
Genre :
File Size : 28.7 MB
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Accurate statistical analysis of spatial data is important in many applications. Failing to properly account for spatial autocorrelation may often lead to false conclusions. At the same time, the ever-increasing sizes of spatial datasets pose a great computational challenge, as many standard methods for spatial analysis are limited to a few thousand data points. In this thesis, we explore how Gaussian Markov random fields (GMRFs) can be used for scalable analysis of spatial data. GMRFs are closely connected to the commonly used Gaussian processes, but have sparsity properties that make them computationally cheap both in time and memory. The Bayesian framework enables a GMRF to be used as a spatial prior, comprising the assumption of smooth variation over space, and gives a principled way to estimate the parameters and propagate uncertainty. We develop new algorithms that enable applying GMRF priors in 3D to the brain activity inherent in functional magnetic resonance imaging (fMRI) data, with millions of observations. We show that our methods are both faster and more accurate than previous work. A method for approximating selected elements of the inverse precision matrix (i.e. the covariance matrix) is also proposed, which is important for evaluating the posterior uncertainty. In addition, we establish a link between GMRFs and deep convolutional neural networks, which have been successfully used in countless machine learning tasks for images, resulting in a deep GMRF model. Finally, we show how GMRFs can be used in real-time robotic search and rescue operations, for modeling the spatial distribution of injured persons. Tillförlitlig statistisk analys av spatiala data är viktigt inom många tillämpningar. Om inte korrekt hänsyn tas till spatial autokorrelation kan det ofta leda till felaktiga slutsatser. Samtidigt ökar ständigt storleken på de spatiala datamaterialen vilket utgör en stor beräkningsmässig utmaning, eftersom många standardmetoder för spatial analys är begränsade till några tusental datapunkter. I denna avhandling utforskar vi hur Gaussiska Markov-fält (eng: Gaussian Markov random fields, GMRF) kan användas för mer skalbara analyser av spatiala data. GMRF-modeller är nära besläktade med de ofta använda Gaussiska processerna, men har gleshetsegenskaper som gör dem beräkningsmässigt effektiva både vad gäller tids- och minnesåtgång. Det Bayesianska synsättet gör det möjligt att använda GMRF som en spatial prior som innefattar antagandet om långsam spatial variation och ger ett principiellt tillvägagångssätt för att skatta parametrar och propagera osäkerhet. Vi utvecklar nya algoritmer som gör det möjligt att använda GMRF-priors i 3D för den hjärnaktivitet som indirekt kan observeras i hjärnbilder framtagna med tekniken fMRI, som innehåller milliontals datapunkter. Vi visar att våra metoder är både snabbare och mer korrekta än tidigare forskning. En metod för att approximera utvalda element i den inversa precisionsmatrisen (dvs. kovariansmatrisen) framförs också, vilket är viktigt för att kunna evaluera osäkerheten i posteriorn. Vidare gör vi en koppling mellan GMRF och djupa neurala faltningsnätverk, som har använts framgångsrikt för mängder av bildrelaterade problem inom maskininlärning, vilket mynnar ut i en djup GMRF-modell. Slutligen visar vi hur GMRF kan användas i realtid av autonoma drönare för räddningsinsatser i katastrofområden för att modellera den spatiala fördelningen av skadade personer.

Markov Random Field Modeling In Image Analysis

Author : Stan Z. Li
ISBN : 9781848002791
Genre : Computers
File Size : 29.96 MB
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Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables us to develop optimal vision algorithms systematically when used with optimization principles. This book presents a comprehensive study on the use of MRFs for solving computer vision problems. Various vision models are presented in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This third edition includes the most recent advances and has new and expanded sections on topics such as: Bayesian Network; Discriminative Random Fields; Strong Random Fields; Spatial-Temporal Models; Learning MRF for Classification. This book is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in these areas.
Category: Computers

Bayesian Statistics 6

Author : José M. Bernardo
ISBN : 0198504853
Genre : Business & Economics
File Size : 45.61 MB
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Bayesian statistics is a dynamic and fast-growing area of statistical research and the Valencia International Meetings provide the main forum for discussion. These resulting proceedings form an up-to-date collection of research.
Category: Business & Economics

Markov Random Fields

Author : Rama Chellappa
ISBN : UOM:39015029555748
Genre : Mathematics
File Size : 71.67 MB
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Introduces the theory and application of Markov random fields in image processing/computer vision. Modelling images through the local interaction of Markov models produces algorithms for use in texture analysis, image synthesis, restoration, segmentation and surface reconstruction.
Category: Mathematics

Information And Control In Networks

Author : Giacomo Como
ISBN : 9783319021508
Genre : Technology & Engineering
File Size : 56.29 MB
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Information and Control in Networks demonstrates the way in which system dynamics and information flows intertwine as they evolve, and the central role played by information in the control of complex networked systems. It is a milestone on the road to that convergence from traditionally independent development of control theory and information theory which has emerged strongly in the last fifteen years, and is now a very active research field. In addition to efforts in control and information theory, the text is witness to strong research in such diverse fields as computer science, mathematics, and statistics. Aspects that are given specialist treatment include: · data-rate theorems; · computation and control over communication networks; · decentralized stochastic control; · Gaussian networks and Gaussian–Markov random fields; and · routability in information networks. Information and Control in Networks collects contributions from world-leading researchers in the area who came together for the Lund Center for Control of Complex Engineering Systems Workshop in Information and Control in Networks from 17th–19th October 2012; the workshop being the centrepiece of a five-week-long focus period on the same theme. A source of exciting cross-fertilization and new ideas for extensive future research, this volume will be of great interest to any researcher or graduate student interested in the interaction of control and information theory.
Category: Technology & Engineering

Library Of Congress Subject Headings

Author : Library of Congress
ISBN : PSU:000058567838
Genre : Subject headings, Library of Congress
File Size : 35.68 MB
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Category: Subject headings, Library of Congress

The Geometry Of Random Fields

Author : Robert J. Adler
ISBN : 9780898716931
Genre : Mathematics
File Size : 51.5 MB
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An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.
Category: Mathematics

Intelligent Data Engineering And Automated Learning Ideal 2013

Author : Hujun Yin
ISBN : 9783642412783
Genre : Computers
File Size : 33.52 MB
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This book constitutes the refereed proceedings of the 14th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2013, held in Hefei, China, in October 2013. The 76 revised full papers presented were carefully reviewed and selected from more than 130 submissions. These papers provided a valuable collection of latest research outcomes in data engineering and automated learning, from methodologies, frameworks and techniques to applications. In addition to various topics such as evolutionary algorithms, neural networks, probabilistic modelling, swarm intelligent, multi-objective optimisation, and practical applications in regression, classification, clustering, biological data processing, text processing, video analysis, including a number of special sessions on emerging topics such as adaptation and learning multi-agent systems, big data, swarm intelligence and data mining, and combining learning and optimisation in intelligent data engineering.
Category: Computers

Bayesian Inference With Inla

Author : Virgilio Gomez-Rubio
ISBN : 9781351707190
Genre : Mathematics
File Size : 57.4 MB
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The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed. Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website. This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.
Category: Mathematics

Image Analysis And Recognition

Author : Aurélio Campilho
ISBN : 9783540232407
Genre : Computers
File Size : 30.68 MB
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ICIAR 2004, the International Conference on Image Analysis and Recognition, was the ?rst ICIAR conference, and was held in Porto, Portugal. ICIAR will be organized annually, and will alternate between Europe and North America. ICIAR 2005 will take place in Toronto, Ontario, Canada. The idea of o?ering these conferences came as a result of discussion between researchers in Portugal and Canada to encourage collaboration and exchange, mainly between these two countries, but also with the open participation of other countries, addressing recent advances in theory, methodology and applications. The response to the call for papers for ICIAR 2004 was very positive. From 316 full papers submitted, 210 were accepted (97 oral presentations, and 113 - sters). The review process was carried out by the Program Committee members and other reviewers; all are experts in various image analysis and recognition areas. Each paper was reviewed by at least two reviewing parties. The high q- lity of the papers in these proceedings is attributed ?rst to the authors, and second to the quality of the reviews provided by the experts. We would like to thank the authors for responding to our call, and we wholeheartedly thank the reviewers for their excellent work in such a short amount of time. We are espe- ally indebted to the Program Committee for their e?orts that allowed us to set up this publication. We were very pleased to be able to include in the conference, Prof. Murat KuntfromtheSwissFederalInstituteofTechnology,andProf. Mario ́ Figueiredo, oftheInstitutoSuperiorT ́ ecnico,inPortugal.
Category: Computers

Richly Parameterized Linear Models

Author : James S. Hodges
ISBN : 9781439866849
Genre : Mathematics
File Size : 32.84 MB
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A First Step toward a Unified Theory of Richly Parameterized Linear Models Using mixed linear models to analyze data often leads to results that are mysterious, inconvenient, or wrong. Further compounding the problem, statisticians lack a cohesive resource to acquire a systematic, theory-based understanding of models with random effects. Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects takes a first step in developing a full theory of richly parameterized models, which would allow statisticians to better understand their analysis results. The author examines what is known and unknown about mixed linear models and identifies research opportunities. The first two parts of the book cover an existing syntax for unifying models with random effects. The text explains how richly parameterized models can be expressed as mixed linear models and analyzed using conventional and Bayesian methods. In the last two parts, the author discusses oddities that can arise when analyzing data using these models. He presents ways to detect problems and, when possible, shows how to mitigate or avoid them. The book adapts ideas from linear model theory and then goes beyond that theory by examining the information in the data about the mixed linear model’s covariance matrices. Each chapter ends with two sets of exercises. Conventional problems encourage readers to practice with the algebraic methods and open questions motivate readers to research further. Supporting materials, including datasets for most of the examples analyzed, are available on the author’s website.
Category: Mathematics

Markov Processes For Stochastic Modeling

Author : Oliver Ibe
ISBN : 9780080922454
Genre : Mathematics
File Size : 35.32 MB
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Markov processes are used to model systems with limited memory. They are used in many areas including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. This book, which is written for upper level undergraduate and graduate students, and researchers, presents a unified presentation of Markov processes. In addition to traditional topics such as Markovian queueing system, the book discusses such topics as continuous-time random walk,correlated random walk, Brownian motion, diffusion processes, hidden Markov models, Markov random fields, Markov point processes and Markov chain Monte Carlo. Continuous-time random walk is currently used in econophysics to model the financial market, which has traditionally been modelled as a Brownian motion. Correlated random walk is popularly used in ecological studies to model animal and insect movement. Hidden Markov models are used in speech analysis and DNA sequence analysis while Markov random fields and Markov point processes are used in image analysis. Thus, the book is designed to have a very broad appeal. - Provides the practical, current applications of Markov processes - Coverage of HMM, Point processes, and Monte Carlo - Includes enough theory to help students gain throrough understanding of the subject - Principles can be immediately applied in many specific research projects, saving researchers time - End of chapter exercises provide reinforcement, practice and increased understanding to the student
Category: Mathematics

Interactive Knowledge Discovery And Data Mining In Biomedical Informatics

Author : Andreas Holzinger
ISBN : 9783662439685
Genre : Computers
File Size : 48.73 MB
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One of the grand challenges in our digital world are the large, complex and often weakly structured data sets, and massive amounts of unstructured information. This “big data” challenge is most evident in biomedical informatics: the trend towards precision medicine has resulted in an explosion in the amount of generated biomedical data sets. Despite the fact that human experts are very good at pattern recognition in dimensions of = 3; most of the data is high-dimensional, which makes manual analysis often impossible and neither the medical doctor nor the biomedical researcher can memorize all these facts. A synergistic combination of methodologies and approaches of two fields offer ideal conditions towards unraveling these problems: Human–Computer Interaction (HCI) and Knowledge Discovery/Data Mining (KDD), with the goal of supporting human capabilities with machine learning./ppThis state-of-the-art survey is an output of the HCI-KDD expert network and features 19 carefully selected and reviewed papers related to seven hot and promising research areas: Area 1: Data Integration, Data Pre-processing and Data Mapping; Area 2: Data Mining Algorithms; Area 3: Graph-based Data Mining; Area 4: Entropy-Based Data Mining; Area 5: Topological Data Mining; Area 6 Data Visualization and Area 7: Privacy, Data Protection, Safety and Security.
Category: Computers