Download or read book Convergence of Markov Chain Monte Carlo Algorithms with Applications to Image Restoration written by Alison L. Gibbs and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convergence of Markov Chain Monte Carlo Algorithms with Applications to Image Restoration microform written by Alison L. (Alison Lee) Gibbs and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 2000 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convergence in Markov Chain Monte Carlo Algorithms written by Valen Earl Johnson and published by . This book was released on 1996 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Markov Chain Monte Carlo Methods written by Faming Liang and published by John Wiley & Sons. This book was released on 2011-07-05 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics. Key Features: Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems. A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants. Up-to-date accounts of recent developments of the Gibbs sampler. Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals. This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial.
Download or read book Image Analysis Random Fields and Dynamic Monte Carlo Methods written by Gerhard Winkler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned with a probabilistic approach to image analysis as initiated by U. GRENANDER, D. and S. GEMAN, B.R. HUNT and many others, and developed and popularized by D. and S. GEMAN in a paper from 1984. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. There has been considerable and still growing interest in prior models and, in particular, in discrete Markov random field methods. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging. Among those are such 'classical' applications like restoration, edge detection, texture discrimination, motion analysis and tomographic reconstruction. The subject is rapidly developing and in the near future is likely to deal with high-level applications like object recognition. Fascinating experiments by Y. CHOW, U. GRENANDER and D.M. KEENAN (1987), (1990) strongly support this belief.
Download or read book Convergence of Markov Chain Monte Carlo Algorithms written by Nicholas G. Polson and published by . This book was released on 1993 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book MCMC from Scratch written by Masanori Hanada and published by Springer Nature. This book was released on 2022-10-20 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explains the fundamentals of Markov Chain Monte Carlo (MCMC) without assuming advanced knowledge of mathematics and programming. MCMC is a powerful technique that can be used to integrate complicated functions or to handle complicated probability distributions. MCMC is frequently used in diverse fields where statistical methods are important – e.g. Bayesian statistics, quantum physics, machine learning, computer science, computational biology, and mathematical economics. This book aims to equip readers with a sound understanding of MCMC and enable them to write simulation codes by themselves. The content consists of six chapters. Following Chap. 2, which introduces readers to the Monte Carlo algorithm and highlights the advantages of MCMC, Chap. 3 presents the general aspects of MCMC. Chap. 4 illustrates the essence of MCMC through the simple example of the Metropolis algorithm. In turn, Chap. 5 explains the HMC algorithm, Gibbs sampling algorithm and Metropolis-Hastings algorithm, discussing their pros, cons and pitfalls. Lastly, Chap. 6 presents several applications of MCMC. Including a wealth of examples and exercises with solutions, as well as sample codes and further math topics in the Appendix, this book offers a valuable asset for students and beginners in various fields.
Download or read book Convergence of Adaptive Markov Chain Monte Carlo Algorithms written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the thesis, we study ergodicity of adaptive Markov Chain Monte Carlo methods (MCMC) based on two conditions(Diminishing Adaptation and Containment which together imply ergodicity), explain the advantages of adaptive MCMC, and apply the theoretical result for some applications. \indent First we show several facts: 1. Diminishing Adaptation alone may not guarantee ergodicity; 2. Containment is not necessary for ergodicity; 3. under some additional condition, Containment is necessary for ergodicity. Since Diminishing Adaptation is relatively easy to check and Containment is abstract, we focus on the sufficient conditions of Containment. In order to study Containment, we consider the quantitative bounds of the distance between samplers and targets in total variation norm. From early results, the quantitative bounds are connected with nested drift conditions for polynomial rates of convergence. For ergodicity of adaptive MCMC, assuming that all samplers simultaneously satisfy nested polynomial drift conditions, we find that either when the number of nested drift conditions is greater than or equal to two, or when the number of drift conditions with some specific form is one, the adaptive MCMC algorithm is ergodic. For adaptive MCMC algorithm with Markovian adaptation, the algorithm satisfying simultaneous polynomial ergodicity is ergodic without those restrictions. We also discuss some recent results related to this topic. \indent Second we consider ergodicity of certain adaptive Markov Chain Monte Carlo algorithms for multidimensional target distributions, in particular, adaptive Metropolis and adaptive Metropolis-within-Gibbs algorithms. We derive various sufficient conditions to ensure Containment, and connect the convergence rates of algorithms with the tail properties of the corresponding target distributions. We also present a Summable Adaptive Condition which, when satisfied, proves ergodicity more easily. \indent Finally, we propose a simple adaptive Metropolis.
Download or read book Convergence of Adaptive Markov Chain Monte Carlo Algorithms written by Yan Bai and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the thesis, we study ergodicity of adaptive Markov Chain Monte Carlo methods (MCMC) based on two conditions(Diminishing Adaptation and Containment which together imply ergodicity), explain the advantages of adaptive MCMC, and apply the theoretical result for some applications. \indent First we show several facts: 1. Diminishing Adaptation alone may not guarantee ergodicity; 2. Containment is not necessary for ergodicity; 3. under some additional condition, Containment is necessary for ergodicity. Since Diminishing Adaptation is relatively easy to check and Containment is abstract, we focus on the sufficient conditions of Containment. In order to study Containment, we consider the quantitative bounds of the distance between samplers and targets in total variation norm. From early results, the quantitative bounds are connected with nested drift conditions for polynomial rates of convergence. For ergodicity of adaptive MCMC, assuming that all samplers simultaneously satisfy nested polynomial drift conditions, we find that either when the number of nested drift conditions is greater than or equal to two, or when the number of drift conditions with some specific form is one, the adaptive MCMC algorithm is ergodic. For adaptive MCMC algorithm with Markovian adaptation, the algorithm satisfying simultaneous polynomial ergodicity is ergodic without those restrictions. We also discuss some recent results related to this topic. \indent Second we consider ergodicity of certain adaptive Markov Chain Monte Carlo algorithms for multidimensional target distributions, in particular, adaptive Metropolis and adaptive Metropolis-within-Gibbs algorithms. We derive various sufficient conditions to ensure Containment, and connect the convergence rates of algorithms with the tail properties of the corresponding target distributions. We also present a Summable Adaptive Condition which, when satisfied,proves ergodicity more easily. \indent Finally, we propose a simple adaptive Metropolis-within-Gibbs algorithm attempting to study directions on which the Metropolis algorithm can be run flexibly. The algorithm avoids the wasting moves in wrong directions by proposals from the full dimensional adaptive Metropolis algorithm. We also prove its ergodicity, and test it on a Gaussian Needle example and a real-life Case-Cohort study with competing risks. For the Cohort study, we describe an extensive version of Competing Risks Regression model, define censor variables for competing risks, and then apply the algorithm to estimate coefficients based on the posterior distribution.
Download or read book Image Analysis Random Fields and Markov Chain Monte Carlo Methods written by Gerhard Winkler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is concerned with a probabilistic approach for image analysis, mostly from the Bayesian point of view, and the important Markov chain Monte Carlo methods commonly used....This book will be useful, especially to researchers with a strong background in probability and an interest in image analysis. The author has presented the theory with rigor...he doesn’t neglect applications, providing numerous examples of applications to illustrate the theory." -- MATHEMATICAL REVIEWS
Download or read book On the Convergence of Unconstrained Adaptive Markov Chain Monte Carlo Algorithms written by Matti Vihola and published by . This book was released on 2010 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computing and Combinatorics written by Hung Q. Ngo and published by Springer Science & Business Media. This book was released on 2009-07-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume were selected for presentation at the 15th Annual InternationalComputing and CombinatoricsConference (COCOON 2009), held during July 13-15, 2009 in Niagara Falls, New York, USA. Previous meetings of this conference were held in Xian (1995), Hong Kong (1996), Shanghai (1997), Taipei(1998), Tokyo(1999), Sydney(2000), Guilin(2001), Singapore(2002), Big Sky (2003), Jeju Island (2004), Kunming (2005), Taipei (2006), Alberta (2007), and Dalian (2008). In response to the Call for Papers, 125 extended abstracts (not counting withdrawn papers) were submitted from 28 countries and regions, of which 51 were accepted. Authors of the submitted papers were from Cyprus (1), The Netherlands (1), Bulgaria (1), Israel (1), Vietnam (2), Finland (1), Puerto Rico (2), Australia (4), Norway (4), Portugal (1) Spain (2), France (16), Republic of Korea(3), Singapore(2), Italy(6), Iran, (4), Greece(7), Poland(4), Switzerland (8), Hong Kong (10), UK (12), India (7), Taiwan (18), Canada (23), China (19), Japan (39), Germany (44), and the USA (77). The submitted papers were evaluated by an international Technical P- gram Committee (TPC) consisting of Srinivas Aluru (Iowa State University, USA), Lars Arge (University of Aarhus, Denmark), Vikraman Arvind (Ins- tute of Mathematical Sciences, India), James Aspnes (Yale University, USA), Mikhail Atallah (Purdue University, USA), Gill Barequet (Technion - Israel - stitute of Technology, Israel), Michael Brudno (University of Toronto, Canada), Jianer Chen (Texas A & M, USA), Bhaskar DasGupta (University of Illinois at Chicago, USA), Anupam Gupta (Carnegie Mellon University, USA), Lane A.
Download or read book Consistency and Convergence Rate of Markov Chain Quasi Monte Carlo with Examples written by Su Chen and published by Stanford University. This book was released on 2011 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chain Monte Carlo methods have been widely used in various scientific disciplines for generation of samples from distributions that are difficult to simulate directly. The random numbers driving Markov Chain Monte Carlo algorithms are modeled as independent $\mathcal{U}[0,1)$ random variables. The class of distributions that could be simulated are largely broadened by using Markov Chain Monte Carlo. Quasi-Monte Carlo, on the other hand, aims to improve the accuracy of estimation of an integral over the multidimensional unit cube. By using more carefully balanced inputs, under some smoothness conditions the estimation error is converging at a higher rate than plain Monte Carlo. We would like to combine these two techniques, so that we can sample more accurately from a larger class of distributions. This method, called Markov Chain quasi-Monte Carlo (MCQMC), is the main topic of this work. We are going to replace the IID driving sequence used in MCMC algorithms by a deterministic sequence which is designed to be more uniform. Previously the justification for MCQMC is proved only for finite state space case. We are going to extend those results to some Markov Chains on continuous state spaces. We also explore the convergence rate of MCQMC under stronger assumptions. Lastly we present some numerical results for demonstration of MCQMC's performance. From these examples, the empirical benefits of more balanced sequences are significant.
Download or read book Advanced Image Acquisition Processing Techniques and Applications written by Dimitrios Ventzas and published by BoD – Books on Demand. This book was released on 2012-03-14 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Advanced Image Acquisition, Processing Techniques and Applications" is the first book of a series that provides image processing principles and practical software implementation on a broad range of applications. The book integrates material from leading researchers on Applied Digital Image Acquisition and Processing. An important feature of the book is its emphasis on software tools and scientific computing in order to enhance results and arrive at problem solution.
Download or read book Assessing Convergence of the Markov Chain Monte Carlo Algorithms written by Sandip Sinharay and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book High Dimensional Markov Chain Monte Carlo Methods written by Alain Durmus and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this thesis is the analysis of Markov Chain Monte Carlo (MCMC) methods and the development of new methodologies to sample from a high dimensional distribution. Our work is divided into three main topics. The first problem addressed in this manuscript is the convergence of Markov chains in Wasserstein distance. Geometric and sub-geometric convergence with explicit constants, are derived under appropriate conditions. These results are then applied to thestudy of MCMC algorithms. The first analyzed algorithm is an alternative scheme to the Metropolis Adjusted Langevin algorithm for which explicit geometric convergence bounds are established. The second method is the pre-Conditioned Crank-Nicolson algorithm. It is shown that under mild assumption, the Markov chain associated with thisalgorithm is sub-geometrically ergodic in an appropriated Wasserstein distance. The second topic of this thesis is the study of the Unadjusted Langevin algorithm (ULA). We are first interested in explicit convergence bounds in total variation under different kinds of assumption on the potential associated with the target distribution. In particular, we pay attention to the dependence of the algorithm on the dimension of the state space. The case of fixed step sizes as well as the case of nonincreasing sequences of step sizes are dealt with. When the target density is strongly log-concave, explicit bounds in Wasserstein distance are established. These results are then used to derived new bounds in the total variation distance which improve the one previously derived under weaker conditions on the target density.The last part tackles new optimal scaling results for Metropolis-Hastings type algorithms. First, we extend the pioneer result on the optimal scaling of the random walk Metropolis algorithm to target densities which are differentiable in Lp mean for p ≥ 2. Then, we derive new Metropolis-Hastings type algorithms which have a better optimal scaling compared the MALA algorithm. Finally, the stability and the convergence in total variation of these new algorithms are studied.
Download or read book Convergence Rates and Monte Carlo Standard Errors for Markov Chain Monte Carlo Algorithms written by Galin L. Jones and published by . This book was released on 2001 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
