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Markov Chain Monte Carlo Methods For Exact Tests In Contingency Tables
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Book Synopsis Markov Chain Monte Carlo Methods for Exact Tests in Contingency Tables by : Shiler Khedri
Download or read book Markov Chain Monte Carlo Methods for Exact Tests in Contingency Tables written by Shiler Khedri and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is mainly concerned with conditional inference for contingency tables, where the MCMC method is used to take a sample of the conditional distribution. One of the most common models to be investigated in contingency tables is the independence model. Classic test statistics for testing the independence hypothesis, Pearson and likelihood chi-square statistics rely on large sample distributions. The large sample distribution does not provide a good approximation when the sample size is small. The Fisher exact test is an alternative method which enables us to compute the exact p-value for testing the independence hypothesis. For contingency tables of large dimension, the Fisher exact test is not practical as it requires counting all tables in the sample space. We will review some enumeration methods which do not require us to count all tables in the sample space. However, these methods would also fail to compute the exact p-value for contingency tables of large dimensions. \cite{DiacStur98} introduced a method based on the Grobner basis. It is quite complicated to compute the Grobner basis for contingency tables as it is different for each individual table, not only for different sizes of table. We also review the method introduced by \citet{AokiTake03} using the minimal Markov basis for some particular tables. \cite{BuneBesa00} provided an algorithm using the most fundamental move to make the irreducible Markov chain over the sample space, defining an extra space. The algorithm is only introduced for $2\times J \times K$ tables using the Rasch model. We introduce direct proof for irreducibility of the Markov chain achieved by the Bunea and Besag algorithm. This is then used to prove that \cite{BuneBesa00} approach can be applied for some tables of higher dimensions, such as $3\times 3\times K$ and $3\times 4 \times 4$. The efficiency of the Bunea and Besag approach is extensively investigated for many different settings such as for tables of low/moderate/large dimensions, tables with special zero pattern, etc. The efficiency of algorithms is measured based on the effective sample size of the MCMC sample. We use two different metrics to penalise the effective sample size: running time of the algorithm and total number of bits used. These measures are also used to compute the efficiency of an adjustment of the Bunea and Besag algorithm which show that it outperforms the the original algorithm for some settings.
Book Synopsis Markov Chain Monte Carlo Exact Tests for Incomplete Two-way Contingency Tables by : Satoshi Aoki
Download or read book Markov Chain Monte Carlo Exact Tests for Incomplete Two-way Contingency Tables written by Satoshi Aoki and published by . This book was released on 2002 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Markov Chain Monte Carlo Method for Approximating 2-way Contingency Tables with Applications in the Stability Analysis of Ecological Ordination by : Stanley S. Bentow
Download or read book A Markov Chain Monte Carlo Method for Approximating 2-way Contingency Tables with Applications in the Stability Analysis of Ecological Ordination written by Stanley S. Bentow and published by . This book was released on 1999 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monte Carlo Methods by : Neal Noah Madras
Download or read book Monte Carlo Methods written by Neal Noah Madras and published by American Mathematical Soc.. This book was released on 2000 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Monte Carlo Methods held at The Fields Institute for Research in Mathematical Sciences (Toronto, 1998). The workshop brought together researchers in physics, statistics, and probability. The papers in this volume - of the invited speakers and contributors to the poster session - represent the interdisciplinary emphasis of the conference. Monte Carlo methods have been used intensively in many branches of scientific inquiry. Markov chain methods have been at the forefront of much of this work, serving as the basis of many numerical studies in statistical physics and related areas since the Metropolis algorithm was introduced in 1953. Statisticians and theoretical computer scientists have used these methods in recent years, working on different fundamental research questions, yet using similar Monte Carlo methodology. This volume focuses on Monte Carlo methods that appear to have wide applicability and emphasizes new methods, practical applications and theoretical analysis. It will be of interest to researchers and graduate students who study and/or use Monte Carlo methods in areas of probability, statistics, theoretical physics, or computer science.
Book Synopsis Advanced Markov Chain Monte Carlo Methods by : Faming Liang
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.
Book Synopsis Markov Chain Monte Carlo Simulations and Their Statistical Analysis by : Bernd A Berg
Download or read book Markov Chain Monte Carlo Simulations and Their Statistical Analysis written by Bernd A Berg and published by World Scientific Publishing Company. This book was released on 2004-10-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.
Book Synopsis Markov Chains for Monte Carlo Tests of Genetic Equilibrium in Multidimensional Contingency Tables by : Stanford University. Department of Statistics
Download or read book Markov Chains for Monte Carlo Tests of Genetic Equilibrium in Multidimensional Contingency Tables written by Stanford University. Department of Statistics and published by . This book was released on 1995 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monte Carlo Methods by : Neal Noah Madras
Download or read book Monte Carlo Methods written by Neal Noah Madras and published by American Mathematical Soc.. This book was released on 2000-01-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Monte Carlo Methods held at The Fields Institute for Research in Mathematical Sciences (Toronto, 1998). The workshop brought together researchers in physics, statistics, and probability. The papers in this volume - of the invited speakers and contributors to the poster session - represent the interdisciplinary emphasis of the conference. Monte Carlo methods have been used intensively in many branches of scientific inquiry. Markov chain methods have been at the forefront of much of this work, serving as the basis of many numerical studies in statistical physics and related areas since the Metropolis algorithm was introduced in 1953. Statisticians and theoretical computer scientists have used these methods in recent years, working on different fundamental research questions, yet using similar Monte Carlo methodology. This volume focuses on Monte Carlo methods that appear to have wide applicability and emphasizes new methods, practical applications and theoretical analysis. It will be of interest to researchers and graduate students who study and/or use Monte Carlo methods in areas of probability, statistics, theoretical physics, or computer science.
Book Synopsis Markov Chain Monte Carlo Simulations and Their Statistical Analysis by : Bernd A. Berg
Download or read book Markov Chain Monte Carlo Simulations and Their Statistical Analysis written by Bernd A. Berg and published by World Scientific. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.
Book Synopsis Handbook of Markov Chain Monte Carlo by : Steve Brooks
Download or read book Handbook of Markov Chain Monte Carlo written by Steve Brooks and published by CRC Press. This book was released on 2011-05-10 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisherie
Book Synopsis Monte Carlo Statistical Methods by : Christian Robert
Download or read book Monte Carlo Statistical Methods written by Christian Robert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.
Book Synopsis Markov Bases in Algebraic Statistics by : Satoshi Aoki
Download or read book Markov Bases in Algebraic Statistics written by Satoshi Aoki and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels. This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.
Book Synopsis Markov Chain Monte Carlo in Practice by : W.R. Gilks
Download or read book Markov Chain Monte Carlo in Practice written by W.R. Gilks and published by CRC Press. This book was released on 1995-12-01 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation. Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application. Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains. Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well.
Book Synopsis Faster Markov Chain Monte Carlo Algorithms for the Permanent and Binary Contingency Tables by : Ivona Bezáková
Download or read book Faster Markov Chain Monte Carlo Algorithms for the Permanent and Binary Contingency Tables written by Ivona Bezáková and published by . This book was released on 2006 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Method of Statistical Testing by : I︠U︡liĭ Anatolʹevich Shreĭder
Download or read book Method of Statistical Testing written by I︠U︡liĭ Anatolʹevich Shreĭder and published by . This book was released on 1964 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematics and Computer Science III by : Michael Drmota
Download or read book Mathematics and Computer Science III written by Michael Drmota and published by Birkhäuser. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and Computer Science III contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the Third International Colloquium on Mathematics and Computer Science, held in Vienna in September 2004. It addresses a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers.
Book Synopsis Monte Carlo Methods by : J. Hammersley
Download or read book Monte Carlo Methods written by J. Hammersley and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness.
