Download or read book A Mixture Model Approach to Empirical Bayes Testing and Estimation written by Omkar Muralidharan and published by Stanford University. This book was released on 2011 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.
Download or read book A Mixture Model Approach to Empirical Bayes Testing and Estimation written by Omkar Muralidharan and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.
Download or read book Large Scale Inference written by Bradley Efron and published by Cambridge University Press. This book was released on 2012-11-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.
Download or read book An Empirical Bayes Procedure for Improving Individual Level Estimates and Predictions from Finite Mixtures of Multinomial Logit Models written by Wagner A. Kamakura and published by . This book was released on 2014 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unobserved heterogeneity in random utility choice models can be dealt with by specifying either a multinomial or a normal distribution of the coefficients, leading to finite mixture logit and mixed logit models. Focusing on the former, we show that individual-level estimates and predictions of finite mixtures estimated by maximizing the likelihood function can be improved through integration over the estimation error of the hyperparameters, using an empirical Bayes approach. We investigate the conjecture that this approach is more robust against departures of the underlying assumptions of the finite mixture model in two Monte Carlo studies. We show that our approach improves the performance of the finite mixture model in representing individual-level parameters and producing hold-out forecasts. We illustrate with two examples that our approach may offer advantages in empirical applications involving the analysis or heterogeneous choice data.
Download or read book Parallel Testings and Variable Selection written by Haim Yehuda Bar and published by . This book was released on 2012 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop efficient and powerful statistical methods for high-dimensional data, where the sample size is much smaller than the number of features (the so-called 'large p, small n' problem). We deal with three important problems. First, we develop a mixture-model approach for parallel testing for unequal variances in two-sample experiments. The treatment effect on the variance has received little attention in the statistical literature, which so far focused mostly on the effect on the mean. The effect on the variance is increasingly recognized in recent biological literature, and we develop an empirical Bayes approach for testing differences in variance when the number of tests is large. We show that the model is useful in a wide range of applications, that our method is much more powerful than traditional tests for unequal variances, and that it is robust to the normality assumption. Second, we extend these ideas and develop a novel bivariate normal model that tests for both differential expression and differential variation between the two groups. We show in simulations that this new method yields a substantial gain in power when differential variation is present. Through a three-step estimation approach, in which we apply the Laplace approximation and the EM algorithm, we get a computationally efficient method, which is particularly well-suited for 'large p, small n' situations. Third, we deal with the problem of variable selection where the number of putative variables is large, possibly much larger than the sample size. We develop a model-based, empirical Bayes approach. By treating the putative variables as random effects, we get shrinkage estimation, which results in increased power and significantly faster convergence, compared with simulation-based methods. Furthermore, we employ computational tricks which allow us to increase the speed of our algorithm, to handle a very large number of putative variables, and to control the multicollinearity in the model. The motivation for developing this approach is QTL analysis, but our method is applicable to a broad range of applications. We use two widely-studied data sets, and show that our model selection algorithm yields excellent results.
Download or read book Empirical Bayes Methods with Applications written by J.S. Maritz and published by CRC Press. This book was released on 2018-01-18 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of Empirical Bayes Methods details are provided of the derivation and the performance of empirical Bayes rules for a variety of special models. Attention is given to the problem of assessing the goodness of an empirical Bayes estimator for a given set of prior data. A chapter is devoted to a discussion of alternatives to the empirical Bayes approach and there is also a chapter giving details of several actual applications of empirical Bayes method.
Download or read book The BUGS Book written by David Lunn and published by CRC Press. This book was released on 2012-10-02 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents
Download or read book Empirical Bayes Methods written by J. S. Maritz and published by . This book was released on 1970 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.
Download or read book Algorithms and Programs of Dynamic Mixture Estimation written by Ivan Nagy and published by Springer. This book was released on 2017-08-14 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general theoretical background for constructing the recursive Bayesian estimation algorithms for mixture models. It collects the recursive algorithms for estimating dynamic mixtures of various distributions and brings them in the unified form, providing a scheme for constructing the estimation algorithm for a mixture of components modeled by distributions with reproducible statistics. It offers the recursive estimation of dynamic mixtures, which are free of iterative processes and close to analytical solutions as much as possible. In addition, these methods can be used online and simultaneously perform learning, which improves their efficiency during estimation. The book includes detailed program codes for solving the presented theoretical tasks. Codes are implemented in the open source platform for engineering computations. The program codes given serve to illustrate the theory and demonstrate the work of the included algorithms.
Download or read book Nonlinear Mixture Models A Bayesian Approach written by Tatiana V Tatarinova and published by World Scientific. This book was released on 2014-12-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by two mathematicians from the University of Southern California, provides a broad introduction to the important subject of nonlinear mixture models from a Bayesian perspective. It contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications. It is self-contained and unified in presentation, which makes it ideal for use as an advanced textbook by graduate students and as a reference for independent researchers. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.In this book the authors present Bayesian methods of analysis for nonlinear, hierarchical mixture models, with a finite, but possibly unknown, number of components. These methods are then applied to various problems including population pharmacokinetics and gene expression analysis. In population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. For gene expression data, one application included in the book is to determine which genes should be associated with the same component of the mixture (also known as a clustering problem). The book also contains examples of computer programs written in BUGS. This is the first book of its kind to cover many of the topics in this field.
Download or read book Proceedings of the International Symposium on Computer Mapping in Epidemiology and Environmental Health written by and published by . This book was released on 1997 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Bayesian Choice written by Christian P. Robert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics, such as complete class theorems, the Stein effect, hierarchical and empirical Bayes modelling, Monte Carlo integration, and Gibbs sampling. In translating the book from the original French, the author has taken the opportunity to add and update material, and to include many problems and exercises for students.
Download or read book Design and Analysis of Clinical Trials for Predictive Medicine written by Shigeyuki Matsui and published by CRC Press. This book was released on 2015-03-19 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design and Analysis of Clinical Trials for Predictive Medicine provides statistical guidance on conducting clinical trials for predictive medicine. It covers statistical topics relevant to the main clinical research phases for developing molecular diagnostics and therapeutics-from identifying molecular biomarkers using DNA microarrays to confirming
Download or read book Model based Classification with Applications to Hyigh dimensional Data in Bioinformatics written by Muting Wan and published by . This book was released on 2015 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, sparse classification problems have emerged in many fields of study. Finite mixture models have been developed to facilitate Bayesian inference where parameter sparsity is substantial. Shrinkage estimation allows strength borrowing across features in light of the parallel nature of multiple hypothesis tests. Important examples that incorporate shrinkage estimation and finite mixture model for sparse classification include the hierarchical model in Smyth (2004) and the explicit mixture model in Bar et al. (2010) for Bayesian microarray analysis. Classification with finite mixture models is based on the posterior expectation of latent indicator variables. These quantities are typically estimated using the expectation-maximization (EM) algorithm in an empirical Bayes approach or Markov chain Monte Carlo (MCMC) in a fully Bayesian approach. MCMC is limited in applicability where high-dimensional data are involved because its sampling-based nature leads to slow computations and hard-to-monitor convergence. In a fully Bayesian framework, we investigate the feasibility and performance of variational Bayes (VB) approximation and apply the VB approach to fully Bayesian versions of several finite mixture models that have been proposed in bioinformatics. We find that it achieves desirable speed and accuracy in sparse classification with hierarchical mixture models for high-dimensional data. Another example of sparse classification in bioinformatics solvable via model-based approaches is expression quantitative trait loci (eQTL) detection, in which determining whether association between a gene and any given single nucleotide polymorphism (SNP) is significant is regarded as classifying genes as null or non-null with respect to the given SNP. High-dimensionality of the data not only causes difficulties in computations, but also renders the confounding impact of unwanted variation in the data irrefutable. Model-based approaches that account for unwanted variation by incorporating a factor analysis term representing hidden factors and their effects have been adopted in applications such as differential analysis and eQTL detection. HEFT (Gao et al., 2014) is a fast approach for model-based eQTL identification while simultaneously learning hidden effects. We develop a hierarchical mixture model-based empirical Bayes approach for sparse classification while simultaneously accounting for unwanted variation, as well as a family of model-based approaches that are its simplifications with the aim of attractive computational efficiency. We investigate feasibility and performance of these model-based approaches in comparison with HEFT using several real data examples in bioinformatics.
Download or read book DNA Microarrays and Related Genomics Techniques written by David B. Allison and published by CRC Press. This book was released on 2005-11-14 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered highly exotic tools as recently as the late 1990s, microarrays are now ubiquitous in biological research. Traditional statistical approaches to design and analysis were not developed to handle the high-dimensional, small sample problems posed by microarrays. In just a few short years the number of statistical papers providing approaches
Download or read book Empirical Bayes and Likelihood Inference written by S.E. Ahmed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian and such approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both emphasize the construction of interval estimates of unknown parameters. In this volume, researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for research in the theory of inference.
