Permutation Based Inference For High Dimensional Data
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| Author | : Carlos Fernandez-Lozano |
| Publisher | : MDPI |
| Total Pages | : 314 |
| Release | : 2021-04-28 |
| Genre | : Science |
| ISBN | : 3036509445 |
• Real-world problems can be high-dimensional, complex, and noisy • More data does not imply more information • Different approaches deal with the so-called curse of dimensionality to reduce irrelevant information • A process with multidimensional information is not necessarily easy to interpret nor process • In some real-world applications, the number of elements of a class is clearly lower than the other. The models tend to assume that the importance of the analysis belongs to the majority class and this is not usually the truth • The analysis of complex diseases such as cancer are focused on more-than-one dimensional omic data • The increasing amount of data thanks to the reduction of cost of the high-throughput experiments opens up a new era for integrative data-driven approaches • Entropy-based approaches are of interest to reduce the dimensionality of high-dimensional data
| Author | : Roman Vershynin |
| Publisher | : Cambridge University Press |
| Total Pages | : 299 |
| Release | : 2018-09-27 |
| Genre | : Business & Economics |
| ISBN | : 1108415199 |
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
| Author | : Fortunato Pesarin |
| Publisher | : John Wiley & Sons |
| Total Pages | : 448 |
| Release | : 2010-02-25 |
| Genre | : Mathematics |
| ISBN | : 9780470689523 |
Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample size and many variables, especially in observational studies. The Authors give a general overview on permutation tests with a focus on recent theoretical advances within univariate and multivariate complex permutation testing problems, this book brings the reader completely up to date with today’s current thinking. Key Features: Examines the most up-to-date methodologies of univariate and multivariate permutation testing. Includes extensive software codes in MATLAB, R and SAS, featuring worked examples, and uses real case studies from both experimental and observational studies. Includes a standalone free software NPC Test Release 10 with a graphical interface which allows practitioners from every scientific field to easily implement almost all complex testing procedures included in the book. Presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses. A supplementary website containing all of the data sets examined in the book along with ready to use software codes. Together with a wide set of application cases, the Authors present a thorough theory of permutation testing both with formal description and proofs, and analysing real case studies. Practitioners and researchers, working in different scientific fields such as engineering, biostatistics, psychology or medicine will benefit from this book.
| Author | : Alan Agresti |
| Publisher | : John Wiley & Sons |
| Total Pages | : 471 |
| Release | : 2015-02-23 |
| Genre | : Mathematics |
| ISBN | : 1118730038 |
A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.
| Author | : Faming Liang |
| Publisher | : CRC Press |
| Total Pages | : 150 |
| Release | : 2023-08-02 |
| Genre | : Mathematics |
| ISBN | : 0429582900 |
This book provides a general framework for learning sparse graphical models with conditional independence tests. It includes complete treatments for Gaussian, Poisson, multinomial, and mixed data; unified treatments for covariate adjustments, data integration, and network comparison; unified treatments for missing data and heterogeneous data; efficient methods for joint estimation of multiple graphical models; effective methods of high-dimensional variable selection; and effective methods of high-dimensional inference. The methods possess an embarrassingly parallel structure in performing conditional independence tests, and the computation can be significantly accelerated by running in parallel on a multi-core computer or a parallel architecture. This book is intended to serve researchers and scientists interested in high-dimensional statistics, and graduate students in broad data science disciplines. Key Features: A general framework for learning sparse graphical models with conditional independence tests Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data Unified treatments for data integration, network comparison, and covariate adjustment Unified treatments for missing data and heterogeneous data Efficient methods for joint estimation of multiple graphical models Effective methods of high-dimensional variable selection Effective methods of high-dimensional inference
| Author | : Alexander Tartakovsky |
| Publisher | : CRC Press |
| Total Pages | : 600 |
| Release | : 2014-08-27 |
| Genre | : Mathematics |
| ISBN | : 1439838216 |
Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detecti
| Author | : |
| Publisher | : North Holland |
| Total Pages | : 496 |
| Release | : 2020-05-27 |
| Genre | : Mathematics |
| ISBN | : 0444642110 |
Principles and Methods for Data Science, Volume 43 in the Handbook of Statistics series, highlights new advances in the field, with this updated volume presenting interesting and timely topics, including Competing risks, aims and methods, Data analysis and mining of microbial community dynamics, Support Vector Machines, a robust prediction method with applications in bioinformatics, Bayesian Model Selection for Data with High Dimension, High dimensional statistical inference: theoretical development to data analytics, Big data challenges in genomics, Analysis of microarray gene expression data using information theory and stochastic algorithm, Hybrid Models, Markov Chain Monte Carlo Methods: Theory and Practice, and more.
| Author | : David J. C. MacKay |
| Publisher | : Cambridge University Press |
| Total Pages | : 694 |
| Release | : 2003-09-25 |
| Genre | : Computers |
| ISBN | : 9780521642989 |
Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.
| Author | : Anthony Almudevar |
| Publisher | : Springer Nature |
| Total Pages | : 361 |
| Release | : 2020-03-11 |
| Genre | : Medical |
| ISBN | : 3030346757 |
This book commemorates the scientific contributions of distinguished statistician, Andrei Yakovlev. It reflects upon Dr. Yakovlev’s many research interests including stochastic modeling and the analysis of micro-array data, and throughout the book it emphasizes applications of the theory in biology, medicine and public health. The contributions to this volume are divided into two parts. Part A consists of original research articles, which can be roughly grouped into four thematic areas: (i) branching processes, especially as models for cell kinetics, (ii) multiple testing issues as they arise in the analysis of biologic data, (iii) applications of mathematical models and of new inferential techniques in epidemiology, and (iv) contributions to statistical methodology, with an emphasis on the modeling and analysis of survival time data. Part B consists of methodological research reported as a short communication, ending with some personal reflections on research fields associated with Andrei and on his approach to science. The Appendix contains an abbreviated vitae and a list of Andrei’s publications, complete as far as we know. The contributions in this book are written by Dr. Yakovlev’s collaborators and notable statisticians including former presidents of the Institute of Mathematical Statistics and of the Statistics Section of the AAAS. Dr. Yakovlev’s research appeared in four books and almost 200 scientific papers, in mathematics, statistics, biomathematics and biology journals. Ultimately this book offers a tribute to Dr. Yakovlev’s work and recognizes the legacy of his contributions in the biostatistics community.
| Author | : Alejandro F. Frangi |
| Publisher | : Springer |
| Total Pages | : 918 |
| Release | : 2018-09-13 |
| Genre | : Computers |
| ISBN | : 3030009289 |
The four-volume set LNCS 11070, 11071, 11072, and 11073 constitutes the refereed proceedings of the 21st International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2018, held in Granada, Spain, in September 2018. The 373 revised full papers presented were carefully reviewed and selected from 1068 submissions in a double-blind review process. The papers have been organized in the following topical sections: Part I: Image Quality and Artefacts; Image Reconstruction Methods; Machine Learning in Medical Imaging; Statistical Analysis for Medical Imaging; Image Registration Methods. Part II: Optical and Histology Applications: Optical Imaging Applications; Histology Applications; Microscopy Applications; Optical Coherence Tomography and Other Optical Imaging Applications. Cardiac, Chest and Abdominal Applications: Cardiac Imaging Applications: Colorectal, Kidney and Liver Imaging Applications; Lung Imaging Applications; Breast Imaging Applications; Other Abdominal Applications. Part III: Diffusion Tensor Imaging and Functional MRI: Diffusion Tensor Imaging; Diffusion Weighted Imaging; Functional MRI; Human Connectome. Neuroimaging and Brain Segmentation Methods: Neuroimaging; Brain Segmentation Methods. Part IV: Computer Assisted Intervention: Image Guided Interventions and Surgery; Surgical Planning, Simulation and Work Flow Analysis; Visualization and Augmented Reality. Image Segmentation Methods: General Image Segmentation Methods, Measures and Applications; Multi-Organ Segmentation; Abdominal Segmentation Methods; Cardiac Segmentation Methods; Chest, Lung and Spine Segmentation; Other Segmentation Applications.
