High-dimensional Data Analysis

Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs and the use of these numerical methods in realistic scientific and engineering applications Part 1: High-Dimensional classification -- Flexible large margin classifiers -- Part II: Large-scale multiple testing -- A compound decisio-theoretic approach to large-scale multiple testing -- Part III: Model building with variables selection -- Model building with variable selection -- Bayesian variable selection in regression with networked predictors -- Part IV: High-dimensional statistics in genomics -- An overview on joint modelling of censored survival time and longitudinal data -- Part V: Analyis of survival and longitudinal data -- Survival analysis with high-dimensional covariates -- Part IV: Sufficient dimension reduction i regression -- Combining statistical procedures -- Subject index Over the last few years, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal processing. In particular, substantial advances have been made in the areas of feature selection, covariance estimation, classification and regression. This book intends to examine important issues arising from high-dimensional data analysis to explore key ideas for statistical inference and prediction. It is structured around topics on multiple hypothesis testing, feature selection, regression, classification, dimension reduction, as well as applications in survival analysis and biomedical research. The book will appeal to graduate students and new researchers interested in the plethora of opportunities available in high-dimensional data analysis Over the years, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal processing. This book intends to examine the issues arising from high-dimensional data analysis to explore key ideas for statistical inference and prediction.