The Nest of Students

INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference. Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download. The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work.

A comprehensive and up-to-date introduction to the fundamentals of regression analysis: Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences. Following a general introduction to regression modeling,including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics,including: * A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models. * Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model. * Tests on individual regression coefficients and subsets of coefficients. * Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition.Numerous exercises have been added throughout, allowing readers to test their understanding of the material. Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences.

Features: Linear models: regression • censored outcomes • endogenous regressors • bootstrap, jackknife, and robust and cluster–robust variance • instrumental variables • three-stage least squares • constraints • quantile regression • GLS • more. Panel/longitudinal data: random and fixed effects with robust standard errors • linear mixed models • random-effects probit • GEE • random- and fixed-effects Poisson • dynamic panel-data models • instrumental variables • panel unit-root tests • more. Multilevel mixed-effects models: continuous, binary, count, and survival outcomes • two-, three-, and higher-level models • generalized linear models • nonlinear models • random intercepts • random slopes • crossed random effects • BLUPs of effects and fitted values • hierarchical models • residual error structures • DDF adjustments • support for survey data • more. Binary, count, and limited outcomes: logistic, probit, tobit • Poisson and negative binomial • conditional, multinomial, nested, ordered, rank-ordered, and stereotype logistic • multinomial probit • zero-inflated and left-truncated count models • selection models • marginal effects • more. Extended regression models (ERMs): combine endogenous covariates, sample selection, and nonrandom treatment in models for continuous, interval-censored, binary, and ordinal outcomes • more.

Regularization, Optimization, Kernels, and Support Vector Machines offers a snapshot of the current state of the art of large-scale machine learning, providing a single multidisciplinary source for the latest research and advances in regularization, sparsity, compressed sensing, convex and large-scale optimization, kernel methods, and support vector machines. Consisting of 21 chapters authored by leading researchers in machine learning, this comprehensive reference: Covers the relationship between support vector machines (SVMs) and the Lasso * Discusses multi-layer SVMs * Explores nonparametric feature selection, basis pursuit methods, and robust compressive sensing * Describes graph-based regularization methods for single- and multi-task learning * Considers regularized methods for dictionary learning and portfolio selection * Addresses non-negative matrix factorization * Examines low-rank matrix and tensor-based models * Presents advanced kernel methods for batch and online machine learning, system identification, domain adaptation, and image processing * Tackles large-scale algorithms including conditional gradient methods, (non-convex) proximal techniques, and stochastic gradient descent. Regularization, Optimization, Kernels, and Support Vector Machines is ideal for researchers in machine learning, pattern recognition, data mining, signal processing, statistical learning, and related areas.

Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data. Many flexible models based on Gaussian processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these Gaussian process regression models in the analysis of functional data. Some MATLAB® and C codes are available on the first author’s website.

Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however,requires a balance of theoretical results, empirical rules, and subjective judgment. Regression Analysis by Example, Fifth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics,transformation, multicollinearity, logistic regression, and robust regression. The book now includes a new chapter on the detection and correction of multicollinearity, while also showcasing the use of the discussed methods on newly added data sets from the fields of engineering, medicine, and business. The Fifth Edition also explores additional topics, including: Surrogate ridge regression * Fitting nonlinear models * Errors in variables * ANOVA for designed experiments. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions, the required assumptions, and the evaluated success of each technique.Additionally, methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R.

Regression analysis is a statistical process which enables prediction of relationships between variables. The predictions are based on the casual effect of one variable upon another. Regression techniques for modeling and analyzing are employed on large set of data in order to reveal hidden relationship among the variables. This book will give you a rundown explaining what regression analysis is, explaining you the process from scratch. The first few chapters give an understanding of what the different types of learning are - supervised and unsupervised, how these learnings differ from each other. We then move to covering the supervised learning in details covering the various aspects of regression analysis. The outline of chapters are arranged in a way that gives a feel of all the steps covered in a data science process - loading the training dataset, handling missing values, EDA on the dataset, transformations and feature engineering, model building, assessing the model fitting and performance, and finally making predictions on unseen datasets. Each chapter starts with explaining the theoretical concepts and once the reader gets comfortable with the theory, we move to the practical examples to support the understanding. The practical examples are illustrated using R code including the different packages in R such as R Stats, Caret and so on. Each chapter is a mix of theory and practical examples. By the end of this book you will know all the concepts and pain-points related to regression analysis, and you will be able to implement your learning in your projects.

The first book to discuss robust aspects of nonlinear regression—with applications using R software: Robust Nonlinear Regression: with Applications using R covers a variety of theories and applications of nonlinear robust regression. It discusses both parts of the classic and robust aspects of nonlinear regression and focuses on outlier effects. It develops new methods in robust nonlinear regression and implements a set of objects and functions in S-language under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by practitioners as well as researchers. The book offers comprehensive coverage of the subject in 9 chapters: Theories of Nonlinear Regression and Inference; Introduction to R; Optimization; Theories of Robust Nonlinear Methods; Robust and Classical Nonlinear Regression with Autocorrelated and Heteroscedastic errors; Outlier Detection; R Packages in Nonlinear Regression; A New R Package in Robust Nonlinear Regression; and Object Sets. The first comprehensive coverage of this field covers a variety of both theoretical and applied topics surrounding robust nonlinear regression
Addresses some commonly mishandled aspects of modeling. R packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying websiteRobust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.

This is today’s most complete guide to regression analysis with Microsoft® Excel for any business analytics or research task. Drawing on 25 years of advanced statistical experience, Microsoft MVP Conrad Carlberg shows how to use Excel’s regression-related worksheet functions to perform a wide spectrum of practical analyses. Carlberg clearly explains all the theory you’ll need to avoid mistakes, understand what your regressions are really doing, and evaluate analyses performed by others. From simple correlations and t-tests through multiple analysis of covariance, Carlberg offers hands-on, step-by-step walkthroughs using meaningful examples. He discusses the consequences of using each option and argument, points out idiosyncrasies and controversies associated with Excel’s regression functions, and shows how to use them reliably in fields ranging from medical research to financial analysis to operations.

You don’t need expensive software or a doctorate in statistics to work with regression analyses. Microsoft Excel has all the tools you need—and this book has all the knowledge! Understand what regression analysis can and can’t do, and why + Master regression-based functions built into all recent versions of Excel + Work with correlation and simple regression + Make the most of Excel’s improved LINEST() function + Plan and perform multiple regression + Distinguish the assumptions that matter from the ones that don’t + Extend your analysis options by using regression instead of traditional analysis of variance + Add covariates to your analysis to reduce bias and increase statistical power.