Wang / Ryan Yue / Faraway Bayesian Regression Modeling with INLA

1. Auflage 2018
ISBN: 978-1-351-16575-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 324 Seiten

Reihe: Chapman & Hall/CRC Computer Science & Data Analysis

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.
Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic.
Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York.
Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.

Autoren/Hrsg.

Wang, Xiaofeng

Ryan Yue, Yu

Faraway, Julian J.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

1.Introduction Quick Start Hubble’s Law Standard Analysis Bayesian Analysis INLA Bayes Theory Prior and Posterior Distributions Model Checking Model Selection Hypothesis testing Bayesian Computation Exact Sampling Approximation 2.Theory of INLA Latent Gaussian Models (LGMs) Gaussian Markov Random Fields (GMRFs) Laplace Approximation and INLA INLA Problems Extensions 3.Bayesian Linear Regression Introduction Bayesian Inference for Linear Regression Prediction Model Selection and Checking Model Selection by DIC Posterior Predictive Model Checking Cross-validation Model Checking Bayesian Residual Analysis Robust Regression Analysis of Variance Ridge Regression for Multicollinearity Regression with Autoregressive Errors 4.Generalized Linear Models GLMs Binary Responses Count Responses Poisson Regression Negative binomial regression Modeling Rates Gamma Regression for Skewed Data Proportional Responses Modeling Zero-inflated Data 5.Linear Mixed and Generalized Linear Mixed Models Linear Mixed Models Single Random Effect Choice of Priors Random Effects Longitudinal Data Random Intercept Random Slope and Intercept Prediction Classical Z-matrix Model Ridge Regression Revisited Generalized Linear Mixed Models Poisson GLMM Binary GLMM Improving the Approximation
6.Survival Analysis Introduction Semiparametric Models Piecewise Constant Baseline Hazard Models Stratified Proportional Hazards Models Accelerated Failure Time Models Model Diagnosis Interval Censored Data Frailty Models Joint Modeling of Longitudinal and Time-to-event Data 7.Random Walk Models for Smoothing Methods Introduction Smoothing Splines Random Walk (RW) Priors for Equally-spaced Locations Choice of Priors on s e and sfRandom Walk Models for Non-equally Spaced Locations Thin-plate Splines Thin-plate Splines on Regular Lattices Thin-plate Splines at Irregularly-spaced Locations Besag Spatial Model Penalized Regression Splines (P-splines) Adaptive Spline Smoothing Generalized Nonparametric Regression Models Excursion Set with Uncertainty 8.Gaussian Process Regression Introduction Penalized Complexity Priors Credible Bands for Smoothness Non-stationary Fields Interpolation with Uncertainty Survival Response 9.Additive and Generalized Additive Models Additive Models Generalized Additive Models Binary response Count response Generalized Additive Mixed Models 10.Errors-in-Variables Regression Introduction Classical Errors-in-Variables Models A simple linear model with heteroscedastic errors-invariablesA general exposure model with replicated measurements Berkson Errors-in-Variables Models
11.Miscellaneous Topics in INLA Splines as a Mixed Model Truncated Power Basis Splines O’Sullivan Splines Example: Canadian Income Data Analysis of Variance for Functional Data Extreme Values Density Estimation using INLA
Appendix A Installation Appendix B Uninformative Priors in Linear Regression Index

Über Autor(innen)

Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic.
Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York.
Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.