Bayesian Regression Modeling with Inla 1st edition By Xiaofeng Wang, Yu Yue Ryan, Julian Faraway – Ebook PDF Instant Download/Delivery: 0367572266, 9780367572266
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ISBN 10: 0367572266
ISBN 13: 9780367572266
Author: Xiaofeng Wang, Yu Yue Ryan, Julian Faraway
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.
Bayesian Regression Modeling with Inla 1st Table of contents:
1 Introduction
1.1 Quick Start
1.1.1 Hubble’s Law
1.1.2 Standard Analysis
1.1.3 Bayesian Analysis
1.1.4 INLA
1.2 Bayes Theory
1.3 Prior and Posterior Distributions
1.4 Model Checking
1.5 Model Selection
1.6 Hypothesis Testing
1.7 Bayesian Computation
1.7.1 Exact
1.7.2 Sampling
1.7.3 Approximation
2 Theory of INLA
2.1 Latent Gaussian Models (LGMs)
2.2 Gaussian Markov Random Fields (GMRFs)
2.3 Laplace Approximation and INLA
2.4 INLA Problems
2.5 Extensions
3 Bayesian Linear Regression
3.1 Introduction
3.2 Bayesian Inference for Linear Regression
3.3 Prediction
3.4 Model Selection and Checking
3.4.1 Model Selection by DIC
3.4.2 Posterior Predictive Model Checking
3.4.3 Cross-Validation Model Checking
3.4.4 Bayesian Residual Analysis
3.5 Robust Regression
3.6 Analysis of Variance
3.7 Ridge Regression for Multicollinearity
3.8 Regression with Autoregressive Errors
4 Generalized Linear Models
4.1 GLMs
4.2 Binary Responses
4.3 Count Responses
4.3.1 Poisson Regression
4.3.2 Negative Binomial Regression
4.4 Modeling Rates
4.5 Gamma Regression for Skewed Data
4.6 Proportional Responses
4.7 Modeling Zero‐Inflated Data
5 Linear Mixed and Generalized Linear Mixed Models
5.1 Linear Mixed Models
5.2 Single Random Effect
5.2.1 Choice of Priors
5.2.2 Random Effects
5.3 Longitudinal Data
5.3.1 Random Intercept
5.3.2 Random Slope and Intercept
5.3.3 Prediction
5.4 Classical Z‐Matrix Model
5.4.1 Ridge Regression Revisited
5.5 Generalized Linear Mixed Models
5.6 Poisson GLMM
5.7 Binary GLMM
5.7.1 Improving the Approximation
6 Survival analysis
6.1 Introduction
6.2 Semiparametric Models
6.2.1 Piecewise Constant Baseline Hazard Models
6.2.2 Stratified Proportional Hazards Models
6.3 Accelerated Failure Time Models
6.4 Model Diagnosis
6.5 Interval censored data
6.6 Frailty models
6.7 Joint Modeling of Longitudinal and Time‐to‐Event Data
7 Random Walk Models for Smoothing Methods
7.1 Introduction
7.2 Smoothing Splines
7.2.1 Random Walk (RW) Priors for Equally-Spaced Locations
7.2.2 Choice of Priors on
7.2.3 Random Walk Models for Non-Equally Spaced Locations
7.3 Thin-Plate Splines
7.3.1 Thin-Plate Splines on Regular Lattices
7.3.2 Thin-Plate Splines at Irregularly-Spaced Locations
7.4 Besag Spatial Model
7.5 Penalized Regression Splines (P-Splines)
7.6 Adaptive Spline Smoothing
7.7 Generalized Nonparametric Regression Models
7.8 Excursion Set with Uncertainty
8 Gaussian Process Regression
8.1 Introduction
8.2 Penalized Complexity Priors
8.3 Credible Bands for Smoothness
8.4 Non-Stationary Fields
8.5 Interpolation with Uncertainty
8.6 Survival Response
9 Additive and Generalized Additive Models
9.1 Additive Models
9.2 Generalized Additive Models
9.2.1 Binary Response
9.2.2 Count Response
9.3 Generalized Additive Mixed Models
10 Errors-in-Variables Regression
10.1 Introduction
10.2 Classical Errors-in-Variables Models
10.2.1 ASimple Linear Model with Heteroscedastic Errors-in-Variables
10.2.2 A General Exposure Model with Replicated Measurements
10.3 Berkson Errors-in-Variables Models
11 Miscellaneous Topics in INLA
11.1 Splines as a Mixed Model
11.1.1 Truncated Power Basis Splines
11.1.2 O’Sullivan Splines
11.1.3 Example: Canadian Income Data
11.2 Analysis of Variance for Functional Data
11.3 Extreme Values
11.4 Density Estimation Using INLA
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Tags: Xiaofeng Wang, Yu Yue Ryan, Julian Faraway, Bayesian Regression