Bayesian inference with INLA

NOTE EDITORE

The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed.Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website.This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.

SOMMARIO

Introduction to Bayesian Inference Introduction Bayesian inference Conjugate priors Computational methods Markov chain Monte Carlo The integrated nested Laplace approximation An introductory example: U’s in Game of Thrones books Final remarks The Integrated Nested Laplace Approximation Introduction The Integrated Nested Laplace Approximation The R-INLA package Model assessment and model choice Control options Working with posterior marginals Sampling from the posterior Mixed-effects Models Introduction Fixed-effects models Types of mixed-effects models Information on the latent effects Additional arguments Final remarks Multilevel Models Introduction Multilevel models with random effects Multilevel models with nested effects Multilevel models with complex structure Multilevel models for longitudinal data Multilevel models for binary data Multilevel models for count data Priors in R-INLA Introduction Selection of priors Implementing new priors Penalized Complexity priors Sensitivity analysis with R-INLA Scaling effects and priors Final remarks Advanced Features Introduction Predictor Matrix Linear combinations Several likelihoods Shared terms Linear constraints Final remarks Spatial Models Introduction Areal data Geostatistics Point patterns Temporal Models Introduction Autoregressive models Non-Gaussian data Forecasting Space-state models Spatio-temporal models Final remarks Smoothing Introduction Splines Smooth terms with INLA Smoothing with SPDE Non-Gaussian models Final remarks Survival Models Introduction Non-parametric estimation of the survival curve Parametric modeling of the survival function Semi-parametric estimation: Cox proportional hazards Accelerated failure time models Frailty models Joint modeling Implementing New Latent Models Introduction Spatial latent effects R implementation with rgeneric Bayesian model averaging INLA within MCMC Comparison of results Final remarks Missing Values and Imputation Introduction Missingness mechanism Missing values in the response Imputation of missing covariates Multiple imputation of missing values Final remarks 13.Mixture models Introduction Bayesian analysis of mixture models Fitting mixture models with INLA Model selection for mixture models Cure rate models Final remarks Packages used in the book

AUTORE

Virgilio Gómez-Rubio is associate professor in the Department of Mathematics, School of Industrial Engineering, Universidad de Castilla-La Mancha, Albacete, Spain. He has developed several packages on spatial and Bayesian statistics that are available on CRAN, as well as co-authored books on spatial data analysis and INLA including Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA (CRC Press, 2019).

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9781032174532
• Dimensioni: 10 x 7 in Ø 1.42 lb
• Formato: Brossura
• Pagine Arabe: 332