Bayesian Inference with Inla

Gomez-Rubio, Virgilio

商品描述

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.

商品描述(中文翻譯)

整合嵌套拉普拉斯近似法(INLA)是一種最近的計算方法,可以在比典型的馬可夫鏈蒙特卡羅(MCMC)方法所需的時間的一小部分內擬合貝葉斯模型。INLA專注於對潛在高斯馬可夫隨機場模型的模型參數進行邊際推斷,並利用模型中的條件獨立性特性以提高計算速度。

《使用INLA進行貝葉斯推斷》介紹了INLA及其相關的R軟件包用於模型擬合。本書描述了底層方法以及如何使用R擬合各種模型。涵蓋的主題包括廣義線性混合效應模型、多層次模型、空間和時空模型、平滑方法、生存分析、缺失值插補和混合模型。還討論了INLA軟件包的高級功能以及如何擴展軟件包中可用的先驗和潛在模型的數量。本書中的所有示例都可以完全重現,數據集和R代碼可從書籍網站上獲取。

本書將對具有貝葉斯推斷背景並希望在其工作中應用INLA方法的不同領域的研究人員有所幫助。示例涵蓋了生物統計學、計量經濟學、教育、環境科學、流行病學、公共衛生和社會科學等主題。

作者簡介

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).

作者簡介(中文翻譯)

Virgilio Gómez-Rubio是西班牙卡斯蒂利亞-拉曼查大學工業工程學院數學系的副教授。他在空間統計學和貝葉斯統計學方面開發了幾個在CRAN上可用的套件,並與他人合著了有關空間數據分析和INLA的書籍,包括《Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA》(CRC Press,2019)。