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Marta Blangiardo and Michela Cameletti. 2015. Spatial and Spatio-temporal Bayesian Models with R-INLA. West Sussex, United Kingdom: John Wiley & Sons, Ltd.
This book presents the principles of Bayesian theory for spatial and spatio-temporal
modeling, combining three aspects: (1) an introduction to Bayesian thinking and
theoretical aspects of the Bayesian approach, (2) a focus on the spatial and
spatio-temporal models used within the Bayesian framework, (3) a series of
practical examples which allow the reader to link the statistical theory presented
to real data problems. All the examples are coded in the R package R-INLA, and
based on the recently developed integrated nested Laplace approximation (INLA)
method, which has proven to be a valid alternative to the commonly used Markov
Chain Monte Carlo (MCMC) simulations.
The book starts with an introduction in Chapter 1, providing the reader with the
importance of spatial and spatio-temporal modeling in several fields, such as social
science, environmental epidemiology, and infectious diseases epidemiology. We
then show why Bayesian models are commonly used in these fields and why we
focus on the INLA approach. We also describe the datasets which will be used
in the rest of the book, providing information on the topics that will be used as
illustration.
As all the examples are run in R, in Chapter 2 we introduce the basic concepts of
the R language. Chapter 3 describes the Bayesian methods: first we introduce the
paradigms of this approach (i.e., the concepts of prior and posterior distributions,
Bayes theorem, conjugacy, how to obtain the posterior distribution, the computational
issues around Bayesian statistics for conjugated and non conjugated models).
We also include a small section on the differences between the frequentist and the
Bayesian approach, focusing on the different interpretation of confidence intervals,
parameters, and hypothesis testing.
Chapter 4 discusses the computational issues regarding Bayesian inference. After
the Monte Carlo method is introduced, we consider MCMC algorithms, providing
some examples in R for the case of conjugated and non conjugated distributions.
The focus of the chapter is the INLA method, which is a computationally powerful
alternative toMCMC algorithms. In particular, the R-INLA library is described by
means of a small tutorial and of a step-by-step example.
Then in Chapter 5 we present the Bayesian modeling framework which is used
in the fields introduced in Chapter 1 and focuses on regression models (linear and
generalized linear models). In this context, we introduce the concept of exchangeability
topic which will be expanded later in the chapters on spatial and spatio-temporal
modeling. The last section of this part is devoted to introducing hierarchical models.
Chapter 6 focuses on models for two types of spatial processes: (1) area
level—introducing disease mapping models and small area ecological regressions
(including risk factors and covariates) and then presenting zero inflated models for
Poisson and Binomial data; (2) point level—presenting Bayesian kriging through
the stochastic partial differential equations (SPDE) approach and showing how
to model observed data and also to predict for new spatial locations. Chapter 7
extends the topics treated in Chapter 6 adding a temporal dimension, where we
also include the time dimension in the models.
Finally, Chapter 8 introduces new developments within INLA and focuses on
the following advanced applications: when data are modeled using different likelihoods,
when missing data are present in covariates, a spatio-temporal model with
dynamic evolution for the regression coefficients, and a spatio-temporal model for
high-frequency data on time where a temporal resolution reduction is needed.
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