Several important topics in spatial and spatio-temporal statistics developed in the last 15 years have not received enough attention in textbooks. Modeling Spatio-Temporal Data: Markov Random Fields, Objectives Bayes, and Multiscale Models aims to fill this gap by providing an overview of a variety of recently proposed approaches for the analysis of spatial and spatio-temporal datasets, including proper Gaussian Markov random fields, dynamic multiscale spatio-temporal models, and objective priors for spatial and spatio-temporal models. The goal is to make these approaches more accessible to practitioners, and to stimulate additional research in these important areas of spatial and spatio-temporal statistics.

Key topics:

• Proper Gaussian Markov random fields and their uses as building blocks for spatio-temporal models and multiscale models.
• Hierarchical models with intrinsic conditional autoregressive priors for spatial random effects, including reference priors, results on fast computations, and objective Bayes model selection.
• Objective priors for state-space models and a new approximate reference prior for a spatio-temporal model with dynamic spatio-temporal random effects.
• Spatio-temporal models based on proper Gaussian Markov random fields for Poisson observations.
• Dynamic multiscale spatio-temporal thresholding for spatial clustering and data compression.
• Multiscale spatio-temporal assimilation of computer model output and monitoring station data.
• Dynamic multiscale heteroscedastic multivariate spatio-temporal models.
• The M-open multiple optima paradox and some of its practical implications for multiscale modeling.
• Ensembles of dynamic multiscale spatio-temporal models for smooth spatio-temporal processes.

The audience for this book are practitioners, researchers, and graduate students in statistics, data science, machine learning, and related fields. Prerequisites for this book are master's-level courses on statistical inference, linear models, and Bayesian statistics. This book can be used as a textbook for a special topics course on spatial and spatio-temporal statistics, as well as supplementary material for graduate courses on spatial and spatio-temporal modeling.