Modeling Spatio-Temporal Data Markov Random Fields, Objective Bayes, and Multiscale Models

Several important topics in spatial and spatio-temporal statistics developed in the last 15 years have not received enough attention in textbooks. This book aims to fill some of 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 discussed in this book include:

- Proper Gaussian Markov random fields and their use as building blocks for spatio-temporal models and multiscale models.

- Hierarchical models with intrinsic conditional autoregressive priors for spatial random effects, including reference prior, 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 stations 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 is 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.