Image data are increasingly encountered and are of growing importance in many
areas of science. Much of these data are quantitative image data, which are
characterized by intensities that represent some measurement of interest in the
scanned images. The data typically consist of multiple images on the same
domain and the goal of the research is to combine the quantitative information
across images to make inference about populations or interventions.
High-dimensional data with hundreds of thousands of observations are becoming
commonplace in many disciplines. The analysis of such data poses many
computational challenges, especially when the observations are correlated over
time and/or across space. In this paper we propose flexible hierarchical
regression models for analyzing such data that accommodate serial and/or
spatial correlation. We address the computational challenges involved in
fitting these models by adopting an approximate inference framework.