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Image data are increasingly encountered and are of growing importance in manyareas of science. Much of these data are quantitative image data, which arecharacterized by intensities that represent some measurement of interest in thescanned images. The data typically consist of multiple images on the samedomain and the goal of the research is to combine the quantitative informationacross images to make inference about populations or interventions. In thispaper we present a unified analysis framework for the analysis of quantitativeimage data using a Bayesian functional mixed model approach. This framework isflexible enough to handle complex, irregular images with many local features,and can model the simultaneous effects of multiple factors on the imageintensities and account for the correlation between images induced by thedesign. We introduce a general isomorphic modeling approach to fitting thefunctional mixed model, of which the wavelet-based functional mixed model isone special case. With suitable modeling choices, this approach leads toefficient calculations and can result in flexible modeling and adaptivesmoothing of the salient features in the data. The proposed method has thefollowing advantages: it can be run automatically, it produces inferentialplots indicating which regions of the image are associated with each factor, itsimultaneously considers the practical and statistical significance offindings, and it controls the false discovery rate.

Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data