In this talk, I will describe flexible new Bayesian methods to analyze functional and quantitative image data. The methods are based on functional mixed models, a framework that can simultaneously model multiple factors and account for correlation within and between the functions. I use an isomorphic basis-space approach to fitting the model, which leads to efficient calculations and adaptive smoothing yet flexibly accommodates the complex features characterizing these data. The method is automated and produces inferential plots indicating regions of the function or image associated with each factor, simultaneously considering practical and statistical significance, and flagging significant regions based on Bayesian false discovery rate. I will discuss both a Gaussian and robust version of the method. The robust approach is able to accommodate outlying curves or regions of curves, down-weighting their effect. Simulation studies show that this robust approach yields estimators and inference with outstandingly adaptive properties, demonstrating a remarkable ability to remove spurious local features induced by outliers and noise while retaining true features characterizing the signal. The approach is robust enough to model data with extremely heavy tails (e.g. Cauchy), and yet still performs well when the data are in fact Gaussian. I will also demonstrate how to perform functional classification using this method, with results competitive with other classification methods in current literature, and with the robust modeling approach having better performance than the Gaussian method. These methods are applicable to any functional or quantitative image data sampled on a fine grid, including many types of high-throughput genomic and proteomic data. We present results applying these methods to MALDI-TOF and 2D gel proteomic data.
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