Bayesian Analysis of Neuroimaging Data
Chris Genovese
Carnegie Mellon University
Statistics
The most famous battle in statistics is the long-running “debate” between Bayesians and Frequentists. While it begins with an abstract disagreement over the nature of probability, it leads to substantial practical differences in data analysis methodology. Within statistics, the debate has largely cooled—most statisticians now make use of techniques from both schools—but in many other disciplines the debate remains heated. Neuroimaging data are well suited to Bayesian analysis, and I will illustrate how Bayesian methods can be used effectively, while also discussing the benefits and limitations of this approach.
I begin with a review of Bayesian statistics in the context of a model relevant to neuroimaging data. I compare and contrast Bayesian and classical approaches in terms of ease of modeling, inferential performance, and interpretation. Both approaches have strengths and weaknesses in each of these dimensions, particularly in high-dimensional models such as those used in neuroimaging.
A particular challenge for Bayesian approaches is computational feasibility. Recent developments in optimization and simulation techniques have made such analyses feasible to an unprecedented degree. I describe current best practices in Markov Chain Monte Carlo simulation and related methods. Bayesian models of neuroimaging data incorporating both temporal and spatial components are presented.
Finally, practical issues in Bayesian modeling are discussed, including hierarchical models, prior selection, model averaging, and model validation.