The most famous battle in Statistics is the long running "debate" between Bayesians
and Frequentists. While that begins with an abstract disagreement over the nature of
probability, it leads to substantial practical differences in data analysis methodology. In
Statistics, the debate has almost cooled -- most statisticians will gladly make use of
techniques from both schools -- but in many other disciplines, the battle continues to be
heated. Neuroimaging data is well suited to Bayesian analysis, and I will try to show how
Bayesian methods can be used effectively. But it is also important to understand both
the benefits and limitations of this approach.
I will start with a review of Bayesian statistics in the context of a model relevant to
neuroimaging data. I will 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, especially with highdimensional
models such as those used in neuroimaging.
A particular challenge for Bayesian approaches is computing the results. Recent
computational developments have made this feasible to an unprecedented degree,
through optimization and simulation techniques. I will describe some of the current best
practices in Markov Chain Monte Carlo simulation and beyond. I will describe Bayesian
models of neuroimaging data with both temporal and spatial components.
Finally, I will discuss practical issues that arise in Bayesian modeling, including
hierarchical models, prior selection, model averaging, and model validation.
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