Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability)
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Functional Magnetic Resonance Imaging (fMRI) is a non-invasive technique for obtaining a series of images over time under a certain stimulation paradigm. We are interested in identifying regions of brain activity by observing differences in blood magnetism due to haemodynamic response to such stimulus. Here, we extend Kornak (2000) work by proposing a fully Bayesian two–stage model for detecting brain activity in fMRI. The only assumptions that the model makes about the activated areas is that they emit higher signals in response to an stimulus than non-activated areas do, and that they form connected regions, providing a framework for detecting activity much as a neurologist might. Due to the model complexity and following the Bayesian paradigm, we use Markov chain Monte Carlo (MCMC) methods to make inference over the parameters. A simulated study is used to check the model applicability and sensitivity.