Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Bayesian Logical Data Analysis for the Physical Sciences
Bayesian Logical Data Analysis for the Physical Sciences
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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Nonlinear hemodynamic models express the BOLD (blood oxygenation level dependent) signal as a nonlinear, parametric functional of the temporal sequence of local neural activity. Several models have been proposed for both the neural activity and the hemodynamics. We compare two such combined models: the original balloon model with a square-pulse neural model (Friston, Mechelli, Turner, & Price, 2000) and an extended balloon model with a more sophisticated neural model (Buxton, Uludag, Dubowitz, & Liu, 2004). We learn the parameters of both models using a Bayesian approach, where the distribution of the parameters conditioned on the data is estimated using Markov chain Monte Carlo techniques. Using a split-half resampling procedure (Strother, Anderson, & Hansen, 2002), we compare the generalization abilities of the models as well as their reproducibility, for both synthetic and real data, recorded from two different visual stimulation paradigms. The results show that the simple model is the better one for these data.