Conclusions
Finally, how does computational modeling help advance cognitive science and neuroscience with respect to decision-making research? One important way that we mentioned earlier is to use predictions from a mathematical/computational model to generate prediction for BOLD fMRI signals in hypothesized brain regions during decision making. The first step in model-based fMRI is to estimate the free parameters in the mathematical/computational model of behavior. Then these estimates are used to generate predictions from the model across time and or trials. The model predictions are then convolved with a hemodynamic response function to produce a regressor that is finally used to predict the BOLD signal across time. Getting accurate parameter estimates is important because they affect the results of the subsequent model-based fMRI analysis (e.g., Tanaka et al., 2004). For example, Ahn and colleagues (2011) compared regressors obtained from maximum likelihood estimates of individuals with regressors obtained from individual estimates derived from hierarchical Bayesian estimation methods. For both estimation methods, they inserted the parameters estimated for an individual into the PVL model to generate the predicted choice probabilities for each trial, and they convolved these predictions with the canonical hemodynamic response filter. The choice probability is a relative measure of the expected value signal (Daw et al., 2006). Finally these regressors were used to predict activation in brain areas including the ventromedial prefrontal cortex (vmPFC), which is known to encode reward (Daw et al., 2006 and Knutson et al., 2005). Subsequent model-based fMRI results were generally consistent with the behavioral results. Importantly, the model based regressor produced substantially stronger correlations with BOLD signals in target areas than regressors simply based on observed behavior in the task. A similar result was also reported by Jessup et al. (2010). Finally, hierarchical Bayesian estimates produced substantially stronger correlations with activation in the vmPFC than maximum likelihood estimates. In conclusion, computational modeling in conjunction with effective parameter estimation methods can substantially improve analyses and understanding of the neural basis of cognition and decision.