Hierarchical Bayesian analyses have become a popular technique for analyzing complex interactions of important experimental variables. One application where these analyses have great potential is in analyzing neural data. However, estimating parameters for these models can be complicated. Although many software programs facilitate the estimation of parameters within hierarchical Bayesian models, due to some restrictions, complicated workarounds are sometimes necessary to implement a model within the software. One such restriction is convolution, a technique often used in neuroimaging analyses to relate experimental variables to models describing neural activation. Here, we show how to perform convolution within the R programming environment. The strategy here is to pass the convolved neural signal to existing software package for fitting hierarchical Bayesian models to data such as JAGS (Plummer 2003) or Stan (Carpenter et al. 2017). We use the convolution technique as a basis for describing neural time series data and develop five models to describe how subject-, condition-, and brain-area-specific effects interact. To provide a concrete example, we apply these models to fMRI data from a stop-signal task. The models are assessed in terms of model fit, parameter constraint, and generalizability. For these data, our results suggest that while subject and condition constraints are important for both fit and generalization, region of interest constraints did not substantially improve performance.
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We began our analysis by first examining pairwise functional correlations of each time series across all ROIs. These analyses revealed a potential need for ROI-based constraints, motivating the development of models 4 and 5.
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The study was approved by the Institutional Review Board of the university.
Appendix A: R Code for the canonical hemodynamic response function
Appendix B: R Code for the boxcar function
Appendix C: R Code for boxcar convolution using discrete approximation
Appendix D: JAGS Code for Model 3
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Molloy, M.F., Bahg, G., Li, X. et al. Hierarchical Bayesian Analyses for Modeling BOLD Time Series Data. Comput Brain Behav 1, 184–213 (2018). https://doi.org/10.1007/s42113-018-0013-5
- Functional magnetic resonance imaging