Honey, I shrunk the parameter space: Dimensionality reduction for hierarchical models.

Joint modelling of behaviour and neural activation poses the potential for a significant advance to methods of linking brain and behaviour. However, methods of joint modelling have been limited by difficulties in estimation, often due to high dimensionality and simultaneous estimation challenges. In this talk, we present a method of model estimation which allows for a significant dimensionality reduction using factor analysis at the group level in a Bayesian hierarchical model based estimation framework. The method is based on the particle metropolis within Gibbs sampling algorithm (Gunawan, Hawkins, Tran, Kohn, & Brown, 2020) - which is robust and reliable - with changes implemented to the standard ‘pmwg’ R package. Additionally, we briefly highlight several alternate solutions to the dimensionality problem. Although we focus on joint modelling methods, this model based estimation approach could be used for any high dimensional modelling problem. We provide open source code and accompanying tutorial documentation to make the method accessible to any researchers.