Extended Data Fig. 3: Framework of Hierarchical Bayesian Inference.
From: Simulation and assimilation of the digital human brain
The hyperparameter layer presents the random walk to updating of the hyperparameter from \(\lambda (t)\) to \({\lambda }^{{\prime} }\). The parameter layer presents the sampling process of the parameter vector \(\theta (t)\) from the hyperparameter by the sampling operator \(\Phi (\bullet )\) and being modified via the changes from \(\lambda (t)\) to \({\lambda }^{{\prime} }\), which gives \(\theta (t+1)\). The computational model layer shows the evolution of the hidden state \(x(t)\) by iteratively computing the computational model \(\dot{x}=F(x,\theta )\), which influenced by the parameter vector \(\theta (t)\). The experimental layer shows how the observation \(y(t+1)\), which is obtained from the hidden state \(x(t+1)\), is used to update the hidden state and the parameters, and in particular, to resample the hyperparameters from \({\lambda }^{{\prime} }\) to \(\lambda (t+1)\).
