Figure 1

Simulations. (A) Three bi-directed nodes shown by the red, green, and blue circles. The first (red) node receives an exogenous input in the form of a Gaussian bump function (inset bottom left), shown as normalized intensity (i.) vs. time steps (t.). (B) The intrinsic coupling matrix with values corresponding to the colour bar shown on the right. Rows and columns correspond to the nodes shown in (A) via the colours shown on the outside of the matrix. (C) The priors set for the intrinsic coupling matrix had values corresponding to the colour bar shown on the right. Rows and columns correspond to the nodes shown in (A) via the colours shown on the outside of the matrix. (D) The synthetic data generated by the original state equation, shown as normalized intensity (i.) vs. time steps (t.), with colours corresponding to those of the nodes shown in (A). (E) The synthetic data generated by the modified state equation, shown as normalized intensity (i.) vs. time steps (t.), with colours corresponding to those of the nodes shown in (A). (F) The posterior estimates for the intrinsic coupling matrix following Bayesian model inversion with the original model for the data generated by the original state equation in (D), with values corresponding to the colour bar shown on the right. Rows and columns correspond to the nodes shown in (A) via the colours shown on the outside of the matrix. (G) The posterior estimates for the intrinsic coupling matrix following Bayesian model inversion with the modified model for the data generated by the original state equation in (D), with values corresponding to the colour bar shown on the right. Rows and columns correspond to the nodes shown in (A) via the colours shown on the outside of the matrix. (H) The posterior estimates for the intrinsic coupling matrix following Bayesian model inversion with the original model for the data generated by the modified state equation in (E), with values corresponding to the colour bar shown on the right. Rows and columns correspond to the nodes shown in (A) via the colours shown on the outside of the matrix. (I) The posterior estimates for the intrinsic coupling matrix following Bayesian model inversion with the modified model for the data generated by the modified state equation in (E), with values corresponding to the colour bar shown on the right. Rows and columns correspond to the nodes shown in (A) via the colours shown on the outside of the matrix. (J) Approximate lower bound log model evidence given by the free energy (F) following Bayesian model inversion for the original (o.) and modified (m.) models using the data generated by the original model in (D). Probabilities (p) derived from the log evidence are shown in the inset top right. (K) Approximate lower bound log model evidence given by the free energy (F) following Bayesian model inversion for the original (o.) and modified (m.) models using the data generated by the modified model in (E). Probabilities (p) derived from the log evidence are shown in the inset left. (L) The intensity (inten.) at every point in time for the non-dissipative form of the modified state equation, i.e., excluding external driving inputs and noise, using the posteriors from (I), using the Hamiltonian (Hamil.) as the observer equation.