On a framework of data assimilation for neuronal networks

When handling real-world data modeled by a complex network dynamical system, the number of the parameters is always even much more than the size of the data. Therefore, in many cases, it is impossible to estimate these parameters and however, the exact value of each parameter is frequently less interesting than the distribution of the parameters may contain important information towards understanding the system and data. In this paper, we propose this question arising by employing a data assimilation approach to estimate the distribution of the parameters in the leakage-integrate-fire (LIF) neuronal network model from the experimental data, for example, the blood-oxygen-level-dependent (BOLD) signal. Herein, we assume that the parameters of the neurons and synapses are inhomogeneous but independently identical distributed following certain distribution with unknown hyperparameters. Thus, we estimate these hyperparameters of the distributions of the parameters, instead of estimating the parameters themselves. We formulate this problem under the framework of data assimilation and hierarchical Bayesian method, and present an efficient method named Hierarchical Data Assimilation (HDA) to conduct the statistical inference on the neuronal network model with the BOLD signal data simulated by the hemodynamic model. We consider the LIF neuronal networks with four synapses and show that the proposed algorithm can estimate the BOLD signals and the hyperparameters with good preciseness. In addition, we discuss the influence on the performance of the algorithm configuration and the LIF network model setup.