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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 thedata. Therefore, in many cases, it is impossible to estimate these parametersand however, the exact value of each parameter is frequently less interestingthan the distribution of the parameters may contain important informationtowards understanding the system and data. In this paper, we propose thisquestion arising by employing a data assimilation approach to estimate thedistribution of the parameters in the leakage-integrate-fire (LIF) neuronalnetwork model from the experimental data, for example, theblood-oxygen-level-dependent (BOLD) signal. Herein, we assume that theparameters of the neurons and synapses are inhomogeneous but independentlyidentical distributed following certain distribution with unknownhyperparameters. Thus, we estimate these hyperparameters of the distributionsof the parameters, instead of estimating the parameters themselves. Weformulate this problem under the framework of data assimilation andhierarchical Bayesian method, and present an efficient method namedHierarchical Data Assimilation (HDA) to conduct the statistical inference onthe neuronal network model with the BOLD signal data simulated by thehemodynamic model. We consider the LIF neuronal networks with four synapses andshow that the proposed algorithm can estimate the BOLD signals and thehyperparameters with good preciseness. In addition, we discuss the influence onthe performance of the algorithm configuration and the LIF network model setup.

On a framework of data assimilation for neuronal networks