A likelihood-free filtering method via approximate Bayesian computation in evaluating biological simulation models

For the evaluation of the dynamic behavior of biological processes, e.g., gene regulatory sequences, we typically utilize nonlinear differential equations within a state space model in the context of genomic data assimilation. For the estimation of the parameter values for such systems, the particle filter can be a strong approach in terms of obtaining their theoretically exact posterior distributions of the parameter values. However, it has some drawbacks for dealing with biological processes in practice: (i) the number of unique particles decreases rapidly since the dimension of the parameter vector and the number of observed time points are higher than its capability, (ii) it cannot be applied when the likelihood function is analytically intractable, and (iii) the prior distributions of the parameter values are often arbitrary determined. To address these problems, we propose a novel method that utilizes the approximate Bayesian computation in filtering the data and self-organizing ensemble Kalman filter in constructing the prior distributions of the parameter values. Simulation studies show that the proposed method can overcome these problems; thus, it can estimate the posterior distributions of the parameter values with automatically setting prior distributions even for the cases that the particle filter cannot perform good results. Finally, we apply the method to real observation data in rat circadian oscillation and demonstrate the usefulness in practical situations.