Copula particle filter algorithm for inferring parameters of regulatory network models with noisy observation data

Biological experimental data normally contain noise due to probabilistic character of biochemical reactions and environmental fluctuations. It has been widely assumed that the observed data is the corresponding system states plus a white noise whose variance is a constant. In addition, all observations are assumed to be independent to each other. However, recently biological studies suggested that the randomness in experimental data may depend on system state and observations of different variables may be highly correlated. To address these issues, this work proposes a new model in which the variance of noise is a function of system state. We design a copula particle filter algorithm that is characterized by using copula density functions in place of multivariable normal density functions. The combination of the noise model and copula particle filter leads to a novel algorithm whose performance is rigorously evaluated by inferring unknown parameters in mathematical models. We test three linear/nonlinear functions to fit the noisy data and numerical results suggest that the nonlinear sigmoid function is the best function to represent the state-dependent variance of noise. Our proposed method has better accuracy of estimated parameters than the widely use the Liu-West filter and copula particle filter algorithm. Numerical results suggest that our proposed method is superior to the other two widely filter algorithms and is very effective for parameter estimation in biochemical network models under noisy dependent observations.