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This paper addresses the problem of estimating the time series of a gene expression using nonlinear Bayesian filtering algorithms. The response of gene regulatory networks (GRNs) to functional requirements in the cell and environmental conditions evolves over time. Dynamic biological processes such as cancer progression and treatment recovery depend on the collected genetic profiles. These processes are behind genetic interactions that rewire over the course of time. The GRN was formulated as a nonlinear and non-Gaussian dynamic system defined by the gene measurement model and the unknown state is an evolution of the gene model. However, the GRN has a high dimensional space where most of nonlinear Bayesian filtering algorithms are ineffective in high dimensional spaces. Therefore, many authors have introduced various techniques to overcome what has become known as the curse of dimensionality. This paper presents a comparative study between extended Kalman filter, unscented Kalman filter and derivatives of particle filters, in tracking the evolution of gene expression over time. Application of the nonlinear Bayesian filtering algorithms to estimate the evolution of gene expression from synthetic and real data, shows that the unscented particle filter (UKFPF) provides promising and robust results compared to other filters. Furthermore, UKF-PF provides an alternative solution to the problem of modeling gene regulatory networks.

A comparative study of nonlinear Bayesian filtering algorithms for estimation of gene expression time series data