Ensemble smoothers for inference of hidden states and parameters in combinatorial regulatory model

Abstract

In time-series analysis, state space models (SSMs) have been widely used to estimate the conditional probability distributions of hidden variables and to clarify statistical models when predicting data. Linear SSMs have often been used because they can be efficiently solved; however, the simulated data is often not consistent with the observed data because of the simplicity. Thus, an alternative nonlinear model, termed the combinatorial regulatory model, have been used as a simple extension, and ensemble-based filters have been applied to estimate their non-Gaussian probability distributions and parameter values in exchange for higher computational cost. In this paper, we extend such methodologies to Rauch–Tung–Striebel (RTS) smoother to simplify the computation. Through a large amount of computational experiments using synthetic data, we compare the computational cost, estimation accuracy of the parameter values, and model selection capability of the ensemble Kalman filter (EnKF), ensemble particle filter (EnPF), unscented Kalman filter, and their RTS smoothers and show the performance and the limitations of these methodologies according to the amount of data and the number of particles. Consequently, we show that EnKF-RTS is efficient and stable if there exists a lot of observation points, and EnPF and EnPF-RTS can be a good choice for estimating accurate parameter values and better classifying statistical models if there are many particles and not many observation points.