Online Bayesian Modeling and Prediction of Nonlinear Systems

Summary

Objectives : Given time-series data from an unknown target system, one often wants to build a model for the system behind the data and make predictions. If the target system can be assumed to be linear, there are means of modeling and predicting the target system in question. If, however, one cannot assume the system is linear, various linear theories have natural limitations in terms of modeling and predictive capabilities. This paper attempts to construct a model from time-series data and make an online prediction when the linear assumption is not valid.

Methods : The problem is formulated within a Bayesian framework implemented by the Sequential Monte Carlo method. Online Bayesian learning/prediction requires computation of a posterior distribution in a sequential manner as each datum arrives. The Sequential Monte Carlo method computes the importance weight in order to draw sample from the posterior distribution. The scheme is tested against time-series data from a noisy Rossler system.

Results : The test time-series data is the x-coordinate of the trajectory generated by a noisy Roessler system. Attempts are made with regard to online reconstruction of the attractor and online prediction of the time-series data.

Conclusions : The proposed algorithm appears to be functional. The algorithm should be tested against real world data.

Keywords

Online learning and prediction - Bayesian learning and prediction - nonlinear dynamical systems - Sequential Monte Carlo (particle filter)

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