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Nonparametric Bayesian models for AR and ARX identification

In this paper, we propose nonparametric Bayesian (NPB) models for autoregressive (AR) and autoregressive exogenous (ARX) identification. In the proposed AR model, we assumed that its coefficients are given by the Bernoulli process. Then, the proposed AR model was extended to the NPB model for ARX identification using two independent Bernoulli processes. The posterior distributions of the proposed models were investigated using the Gibbs sampler, and the coefficients and the order of the systems were simultaneously estimated. The effectiveness of the proposed methods was confirmed using numerical simulations.