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Self-Organizing Time Series Model

  • Tomoyuki Higuchi
Chapter
Part of the Statistics for Engineering and Information Science book series (ISS)

Abstract

The generalised state-space model (GSSM) that we deal with in this study is defined by a set of two equations,
$$system\;\bmod el\quad {x_t} = f({x_{t - 1}},{v_t})$$
(20.1.1)
$$observation\;\bmod el\quad {y_t} \sim r( \cdot |{x_t},{\theta _{obs}})$$
(20.1.2)
where x t is an n x × 1 vector of unobserved sate variables, and y t is an n y dimensional vector observation. \( {\mathbb{R}^{{n_x}}} \times {\mathbb{R}^{{n_v}}} \to {\mathbb{R}^{{n_x}}} \) is a given function. {v t } is an independent and identically distributed (i.i.d.) random process with v t ~ q(v|θ sys ). r is the conditional distribution of y t given x t q(∙|∙) and r(∙|∙) are, in general, non-Gaussian densities specified by the unknown parameter vectors, θ sys and θ obs respectively. In this study, we set θ = [θ sys ,θ obs ]′. The initial state x 0 is distributed according to the density p 0(x).

Keywords

Roulette Wheel Roulette Wheel Selection Marginal Posterior Distribution Spiral Density Wave Deterministic Sampling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Tomoyuki Higuchi

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