Bayes Nets of Time Series: Stochastic Realizations and Projections

Part of the Springer Optimization and Its Applications book series (SOIA, volume 28)


Graphical models in which every node holds a time-series are developed using special conditions from static multivariate Gaussian processes, particularly the notion of lattice conditional independence (LCI), due to Anderson and Perlman (1993). Under certain “feedback free” conditions, LCI imposes a special zero structure on the state space representation of processes which have a stochastic realisation. This structure comes directly from the transitive directed acyclic graph (TDAG) which is in one-to-one correspondence with the Boolean Hilbert lattice of the LCO formulation. Simple AR(1) examples are presented.


Conditional Independence Multivariate Normal Distribution Gaussian Case Boolean Lattice Conditional Covariance 
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© Springer Science+Business Media LLC 2009

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringMcGill UniversityMontrealCanada
  2. 2.Department of Mathematics and StatisticsUniversity of GuelphCanada

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