2018/11/19 by Reza Rezaie, X. Rong Li, Rezaie, Reza +1
Computer Science · #Bayesian Modeling and Causal Inference #Blind Source Separation Techniques #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Neural Networks and Applications #Probability (math.PR) #Signal Processing (eess.SP) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1811.07804
openalex publication_date 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The conditionally Markov (CM) sequence contains different classes including Markov, reciprocal, and so-called CML and CMF (two special classes of CM sequences). Each class has its own forward and backward dynamic models. The evolution of a CM sequence can be described by different models. For example, a Markov sequence can be described by a Markov model, as well as by reciprocal, CML, and CMF models. Also, sometimes a forward model is available, but it is desirable to have a backward model for the same sequence (e.g., in smoothing). Therefore, it is important to study relationships between different dynamic models of a CM sequence. This paper discusses such relationships between models of nonsingular Gaussian (NG) CML, CMF, reciprocal, and Markov sequences. Two models are said to be explicitly sample-equivalent if not only they govern the same sequence, but also a one-one correspondence between their sample paths is made explicitly. A unified approach is presented, such that given a forward/backward CML/CMF/reciprocal/Markov model, any explicitly equivalent model can be obtained. As a special case, a backward Markov model explicitly equivalent to a given forward Markov model can be obtained regardless of the singularity/nonsingularity of the state transition matrix of the model.