{
  "id": "1811.07804",
  "version": "v2",
  "published": "2018-11-19T17:03:45.000Z",
  "updated": "2019-12-03T01:35:56.000Z",
  "title": "Explicitly Sample-Equivalent Dynamic Models for Gaussian Markov, Reciprocal, and Conditionally Markov Sequences",
  "authors": [
    "Reza Rezaie",
    "X. Rong Li"
  ],
  "categories": [
    "math.PR",
    "cs.SY",
    "eess.SP",
    "math.DS"
  ],
  "abstract": "The conditionally Markov (CM) sequence contains different classes including Markov, reciprocal, and so-called $CM_L$ and $CM_F$ (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, $CM_L$, and $CM_F$ 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) $CM_L$, $CM_F$, 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 $CM_L$/$CM_F$/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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-12-03T01:35:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicitly sample-equivalent dynamic models",
      "conditionally markov sequences",
      "gaussian markov",
      "reciprocal",
      "cm sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}