Graphical models for composable finite Markov processes

Composable Markov processes were introduced by Schweder (1970) in order to capture the idea that a process can be composed of different components where some of these only depend on a subset of the other components. Here we propose a graphical representation of this kind of dependence which has been called 'local dependence'. It is shown that the graph allows to read off further independencies characterizing the underlying Markov process. Also, some standard methods for inference are adapted to exploit the graphical representation, e.g. for testing local independence. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..

[1]  Daphne Koller,et al.  Learning Continuous Time Bayesian Networks , 2002, UAI.

[2]  Odd O. Aalen,et al.  Dynamic modelling and causality , 1987 .

[3]  David J. Spiegelhalter,et al.  Probabilistic Networks and Expert Systems , 1999, Information Science and Statistics.

[4]  Michael Eichler,et al.  Graphical Models in Time Series Analysis , 1999 .

[5]  M. Frydenberg.  The chain graph Markov property , 1990 .

[6]  Tore Schweder,et al.  Composable Markov processes , 1970, Journal of Applied Probability.

[7]  Jan M. Hoem,et al.  Purged and partial Markov chains , 1969 .

[8]  Vanessa Didelez,et al.  Asymmetric Separation for Local Independence Graphs , 2006, UAI.

[9]  Anna Gottard.  GRAPHICAL DURATION MODELS , 2002 .

[10]  N. Wermuth,et al.  On Substantive Research Hypotheses, Conditional Independence Graphs and Graphical Chain Models , 1990 .

[11]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[12]  Michael I. Jordan.  Graphical Models , 2003 .

[13]  Jean-Pierre Florens,et al.  Noncausality in Continuous Time , 1996 .

[14]  Vanessa Didelez,et al.  Graphical models for marked point processes based on local independence , 2007, 0710.5874.

[15]  Daphne Koller,et al.  Continuous Time Bayesian Networks , 2012, UAI.

[16]  Judea Pearl,et al.  GRAPHOIDS: A Graph-based logic for reasoning about relevance relations , 1985 .

[17]  Graham J. Wills,et al.  Introduction to graphical modelling , 1995 .

[18]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[19]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .