Necessary and sufficient conditions for a maximal ancestral graph (MAnG)to be Markov equivalent to another MAnG and to a DAG are provided respectively. Also a polynomial-time algorithm for converting a MAnG into its e...Necessary and sufficient conditions for a maximal ancestral graph (MAnG)to be Markov equivalent to another MAnG and to a DAG are provided respectively. Also a polynomial-time algorithm for converting a MAnG into its equivalent DAG is given for the first time.展开更多
A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind o...A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.展开更多
基金This research was partly supported by the National Natural Science Foundation of China(Grant Nos.39930160&19871003).
文摘Necessary and sufficient conditions for a maximal ancestral graph (MAnG)to be Markov equivalent to another MAnG and to a DAG are provided respectively. Also a polynomial-time algorithm for converting a MAnG into its equivalent DAG is given for the first time.
基金supported in part by the National Natural Science Foundation of China(60375003)the Aeronautics and Astronautics Basal Science Foundation of China(03I53059)
文摘A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.
