TY - GEN
T1 - Pairwise and uniformly hidden markov fields
AU - Pieczynski, Wojciech
PY - 2009/12/1
Y1 - 2009/12/1
N2 - In Hidden Markov Fields (HMF) models there are two random fields: the hidden Markov field X and the observed field Y. In Pairwise Markov Fields (PMF) models one directly assumes the Markovianity of the couple (X, Y). PMF are more general than HMF; in fact, in PMF X is not necessarily Markovian. The aim of the paper is to provide some necessary and sufficient conditions under which PMF are HMF. We introduce the notion of "uniformly" HMF (UHMF) and we provide a general condition under which a PMF is an UHMF. Some interest of the presented results in the frame of Triplet Markov Fields (TMF) models, in which a third auxiliary random field is added and one considers the Markovianity of (X, U, Y), is also briefly discussed.
AB - In Hidden Markov Fields (HMF) models there are two random fields: the hidden Markov field X and the observed field Y. In Pairwise Markov Fields (PMF) models one directly assumes the Markovianity of the couple (X, Y). PMF are more general than HMF; in fact, in PMF X is not necessarily Markovian. The aim of the paper is to provide some necessary and sufficient conditions under which PMF are HMF. We introduce the notion of "uniformly" HMF (UHMF) and we provide a general condition under which a PMF is an UHMF. Some interest of the presented results in the frame of Triplet Markov Fields (TMF) models, in which a third auxiliary random field is added and one considers the Markovianity of (X, U, Y), is also briefly discussed.
KW - Pairwise Markov Fields
KW - Triplet Markov fields
KW - Uniformly Hidden Markov Fields
U2 - 10.1063/1.3225271
DO - 10.1063/1.3225271
M3 - Conference contribution
AN - SCOPUS:84887589340
SN - 9780735406858
T3 - AIP Conference Proceedings
SP - 193
EP - 196
BT - Computational Methods in Science and Engineering - Advances in Computational Science, Lectures Presented at the Int. Conference on Computational Methods in Science and Engineering 2008, ICCMSE 2008
T2 - 6th International Conference on Computational Methods in Sciences and Engineering 2008, ICCMSE 2008
Y2 - 25 September 2008 through 30 September 2008
ER -