TY - JOUR

T1 - Graphical modeling of stochastic processes driven by correlated noise

AU - Mogensen, Søren Wengel

AU - Hansen, Niels Richard

N1 - Publisher Copyright: © 2022 ISI/BS.

PY - 2022

Y1 - 2022

N2 - We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated noise processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolyno-mially as a function of the size of the node set in the graph. We show that deciding Markov equivalence of graphs from this class is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.

AB - We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated noise processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolyno-mially as a function of the size of the node set in the graph. We show that deciding Markov equivalence of graphs from this class is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.

KW - Graphical models

KW - local independence

KW - Markov equivalence

KW - Ornstein–Uhlenbeck processes

KW - stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85136269564&partnerID=8YFLogxK

U2 - 10.3150/21-BEJ1446

DO - 10.3150/21-BEJ1446

M3 - Journal article

AN - SCOPUS:85136269564

VL - 28

SP - 3028

EP - 3050

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 4

ER -