Graphical modeling of stochastic processes driven by correlated noise
(2022) In Bernoulli 28(4). p.3028-3050- Abstract
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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/70999c21-f255-4766-814d-b657eb347291
- author
- Mogensen, Søren Wengel LU and Hansen, Niels Richard
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Graphical models, local independence, Markov equivalence, Ornstein–Uhlenbeck processes, stochastic processes
- in
- Bernoulli
- volume
- 28
- issue
- 4
- pages
- 23 pages
- publisher
- Chapman and Hall
- external identifiers
-
- scopus:85136269564
- ISSN
- 1350-7265
- DOI
- 10.3150/21-BEJ1446
- language
- English
- LU publication?
- yes
- id
- 70999c21-f255-4766-814d-b657eb347291
- date added to LUP
- 2022-09-05 15:06:45
- date last changed
- 2022-09-05 15:06:45
@article{70999c21-f255-4766-814d-b657eb347291, abstract = {{<p>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.</p>}}, author = {{Mogensen, Søren Wengel and Hansen, Niels Richard}}, issn = {{1350-7265}}, keywords = {{Graphical models; local independence; Markov equivalence; Ornstein–Uhlenbeck processes; stochastic processes}}, language = {{eng}}, number = {{4}}, pages = {{3028--3050}}, publisher = {{Chapman and Hall}}, series = {{Bernoulli}}, title = {{Graphical modeling of stochastic processes driven by correlated noise}}, url = {{http://dx.doi.org/10.3150/21-BEJ1446}}, doi = {{10.3150/21-BEJ1446}}, volume = {{28}}, year = {{2022}}, }