Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables

Allman Elizabeth S. (), Rhodes John A. (), Elena Stanghellini and Valtorta Marco ()
Additional contact information
Allman Elizabeth S.: Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, USA
Rhodes John A.: Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, USA
Valtorta Marco: Department of Computer Science and Engineering, University of South Carolina, Columbia, SC, USA

Journal of Causal Inference, 2015, vol. 3, issue 2, 189-205

Abstract: Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishing identifiability of some special models on small directed acyclic graphs (DAGs). We also establish that, for fixed state spaces, generic identifiability of parameters depends only on the Markov equivalence class of the DAG. To illustrate the use of these results, we investigate identifiability for all binary Bayesian networks with up to five variables, one of which is hidden and parental to all observable ones. Surprisingly, some of these models have parameterizations that are generically 4-to-one, and not 2-to-one as label swapping of the hidden states would suggest. This leads to interesting conflict in interpreting causal effects.

Keywords: parameter identifiability; discrete Bayesian network; hidden variables (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1515/jci-2014-0021 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:3:y:2015:i:2:p:189-205:n:4

DOI: 10.1515/jci-2014-0021

Access Statistics for this article

Journal of Causal Inference is currently edited by Elias Bareinboim, Jin Tian and Iván Díaz

More articles in Journal of Causal Inference from De Gruyter
Bibliographic data for series maintained by Peter Golla ().