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Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables

Author

Listed:
  • Allman Elizabeth S.
  • Rhodes John A.

    (Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, USA)

  • Stanghellini Elena

    (Dipartimento di Economia Finanza e Statistica, Universita di Perugia, Perugia, Italy)

  • Valtorta Marco

    (Department of Computer Science and Engineering, University of South Carolina, Columbia, SC, USA)

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.

Suggested Citation

  • Allman Elizabeth S. & Rhodes John A. & Stanghellini Elena & Valtorta Marco, 2015. "Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables," Journal of Causal Inference, De Gruyter, vol. 3(2), pages 189-205, September.
    • Handle: RePEc:bpj:causin:v:3:y:2015:i:2:p:189-205:n:4
    DOI: 10.1515/jci-2014-0021
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    References listed on IDEAS

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    1. Manabu Kuroki & Judea Pearl, 2014. "Measurement bias and effect restoration in causal inference," Biometrika, Biometrika Trust, vol. 101(2), pages 423-437.
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    Cited by:

    1. Fabrizia Mealli & Barbara Pacini & Elena Stanghellini, 2016. "Identification of Principal Causal Effects Using Additional Outcomes in Concentration Graphs," Journal of Educational and Behavioral Statistics, , vol. 41(5), pages 463-480, October.

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