IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v207y2025ics0047259x25000132.html
   My bibliography  Save this article

Tree-structured Markov random fields with Poisson marginal distributions

Author

Listed:
  • Côté, Benjamin
  • Cossette, Hélène
  • Marceau, Etienne

Abstract

A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson with the same mean, and are untied from the strength or structure of their built-in dependence. This key feature is uncommon for Markov random fields and most convenient for applications purposes. The specific properties of this new family confer a straightforward sampling procedure and analytic expressions for the joint probability mass function and the joint probability generating function of the vector of counting random variables, thus granting computational methods that scale well to vectors of high dimension. We study the distribution of the sum of random variables constituting a Markov random field from the proposed family, analyze a random variable’s individual contribution to that sum through expected allocations, and establish stochastic orderings to assess a wide understanding of their behavior.

Suggested Citation

  • Côté, Benjamin & Cossette, Hélène & Marceau, Etienne, 2025. "Tree-structured Markov random fields with Poisson marginal distributions," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:jmvana:v:207:y:2025:i:c:s0047259x25000132
    DOI: 10.1016/j.jmva.2025.105418
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X25000132
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2025.105418?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    2. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    3. Michel Denuit & Christian Y. Robert, 2024. "Conditional Mean Risk Sharing of Independent Discrete Losses in Large Pools," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-22, December.
    4. Kaiser, Mark S. & Cressie, Noel, 1997. "Modeling Poisson variables with positive spatial dependence," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 423-432, November.
    5. Alan Julian Izenman, 2021. "Sampling Algorithms for Discrete Markov Random Fields and Related Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2065-2086, October.
    6. Denuit, Michel & Robert, Christian Y., 2022. "Conditional mean risk sharing in the individual model with graphical dependencies," Annals of Actuarial Science, Cambridge University Press, vol. 16(1), pages 183-209, March.
    7. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    8. Kaiser, Mark S. & Cressie, Noel, 2000. "The Construction of Multivariate Distributions from Markov Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 199-220, May.
    9. Denuit, Michel & Robert, Christian Y., 2024. "Conditional Mean Risk Sharing of Independent Discrete Losses in Large Pools," LIDAM Reprints ISBA 2024022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Denuit, Michel & Robert, Christian Y., 2022. "Conditional mean risk sharing in the individual model with graphical dependencies," LIDAM Reprints ISBA 2022020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Helmut Mausser & Oleksandr Romanko, 2018. "Long-only equal risk contribution portfolios for CVaR under discrete distributions," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1927-1945, November.
    12. Richard A. Davis & Konstantinos Fokianos & Scott H. Holan & Harry Joe & James Livsey & Robert Lund & Vladas Pipiras & Nalini Ravishanker, 2021. "Count Time Series: A Methodological Review," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1533-1547, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. H'el`ene Cossette & Benjamin C^ot'e & Alexandre Dubeau & Etienne Marceau, 2024. "Risk models from tree-structured Markov random fields following multivariate Poisson distributions," Papers 2412.00607, arXiv.org.
    2. Kang, Yao & Zhang, Yuqing & Wang, Shuhui & Zhao, Zhiwen, 2025. "A new class of Z-valued INAR(1) models with application to mutual fund flows," Economics Letters, Elsevier, vol. 252(C).
    3. Yuhyeong Jang & Raanju R. Sundararajan & Wagner Barreto-Souza & Elizabeth Wheaton-Paramo, 2024. "Determining economic factors for sex trafficking in the United States using count time series regression," Empirical Economics, Springer, vol. 67(1), pages 337-354, July.
    4. Huaping Chen & Fukang Zhu & Xiufang Liu, 2022. "A New Bivariate INAR(1) Model with Time-Dependent Innovation Vectors," Stats, MDPI, vol. 5(3), pages 1-22, August.
    5. Lee, Jaehyung & Kaiser, Mark S. & Cressie, Noel, 2001. "Multiway Dependence in Exponential Family Conditional Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 171-190, November.
    6. Goovaerts, M. J. & Dhaene, J., 1999. "Supermodular ordering and stochastic annuities," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 281-290, May.
    7. Chateauneuf, Alain & Mostoufi, Mina & Vyncke, David, 2015. "Multivariate risk sharing and the derivation of individually rational Pareto optima," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 73-78.
    8. Huaping Chen & Qi Li & Fukang Zhu, 2023. "A covariate-driven beta-binomial integer-valued GARCH model for bounded counts with an application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 805-826, October.
    9. Cathy W. S. Chen & Sangyeol Lee, 2017. "Bayesian causality test for integer-valued time series models with applications to climate and crime data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 797-814, August.
    10. Linda Khachatryan & Boris S. Nahapetian, 2023. "On the Characterization of a Finite Random Field by Conditional Distribution and its Gibbs Form," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1743-1761, September.
    11. Kachour Maher & Bakouch Hassan S. & Mohammadi Zohreh, 2023. "A New INAR(1) Model for ℤ-Valued Time Series Using the Relative Binomial Thinning Operator," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 243(2), pages 125-152, April.
    12. Feng, Runhuan & Liu, Ming & Zhang, Ning, 2024. "A unified theory of decentralized insurance," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 157-178.
    13. Tim J. Boonen & Wing Fung Chong & Mario Ghossoub, 2024. "Pareto‐efficient risk sharing in centralized insurance markets with application to flood risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 91(2), pages 449-488, June.
    14. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2021. "Mortality credits within large survivor funds," LIDAM Discussion Papers ISBA 2021038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Denuit, Michel & Dhaene, Jan & Ghossoub, Mario & Robert, Christian Y., 2025. "Comonotonicity and Pareto optimality, with application to collaborative insurance," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 1-16.
    16. Yeo, Keng Leong & Valdez, Emiliano A., 2006. "Claim dependence with common effects in credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 609-629, June.
    17. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    18. Christian Weiss, 2009. "Monitoring correlated processes with binomial marginals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(4), pages 399-414.
    19. repec:ipg:wpaper:2014-074 is not listed on IDEAS
    20. da Costa, B. Freitas Paulo & Pesenti, Silvana M. & Targino, Rodrigo S., 2023. "Risk budgeting portfolios from simulations," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1040-1056.
    21. Fallou Niakh, 2023. "A fixed point approach for computing actuarially fair Pareto optimal risk-sharing rules," Papers 2303.05421, arXiv.org, revised Jul 2023.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:207:y:2025:i:c:s0047259x25000132. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.