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A note on faithfulness and total positivity

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  • Li, Benchong
  • Li, Yang

Abstract

The concept of faithfulness is important for statistical learning of graphical models. In this paper, we show that a faithful positive binary multivariate totally positive of order two (MTP2) distribution exists for every undirected graph, and generalize this result to the case of undirected graphs and positive discrete MTP2 distributions with fixed sample space.

Suggested Citation

  • Li, Benchong & Li, Yang, 2017. "A note on faithfulness and total positivity," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 168-172.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:168-172
    DOI: 10.1016/j.spl.2016.11.013
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    References listed on IDEAS

    as
    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    2. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
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