Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Multivariate total positivity of order 2

Piotr Zwiernik

created by calamai on 11 Sep 2015

17 sep 2015 -- 12:00

sala conferenze Tricerri, DiMaI, Firenze


Probability distributions that are multivariate totally positive of order 2 (MTP2) appeared in the theory of positive dependence and in statistical physics through the celebrated FKG inequality. The MTP2 property is stable under marginalization, conditioning and it appears naturally in various probabilistic graphical models with hidden variables. Models of exponential families with the MTP2 property admit a unique maximum likelihood estimator. In the Gaussian case, the MLE exists also in high-dimensional settings, when p>>n, and it leads to sparse solutions. I will also show how the MTP2 property appears in the semialgebraic description of tensors of nonnegative rank 2.

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