webpage at the Institute of Mathematics of Czech Academy of Sciences in Prague

Selected writings

Hông Vân Lê, Geometric structures associated with a simple Cartan 3-form, J. of Geometry and Physics 70 (2013) 205–223 arXiv:1103.1201

Nihat Ay, Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer, Information geometry, Ergeb. der Mathematik and ihrer Grenzgebiete 3. Folge, 64, Springer 2017

Hông Vân Lê, Natural differentiable structures on statistical models and the Fisher metric, Information Geometry (2022) arXiv:2208.06539doi

Hông Vân Lê, Diffeological statistical models and diffeological Hausdorff measures, video yt, slides pdf

Hông Vân Lê, Alexey A. Tuzhilin, Nonparametric estimations and the diffeological Fisher metric, In: Barbaresco F., Nielsen F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning, p. 120–138, SPIGL 2020. Springer Proceedings in Mathematics & Statistics 361, doi

In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending Lê’s theory in (Le2020) to include weakly $C^k$-diffeological statistical models. Then we introduce the resulting notions of the diffeological Fisher distance, the diffeological Hausdorff–Jeffrey measure and explain their role in classical and Bayesian nonparametric estimation problems in statistics.