Hilbert Space of Probability Density Functions Based on Aitchison Geometry

By Juan José Egozcue, José Luis Díaz-Barrero, Vera Pawlowsky-Glahn. 2006

151 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering, Media Technology

View Paper: https://www.semanticscholar.org/paper/d54c7667b99efa1f83f4e74d099a0da211bcf8f3

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Citations in the corpus

A latent Gaussian model for compositional data with zeros (2008, background): “…ideas have subsequently been developed into a comprehensive set of statistical tools (Aitchison and Egozcue, 2005), and the theoretical and practical aspects of compositional data analysis remain active fields of methodological research (e.g. Egozcue et al. (2006) and von Eynatten et al. (2002)).”
Bayes linear spaces (2010, methodology): “This idea has been previously used for densities on an interval in (Egozcue et al., 2006) and goes back to a similar”
Wasserstein autoregressive models for density time series (2020, methodology): “…the modeling of distributional data include the Fisher–Rao metric (Srivastava et al., 2007), an infinite-dimensional version of the Aitchison metric (Egozcue et al., 2006; Hron et al., 2016), and the Wasserstein optimal transport metric (Panaretos and Zemel, 2016; Bigot et al., 2017; Petersen and…”
Bayes Hilbert Spaces (2014, methodology): “However, the present B2(P) definition differs from the definition given in Egozcue et al. (2006) by a factor of (b−a)−2 in the inner product, and the squared distance.”
Additive Functional Regression for Densities as Responses (2020, methodology): “Various tools for the analysis of samples of densities as data objects have been proposed over the last decade (Egozcue et al., 2006; Delicado, 2007, 2011; Zhang and Müller, 2011; Panaretos and Zemel, 2016; Petersen and Müller, 2016; Bigot et al., 2017), extending the pioneering work of Kneip and Ut”