Path connectedness on a space of probability density functions  Osamu Komori, Shinto Eguchi

Authors : Osamu Komori, Shinto Eguchi
DOI URL : http://dx.doi.org/10.1007/9783319250403_66
Video : http://www.youtube.com/watch?v=KooWAyot6U0
Slides: Komori_path connectedness.pdf
Presentation : https://www.see.asso.fr/node/14267
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
We introduce a class of paths or oneparameter models connecting arbitrary two probability density functions (pdf’s). The class is derived by employing the KolmogorovNagumo average between the two pdf’s. There is a variety of such path connectedness on the space of pdf’s since the KolmogorovNagumo average is applicable for any convex and strictly increasing function. The information geometric insight is provided for understanding probabilistic properties for statistical methods associated with the path connectedness. The oneparameter model is extended to a multidimensional model, on which the statistical inference is characterized by sufficient statistics.