Deformed exponential families in Statistical Physics and beyond

Two recent developments are discussed from the point of view, expressed by Jaynes in 1957, that Statistical Physics is statistics applied to physics. 1. Information geometry aims to replace the maximum likelihood method of statistics by a geometric approach. Many of the techniques involved sound familiar to physicists because they are used in classical mechanics, relativity, or thermodynamics. 2. The study of deformed exponential families started with the non-extensive statistical physics of Tsallis. New classes of statistical models will hopefully find application in many areas of research. A short presentation is given of the formalism of phi-deformed exponential families and their dual rho-tau geometries.