In this lecture, recent developments on connections between Markov processes and nonequilibrium statistical mechanical systems are discussed. A statistical mechanical analogy is developed for Markov processes and a local entropic measure of their true asymmetry is defined. Introducing partial observations, conditional and joint analogies are developed for Markov processes and their optimal filt...

Graphical methods have entered the mainstream of both statistical applications and research in statistical methodology. This development is due in part to the revolution in computing and in part to the stimulating ideas of exploratory data analysis, but the main reason is simply that graphical methods work. Appropriately chosen plots reveal much about the data, and people who start to use them ...

Abstract In this paper, we introduce and study Golden-like statistical manifolds. We obtain some basic inequalities for curvature invariants of submanifolds in Also, support our definition, provide a couple examples.