This is the first comprehensive book on information geometry, written by the founder of the
field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide …

How can one construct dynamical systems obeying the first and second laws of
thermodynamics: mean energy is conserved and entropy increases with time? This book …

An information-geometrical foundation is established for the deformed exponential families
of probability distributions. Two different types of geometrical structures, an invariant …

We consider the non-parametric statistical model ε (p) of all positive densities q that are
connected to a given positive density p by an open exponential arc, ie a one-parameter …

We construct an infinite-dimensional Hilbert manifold of probability measures on an abstract
measurable space. The manifold, M, retains the first-and second-order features of finite …

Abstract The Expectation–Maximization (EM) algorithm is a simple meta-algorithm that has
been used for many years as a methodology for statistical inference when there are missing …

The differential-geometric structure of the set of positive densities on a given measure space
has raised the interest of many mathematicians after the discovery by CR Rao of the …

Divergence functions are the non-symmetric “distance” on the manifold, M θ, of parametric
probability density functions over a measure space,(X, μ). Classical information geometry …

We generalize the exponential family of probability distributions. In our approach, the
exponential function is replaced by a φ-function, resulting in a φ-family of probability …

Abstract Markov chain Monte Carlo methods for sampling from complex distributions and
estimating normalization constants often simulate samples from a sequence of intermediate …