10,635 research outputs found
A categorical characterization of relative entropy on standard Borel spaces
We give a categorical treatment, in the spirit of Baez and Fritz, of relative
entropy for probability distributions defined on standard Borel spaces. We
define a category suitable for reasoning about statistical inference on
standard Borel spaces. We define relative entropy as a functor into Lawvere's
category and we show convexity, lower semicontinuity and uniqueness.Comment: 16 page
Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
A new information-geometric approach to chaotic dynamics on curved
statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown
that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical
manifold M_{s} underlying an ED Gaussian model describing an arbitrary system
of 3N degrees of freedom leads to linear information-geometric entropy growth
and to exponential divergence of the Jacobi vector field intensity, quantum and
classical features of chaos respectively.Comment: 8 pages, final version accepted for publicatio
On choosing and bounding probability metrics
When studying convergence of measures, an important issue is the choice of
probability metric. In this review, we provide a summary and some new results
concerning bounds among ten important probability metrics/distances that are
used by statisticians and probabilists. We focus on these metrics because they
are either well-known, commonly used, or admit practical bounding techniques.
We summarize these relationships in a handy reference diagram, and also give
examples to show how rates of convergence can depend on the metric chosen.Comment: To appear, International Statistical Review. Related work at
http://www.math.hmc.edu/~su/papers.htm
- …