3 papers
math.PR2018
A Class of Non-Parametric Statistical Manifolds modelled on Sobolev Space
Nigel J. Newton
We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on . The manifolds are modelled on a variety of weighted Sobolev spaces, including…
math.PR2016
Manifolds of Differentiable Densities
Nigel J. Newton
We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class $C_b…
math.PR2016
Transfer Entropy and Directed Information in Gaussian diffusion processes
Nigel J. Newton
Transfer Entropy and Directed Information are information-theoretic measures of the directional dependency between stochastic processes. Following the definitions of Schreiber and…