New results on mixture and exponential models by Orlicz spaces

New results and improvements in the study of nonparametric exponential and mixture models are proposed. In particular, different equivalent characterizations of maximal exponential models, in terms of open exponential arcs and Orlicz spaces, are given. Our theoretical results are supported by several examples and counterexamples and provide an answer to some open questions in the literature.Comment: Published at http://dx.doi.org/10.3150/15-BEJ698 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Nonparametric Information Geometry

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 C.R. Rao of the geometric meaning of the Fisher information. Most of the research is focused on parametric statistical models. In series of papers by author and coworkers a particular version of the nonparametric case has been discussed. It consists of a minimalistic structure modeled according the theory of exponential families: given a reference density other densities are represented by the centered log likelihood which is an element of an Orlicz space. This mappings give a system of charts of a Banach manifold. It has been observed that, while the construction is natural, the practical applicability is limited by the technical difficulty to deal with such a class of Banach spaces. It has been suggested recently to replace the exponential function with other functions with similar behavior but polynomial growth at infinity in order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give first a review of our theory with special emphasis on the specific issues of the infinite dimensional setting. In a second part we discuss two specific topics, differential equations and the metric connection. The position of this line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30 2013 Pari

Parameter-free description of the manifold of non-degenerate density matrices

The paper gives a definition of exponential arcs in the manifold of non-degenerate density matrices and uses it as a starting point to develop a parameter-free version of non-commutative Information Geometry in the finite-dimensional case. Given the Bogoliubov metric the m- and e-connections are each other dual. Convex potentials are introduced. They allow to introduce dual charts. Affine coordinates are introduced at the end to make the connection with the more usual approach

Reaction kinetics of protons and oxide ions in LSM/lanthanum tungstate cathodes with Pt nanoparticle activation

Composite electrodes of La0.8Sr0.2MnO3 (LSM)/La28–xW4+xO54+3x/2 (x = 0.85, “LWO56”) on LWO56 electrolytes have been characterized by use of electrochemical impedance spectroscopy vs. pO2 and temperature from 900°C, where LWO56 is mainly oxide ion conducting, to 450°C, where it is proton conducting in wet atmospheres. The impedance data are analyzed in a model which takes into account the simultaneous flow of oxide ions and protons across electrolyte and electrodes, allowing extraction of activation energies and pre-exponential factors for the partial electrode reactions of protons and oxide ions. One composite electrode was infiltrated with Pt nanoparticles with average diameter of 5 nm, lowering the overall electrode polarization resistance (Rp) at 650°C from 260 to 40 Ω cm2. The Pt-infiltrated electrode appears to be rate limited by surface reactions with activation energy of ∼90 kJ mol−1 in the low temperature proton transport regime and ∼150 kJ mol−1 in the high temperature oxide ion transport regime. The charge transfer reaction, which makes a minor contribution to Rp, exhibits activation energies of ∼85 kJ mol−1 for both oxide ion and proton charge transfer

Exponential models by Orlicz spaces and applications

We use maximal exponential models to characterize a suitable polar cone in a mathematical convex optimization framework. A financial application of this result is provided, leading to a duality minimax theorem related to portfolio exponential utility maximization

Complex Scaled Spectrum Completeness for Coupled Channels

The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case of inelastic scattering with many channels, the existence of such a resolution under complex scaling is still debated. Taking advantage of results obtained earlier for the two channel case, this paper proposes a representation in which the convergence of a resolution of the identity can be more easily tested. The representation is valid for any finite number of coupled channels for inelastic scattering without rearrangement.Comment: Latex file, 13 pages, 4 eps-figure