• Count data are often modeled using a Poisson model. • If y ∼ Poisson(μ) then E(y) = var(y) = μ. • When counts are assumed exchangeable given μ and the rates μ can also be assumed to be exchangeable, a Gamma population model for the rates is often chosen. • The hierarchical model is then yi ∼ Poisson(μi) μi ∼ Gamma(α, β). • Priors for the hyperparameters are often taken to be Gamma (or exponen...

Abstract We construct a bi-Hamiltonian structure for the holomorphic spin Sutherland hierarchy based on collective variables. The construction relies Poisson reduction of cotangent bundle $$\mathrm{GL}(n,\mathbb {C})$$ GL ( n , C )</mm...

Definition 1.1. A Poisson algebra is an associative algebra A over a field K (fixed, of characteristic zero), equipped with a Lie bracket {−,−} such that {x,−} is a derivation for any x ∈ A, i.e. {x, yz} = {x, y}z + y{x, z}. Definition 1.2. A Poisson structure on a manifold M is a Poisson bracket {−,−} on the algebra C∞(M). Example 1.3. On T ∗Rn with position coordinates q1, ..., qn and momentu...

We prove that any perturbation of the symplectic part of the derivative of a Poisson diffeomorphism can be realized as the derivative of a C-close Poisson diffeomorphism. We also show that a similar property holds for the Poincaré map of a Hamiltonian on a Poisson manifold. These results are the conservative counterparts of the Franks lemma, a perturbation tool used in several contexts most not...

In this paper, we want to associate to a n-vector on a manifold of dimension n a cohomology which generalizes the Poisson cohomology of a 2-dimensional Poisson manifold. Two possibilities are given here. One of them, the Nambu-Poisson cohomology, seems to be the most pertinent. We study these two cohomologies locally, in the case of germs of n-vectors on Kn (K = R or C).

Abstract We are concerned with a certain class of Schlömilch series that arise naturally in the study of diffraction problems when the scatterer is a periodic structure. By combining new results derived from integral representations and the Poisson summation formula with known identities, we obtain expressions which enable the series to be computed accurately and efficiently. Most of the techni...

&lrm;Multivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie models&lrm;. &lrm;The model is composed of a univariate Poisson variable&lrm;, &lrm;and the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson component&lrm;. &lrm;Two characterizations of this model are shown&lrm;, &lrm;...

It is well known that a measured groupoid G defines a von Neumann algebra W ∗(G), and that a Lie groupoid G canonically defines both a C∗-algebra C∗(G) and a Poisson manifold A∗(G). We construct suitable categories of measured groupoids, Lie groupoids, von Neumann algebras, C∗-algebras, and Poisson manifolds, with the feature that in each case Morita equivalence comes down to isomorphism of obj...

A Riemann-Lie algebra is a Lie algebra G such that its dual G∗ carries a Riemannian metric compatible (in the sense introduced by the author in C. R. Acad. Sci. Paris, t. 333, Série I, (2001) 763–768) with the canonical linear Poisson structure of G∗ . The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Differential Geometry and its A...

The Poisson regression model is frequently used to analyze count data. Pseudo R-squared measures for Poisson regression models have recently been proposed and bias adjustments recommended in the presence of small samples and/or a large number of covariates. In practice, however, data are often overor sometimes even underdispersed as compared to the standard Poisson model. The de5nition of Poiss...