We propose an efficient and accurate approximate Bayesian Markov chain Monte Carlo methodology for the estimation of event rates under an overdispersed Poisson distribution. A Gibbs sampling algorithm is derived, based on a log-normal/gamma mixture density that closely approximates the conditional distribution of the Poisson parameters. This involves a moment matching process, with the exact co...

The theory of formation of an ideal image has been described which shows that the gray level in an image [ollows the Poisson distribution. Based on this concept, various algorithms for object background classification have been developed. Proposed algorithms involve either the maximum entropy principle or the minimum X statistic. The appropriateness of the Poisson distributiou is fun:her streng...

Silicon nanowires (SiNW) are quasi-one-dimensional structures in which the electrons are spatially confined in two directions, and they are free to move along the axis of the wire. The spatial confinement is governed by the Schrödinger–Poisson system, which must be coupled to the transport in the free motion direction. For devices with the characteristic length of a few tens of nanometers, the ...

1639 the average frequency distribution H avg (s) := (1=N) N i=1 H(s; i): The behavior of the distributions for different values of K is discussed in Fig. 4. For M = 9 and K = 12; 16; 20; 24 the average frequency distribution Havg(s) (solid lines) and the approximation Happ(s) (dashed lines) are compared to the Maxwell–Boltzmann distribution H M-B (s) (dash-dotted lines). Here, the parameter is...

We study the hyperbolic system of Euler equations for an isentropic, compressible fluid governed by a general pressure law. The existence and regularity of the entropy kernel that generates the family of weak entropies is established by solving a new Euler-Poisson-Darboux equation, which is highly singular when the density of the fluid vanishes. New properties of cancellation of singularities i...

We propose a new class of distributions called the Lomax generator with two extra positive parameters to generalize any continuous baseline distribution. Some special models such as the Lomax-normal, Lomax–Weibull, Lomax-log-logistic and Lomax–Pareto distributions are discussed. Some mathematical properties of the new generator including ordinary and incomplete moments, quantile and generating ...

It is well understood that the two most popular empirical models of location choice conditional logit and Poisson return identical coefficient estimates when the regressors are not individual specific. We show that these two models differ starkly in terms of their implied predictions. The conditional logit model represents a zero-sum world, in which one region's gain is the other regions' loss....

We investigate the Rényi entropy of sums independent integer-valued random variables through Fourier theoretic means, and give sharp comparisons between variance for Bernoulli variables. As applications, we prove that a discrete “min-entropy power” is superadditive with respect to convolution modulo universal constant, new bounds on an entropic generalization Littlewood-Offord problem are in “P...

The Poisson boundary of a group G with a probability measure μ on it is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an integral representation of bounded μ-harmonic functions on G. In this paper we develop a new method of identifying the Poisson boundary based on entropy estimat...

A kinetic approach to the notion of information is proposed, based on Liouville kinetic theory. The general kinetic equation for the evolution of the N-particle information IN in a Hamiltonian system of large particle number N >> 1 is obtained. It is shown that the N-particle information is strictly conserved. Defining reduced particle number information densities in phase space should be possi...