Wüthrich and Buser (DOI:10.2139/ssrn.2870308, 2020) studied the generalization error for Poisson regression models. This short note aims to extend their results Tweedie family of distributions, which law belongs. In case bagging, a new condition emerges that becomes increasingly binding with power parameter involved in variance function.

The Multi-scale Variance Stabilization Transform (MSVST) has recently been proposed for 2D Poisson data denoising. In this work, we present an extension of the MSVST with the wavelet transform to multivariate data–each pixel is vector-valued–, where the vector field dimension may be the wavelength, the energy, or the time. Such data can be viewed naively as 3D data where the third dimension may...

Abstract. Most of the proposed self-similar traffic models could not address fractal onset time at which self-similar behavior actually begins. This parameter has considerable impact on network performance. Fractal point process (FPP) emulates self-similar traffic and involves fractal onset time (FOT). However, this process is asymptotic in nature and has less effective in queueing based perfor...

This research is a follow-up of Utama (2022) on asymptotic distribution an estimator for variance function compound periodic Poisson with the power trend. The objectives this are (i) to formulate confidence interval process trend and (ii) prove convergence 1-α probability parameter included in interval. begins review existing formulation its distribution. Next, formulated determined. After obta...

Getting and analyzing biological interaction networks is at the core of systems biology. To help understanding these complex networks, many recent works have suggested to focus on motifs which occur more frequently than expected in random. To identify such exceptional motifs in a given network, we propose a statistical and analytical method which does not require any simulation. For this, we fi...

We discuss how the integrators used for the Hybrid Monte Carlo (HMC) algorithm not only approximately conserve some Hamiltonian H but exactly conserve a nearby shadow Hamiltonian H̃, and how the difference ∆H ≡ H̃ −H may be expressed as an expansion in Poisson brackets. By measuring average values of these Poisson brackets over the equilibrium distribution ∝ e−H generated by HMC we can find the o...

We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate ...

In this paper, we propose a new denoising method for Poisson noise corrupted images based on the Anscombe variance stabilizing transformation (VST) with a new inversion. The VST is used to approximately convert a Poisson noise image into a Gaussian distributed image, so that the denoising methods aiming at Gaussian noise can be applied subsequently. The motivation for the new inversion originat...

We define the Boltzmann-Gibbs entropy of random finite set on a general space X as the integration of logarithm of density function over the space of finite sets of X , where the measure for this integration is the dominating measure over this space. We show that with a unit adjustment term, the same value for entropy can be obtained using the calculus of set integrals which applies integration...