Related papers: The Lent Particle Method, Application to Multiple …
The problem of phase retrieval has many applications in the field of optical imaging. Motivated by imaging experiments with biological specimens, we primarily consider the setting of low-dose illumination where Poisson noise plays the…
In this paper we present a model based on dynamics of the electrons in the plasma using a simplified Boltzmann equation coupled with a Poisson equation. The motivation arose to simulate active plasma resonance spectroscopy which is used for…
Several approaches are discussed how to understand the solution of the Dirichlet problem for the Poisson equation when the Dirichlet data are non-smooth such as if they are in $L^2$ only. For the method of transposition (sometimes called…
We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…
The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…
We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an…
Using the Poisson bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified in terms of two continuum fields: an anisotropy density field that captures the deformations…
The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the Poisson equations on manifolds from point clouds. In this…
We describe a simple and efficient procedure for approximating the L\'evy measure of a $\text{Gamma}(\alpha,1)$ random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's…
In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in $\mathbb{R}^n$. Green's functions and Poisson kernels are important tools needed in our study. We first establish the…
The fundamental concept of phase space for particles moving in the four-dimensional spacetime is analyzed. Particle distribution density is defined as differential form, which degree may be different in various cases. It should be…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
Langevin (stochastic differential) equations are routinely used to describe particle-laden flows. They predict Gaussian probability density functions (PDFs) of a particle's trajectory and velocity, even though experimentally observed…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
We construct a new random probability measure on the sphere and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
We propose a novel efficient algorithm to solve Poisson equation in irregular two dimensional domains for electrostatics. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or…
This paper explores large sample properties of the two-parameter $(\alpha,\theta)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension…
The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…