相关论文: Stein's method, Palm theory and Poisson process ap…

We show how the infinitesimal exchangeable pairs approach to Stein's method combines naturally with the theory of Markov semigroups. We present a multivariate normal approximation theorem for functions of a random variable invariant with…

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in…

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…

The polynomial birth-death distribution (abbr. as PBD) on $\ci=\{0,1,2, >...\}$ or $\ci=\{0,1,2, ..., m\}$ for some finite $m$ introduced in Brown & Xia (2001) is the equilibrium distribution of the birth-death process with birth rates…

We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…

This article deals with Stein characterizations of probability distributions. We provide a general framework for interpreting these in terms of the parameters of the underlying distribution. In order to do so we introduce two concepts (a…

In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding…

In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…

This paper uses the generator approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. Until now, the standard way to invoke Stein's method for this problem was to use the…

Filtering algorithms are fundamental for inference on partially observed stochastic dynamic systems, since they provide access to the likelihood function and hence enable likelihood-based or Bayesian inference. A novel Poisson approximate…

By the continuous mapping theorem, if a sequence of $d$-dimensional random vectors $(\mathbf{W}_n)_{n\geq1}$ converges in distribution to a multivariate normal random variable $\Sigma^{1/2}\mathbf{Z}$, then the sequence of random variables…

This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…

Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a…

Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampling of high-dimensional distributions. However, existing approximation techniques primarily…

How much dependence is there in the prime factorization of a random integer distributed uniformly from 1 to n? How much dependence is there in the decomposition into cycles of a random permutation of n points? What is the relation between…

We prove a Poisson process approximation result for stabilizing functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association…

We prove an exact fourth moment bound for the normal approximation of random variables belonging to the Wiener chaos of a general Poisson random measure. Such a result -- that has been elusive for several years -- shows that the so-called…