Related papers: On A Stein Method Based Approximation for A Two-Di…

We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…

We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…

In this paper, we quantify some known approximation to the Curie-Weiss model via applying the Stein method to the Markov chain whose stationary distribution coincides with Curie-Weiss model.

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…

Stein's (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein's method, one needs to establish a Stein…

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…

A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…

We explore two aspects of geometric approximation via a coupling approach to Stein's method. Firstly, we refine precision and increase scope for applications by convoluting the approximating geometric distribution with a simple translation…

Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…

An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by…

In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, Stein operators…

This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…

Stein's method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we…

This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…

One of the key ingredients to successfully apply Stein's method for distributional approximation are solutions to the Stein equations and their derivatives. Using Barbour's generator approach, one can solve for the solutions to the Stein…

A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex orders are discussed. Attention is focused on…

We obtain Stein approximation bounds for stochastic integrals with respect to a Poisson random measure over ${\Bbb R}^d$, $d\geq 2$. This approach relies on third cumulant Edgeworth-type expansions based on derivation operators defined by…

This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased…

Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…