Stein's method and the zero bias transformation with application to simple random sampling
- L. Goldstein, G. Reinert
- Mathematics
- 1 November 1997
Let W be a random variable with mean zero and variance 2 . The distribution of a variate W , satisfying EWf(W) = 2 Ef 0 (W ) for smooth functions f, exists uniquely and defines the zero bias…
Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition
- G. Reinert, Adrian Röllin
- Mathematics
- 7 November 2007
In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal…
Use of exchangeable pairs in the analysis of simulations
- C. Stein, P. Diaconis, S. Holmes, G. Reinert
- Mathematics
- 2004
The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approx- imations. Here the method is used in a simulation context.…
Approximating the epidemic curve
- A. Barbour, G. Reinert
- Mathematics
- 15 January 2013
Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process,…
Estimating the number of communities in a network
- M. Newman, G. Reinert
- Computer SciencePhysical Review Letters
- 9 May 2016
A mathematically principled approach for finding the number of communities in a network by maximizing the integrated likelihood of the observed network structure under an appropriate generative model is described.
Alignment-Free Sequence Comparison (I): Statistics and Power
- G. Reinert, David S. H. Chew, Fengzhu Sun, M. Waterman
- MathematicsJ. Comput. Biol.
- 1 December 2009
This article suggests two new variants of the D(2) word count statistic, which it is shown that the statistic is asymptotically normally distributed, when sequence lengths tend to infinity, and not dominated by the noise in the individual sequences.
Invariance Principles for Homogeneous Sums: Universality of Gaussian Wiener Chaos
- I. Nourdin, G. Peccati, G. Reinert
- Mathematics
- 7 April 2009
We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. Our…
Second order Poincaré inequalities and CLTs on Wiener space
- I. Nourdin, G. Peccati, G. Reinert
- Mathematics
- 27 November 2008
Stein’s method for discrete Gibbs measures
- P. Eichelsbacher, G. Reinert
- Mathematics
- 1 August 2008
Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a…
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