Related papers: A simple wide range approximation of symmetric bin…

In every finite mixture of different normal distributions, there will always be exactly one of those distributions that not only is over-represented in the right tail of the mixture, but even completely overwhelms all other subpopulations…

Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…

A non trivial problem that arises in several applications is the estimation of the mean of a truncated normal distribution. In this paper, an iterative deterministic scheme for approximating this mean is proposed. It has been inspired from…

The Kolmogorov distances between a symmetric hypergeometric law with standard deviation $\sigma$ and its usual normal approximations are computed and shown to be less than $1/(\sqrt{8\pi}\,\sigma)$, with the order $1/\sigma$ and the…

We approximate the uniform measure on an equilateral triangle by a measure supported on $n$ points. We find the optimal sets of points ($n$-means) and corresponding approximation (quantization) error for $n\leq4$, give numerical…

This paper gives a new approach for the maximum likelihood estimation of the joint of the location and scale of the Cauchy distribution. We regard the joint as a single complex parameter and derive a new form of the likelihood equation of a…

We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…

We study the problem of distinguishing between two symmetric probability distributions over $n$ bits by observing $k$ bits of a sample, subject to the constraint that all $k-1$-wise marginal distributions of the two distributions are…

Gaussian approximations are routinely employed in Bayesian statistics to ease inference when the target posterior is intractable. Although these approximations are asymptotically justified by Bernstein-von Mises type results, in practice…

Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…

We introduce the notion of approximate smoothness in a normed linear space. We characterize this property and show the connections between smoothness and approximate smoothness for some spaces. As an application, we consider in particular…

This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a…

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

Finite precision approximations of discrete probability distributions are considered, applicable for distribution synthesis, e.g., probabilistic shaping. Two algorithms are presented that find the optimal $M$-type approximation $Q$ of a…

In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…

A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…

Singular perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact…

When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…