Related papers: A simple wide range approximation of symmetric bin…
We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform…
Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…
Motivated by molecular biology, there has been an upsurge of research activities in directional statistics in general and its Bayesian aspect in particular. The central distribution for the circular case is von Mises distribution which has…
The negative binomial distribution is self similar: If the spectrum over the whole rapidity range gives rise to a negative binomial, in absence of correlation and if the source is unique, also a partial range in rapidity gives rise to the…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
The paper concerns the uniform polynomial approximation of a function $f$, continuous on the unit Euclidean sphere of ${\mathbb R}^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere. First we…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
We present a new approximation to the normal distribution quantile function. It has a similar form to the approximation of Beasley and Springer [3], providing a maximum absolute error of less than $2.5 \cdot 10^{-5}$. This is less accurate…
We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as…
We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…
Given a collection of categorical data, we want to find the parameters of a Dirichlet distribution which maximizes the likelihood of that data. Newton's method is typically used for this purpose but current implementations require reading…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…
Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension.…